Non-linear vibrations of shells: A literature review from 2003 to 2013

[1]  J. Bandyopadhyay,et al.  Nonlinear Transient Response of Laminated Composite Shells , 2008 .

[2]  L. Donnell,et al.  A New Theory for the Buckling of Thin Cylinders Under Axial Compression and Bending , 1934, Journal of Fluids Engineering.

[3]  Marco Amabili,et al.  A new non-linear higher-order shear deformation theory for large-amplitude vibrations of laminated doubly curved shells , 2010 .

[4]  James K. Knowles,et al.  On a Class of Oscillations in the Finite-Deformation Theory of Elasticity , 1962 .

[5]  Won-Ho Shin,et al.  Nonlinear flutter of aerothermally buckled composite shells with damping treatments , 2009 .

[6]  T. Yamaguchi,et al.  Experiments and analysis on chaotic vibrations of a shallow cylindrical shell-panel , 2007 .

[7]  J. N. Reddy,et al.  Shear Deformation Plate and Shell Theories: From Stavsky to Present , 2004 .

[8]  R. Mongrain,et al.  A three‐layer model for buckling of a human aortic segment under specific flow‐pressure conditions , 2012, International journal for numerical methods in biomedical engineering.

[9]  Paulo B. Gonçalves,et al.  Effect of non-linear modal interaction on the dynamic instability of axially excited cylindrical shells , 2004 .

[10]  Marco Amabili,et al.  Thermal effects on nonlinear vibrations of functionally graded doubly curved shells using higher order shear deformation theory , 2011 .

[11]  Carlo Sansour,et al.  A time integration scheme with energy–momentum conservation for a shell formulation with arbitrary geometric and material non-linearities , 2004 .

[12]  Cyril Touzé,et al.  Nonlinear vibrations and chaos in gongs and cymbals , 2005 .

[13]  K. Avramov.  Nonlinear modes of vibrations for simply supported cylindrical shell with geometrical nonlinearity , 2012 .

[14]  H. Saunders,et al.  Book Reviews : THIN SHELL STRUCTURES - THEORY, EXPERIMENT & DESIGN Edited by: Y. C. Fung & E. E. Sechler Prentice-Hall Inc., Englewood Cliffs, New Jersey (1974) , 1976 .

[15]  Marco Amabili,et al.  Reduced-order models for large-amplitude vibrations of shells including in-plane inertia , 2008 .

[16]  P. S. Koval’chuk,et al.  The Problem of Forced Nonlinear Vibrations of Cylindrical Shells Completely Filled with Liquid , 2005 .

[17]  P. S. Koval’chuk,et al.  Experimental studies of the vibrations and dynamic stability of laminated composite shells , 2009 .

[18]  K. A. Lazopoulos,et al.  Nonlinear strain gradient elastic thin shallow shells , 2011 .

[19]  Guo Yao,et al.  1/3 Subharmonic resonance of a nonlinear composite laminated cylindrical shell in subsonic air flow , 2013 .

[20]  Pedro Ribeiro,et al.  Non-linear Vibrations of Deep Cylindrical Shells by the p-Version Finite Element Method , 2010 .

[21]  Abhishek Gupta,et al.  Nonlinear dynamic stability of laminated composite shells integrated with piezoelectric layers in thermal environment , 2011 .

[22]  E. Grinevich,et al.  An experimental study of the nonlinear dynamics of cylindrical shells with clamped ends subjected to axial flow , 2005 .

[23]  A. Nayfeh,et al.  Axisymmetric vibrations of closed spherical shells: equations of motion and bifurcation analysis , 2006 .

[24]  M. P. Païdoussis,et al.  NON-LINEAR DYNAMICS AND STABILITY OF CIRCULAR CYLINDRICAL SHELLS CONTAINING FLOWING FLUID. PART I: STABILITY , 1999 .

[25]  Earl H. Dowell,et al.  Modal equations for the nonlinear flexural vibrations of a cylindrical shell , 1968 .

[26]  W. Yong-gang,et al.  Thermoelastically coupled axisymmetric nonlinear vibration of shallow spherical and conical shells , 2004 .

[27]  Huiming Wang,et al.  Three-dimensional non-linear buckling of thick-walled elastic tubes under pressure , 2013 .

[28]  S. Panda,et al.  Nonlinear finite element analysis of thermal post-buckling vibration of laminated composite shell panel embedded with SMA fibre , 2013 .

[29]  Paulo B. Gonçalves,et al.  An alternative procedure for the non-linear vibration analysis of fluid-filled cylindrical shells , 2011 .

[30]  Somnath Sarangi,et al.  Active damping of geometrically nonlinear vibrations of laminated composite shallow shells using vertically/obliquely reinforced 1-3 piezoelectric composites , 2011 .

[31]  E. Carrera,et al.  Effects of thickness stretching in functionally graded plates and shells , 2011 .

[32]  Eelco Jansen,et al.  Effect of Boundary Conditions on Nonlinear Vibration and Flutter of Laminated Cylindrical Shells , 2008 .

[33]  Yukinori Kobayashi,et al.  Nonlinear dynamic behaviors of clamped laminated shallow shells with one-to-one internal resonance , 2007 .

[34]  A. Hashemian,et al.  Nonlinear free dynamic response of laminated compressible cylindrical shell panels , 2010 .

[35]  Hui-Shen Shen,et al.  Boundary layer theory for the nonlinear vibration of anisotropic laminated cylindrical shells , 2013 .

[36]  M. Amabili.  Nonlinear vibrations of laminated circular cylindrical shells: Comparison of different shell theories , 2011 .

[37]  M. P. Païdoussis,et al.  Nonlinear vibrations of fluid-filled clamped circular cylindrical shells , 2005 .

[38]  M. C. Ray,et al.  Active damping of geometrically nonlinear vibrations of doubly curved laminated composite shells , 2011 .

[39]  Dao Huy Bich,et al.  Nonlinear dynamic analysis of eccentrically stiffened imperfect functionally graded doubly curved thin shallow shells , 2013 .

[40]  J. Nowinski,et al.  Exact solution to the problem of forced large amplitude radial oscillations of a thin hyperelastic tube , 1971 .

[41]  B. Eshmatov.  Nonlinear vibrations and dynamic stability of a viscoelastic circular cylindrical shell with shear strain and inertia of rotation taken into account , 2009 .

[42]  N. P. Podchasov,et al.  Analysis of nonstationary processes in cylindrical shells interacting with a fluid flow , 2011 .

[43]  D. H. Bich,et al.  Nonlinear vibration of functionally graded circular cylindrical shells based on improved Donnell equations , 2012 .

[44]  Ya. V. Tkachenko,et al.  Active damping of the resonant vibrations of a flexible cylindrical panel with sensors and actuators , 2011 .

[45]  L. Kurpa.  Nonlinear free vibrations of multilayer shallow shells with a symmetric structure and with a complicated form of the plan , 2009 .

[46]  Stefano Lenci,et al.  Global dynamics and integrity of a two-dof model of a parametrically excited cylindrical shell , 2011 .

[47]  Nonlinear vibration of corrugated shallow shells under uniform load , 2007 .

[48]  Henk Nijmeijer,et al.  Dynamic stability of a thin cylindrical shell with top mass subjected to harmonic base-acceleration☆ , 2008 .

[49]  K. Chandrashekhara,et al.  Geometrically non-linear transient analysis of laminated, doubly curved shells , 1985 .

[50]  J. Awrejcewicz,et al.  Chaotic vibrations of spherical and conical axially symmetric shells , 2005 .

[51]  L. Dai,et al.  Nonlinear vibration and stability of a rotary truncated conical shell with intercoupling of high and low order modals , 2009 .

[52]  K. Avramov,et al.  Parametric vibration of cylindrical shells in the region of combination resonances under geometrically nonlinear deformation , 2011 .

[53]  Wojciech Pietraszkiewicz,et al.  The Nonlinear Theory of Elastic Shells with Phase Transitions , 2004 .

[54]  E. A. Kurilov,et al.  Asymptotic analysis of nonlinear dynamics of simply supported cylindrical shells , 2007 .

[55]  王新志,et al.  Nonlinear dynamical behavior of shallow cylindrical reticulated shells , 2007 .

[56]  Wei Zhang,et al.  Nonlinear Dynamics of Cantilever FGM Cylindrical Shell under 1:2 Internal Resonance Relations , 2013 .

[57]  A. Popov.  The application of Hamiltonian dynamics and averaging to nonlinear shell vibration , 2004 .

[58]  V. F. Meish,et al.  Solving axisymmetric dynamic problems for reinforced shells of revolution on an elastic foundation , 2009 .

[59]  M. Païdoussis.  Fluid-Structure Interactions: Slender Structures and Axial Flow , 2014 .

[60]  Xumin Guo,et al.  Nonlinear dynamic response of rotating circular cylindrical shells with precession of vibrating shape—Part I: Numerical solution , 2010 .

[61]  Marco Amabili,et al.  Polynomial versus trigonometric expansions for nonlinear vibrations of circular cylindrical shells with different boundary conditions , 2010 .

[62]  J. Awrejcewicz,et al.  TRANSITIONS FROM REGULAR TO CHAOTIC VIBRATIONS OF SPHERICAL AND CONICAL AXIALLY-SYMMETRIC SHELLS , 2005 .

[63]  J. Awrejcewicz,et al.  Chaotic Vibrations of Sector-Type Spherical Shells , 2008 .

[64]  Eelco Jansen,et al.  Non-linear vibrations of laminated cylindrical shallow shells under thermomechanical loading , 2008 .

[65]  Shu Xue-feng,et al.  Analysis of thermal-elastic coupling vibration of large deflection cylindrical shell , 2004 .

[66]  L. Zubov,et al.  On constitutive inequalities in nonlinear theory of elastic shells , 2007 .

[67]  F. Alijani,et al.  Nonlinear vibrations of thick laminated circular cylindrical panels , 2013 .

[68]  Stefan Bilbao,et al.  Percussion Synthesis Based on Models of Nonlinear Shell Vibration , 2010, IEEE Transactions on Audio, Speech, and Language Processing.

[69]  S. Atluri,et al.  A perturbation analysis of non-linear free flexural vibrations of a circular cylindrical shell , 1972 .

[70]  Frederico M. A. Silva,et al.  Parametric Instability and Snap-Through of Partially Fluid- Filled Cylindrical Shells , 2011 .

[71]  Kyoko Nagai,et al.  Modal interaction in chaotic vibrations of a shallow double-curved shell-panel , 2008 .

[72]  I. Chueshov,et al.  Unsteady interaction of a viscous fluid with an elastic shell modeled by full von Karman equations , 2011, 1112.6094.

[73]  Yu. V. Mikhlin,et al.  Nonlinear vibrations of cylindrical shells with initial imperfections in a supersonic flow , 2007 .

[74]  V. Meish,et al.  Nonaxisymmetric vibrations of ellipsoidal shells under nonstationary distributed loads , 2008 .

[75]  Ghassan Odeh,et al.  Nonlinear Dynamics of Shallow Spherical Caps Subjected to Peripheral Loading , 2003 .

[76]  M. P. Paı¨doussis,et al.  Transmural pressure effects on the stability of clamped cylindrical shells subjected to internal fluid flow: Theory and experiments , 2007 .

[77]  E. Bespalova,et al.  Identifying the domains of dynamic instability for inhomogeneous shell systems under periodic loads , 2011 .

[78]  Jan Awrejcewicz,et al.  Routes to chaos in continuous mechanical systems. Part 3: The Lyapunov exponents, hyper, hyper-hyper and spatial–temporal chaos , 2012 .

[79]  王新志,et al.  NONLINEAR DYNAMICAL BIFURCATION AND CHAOTIC MOTION OF SHALLOW CONICAL LATTICE SHELL , 2006 .

[80]  O. Thomas,et al.  Non-linear behaviour of free-edge shallow spherical shells: Effect of the geometry , 2006 .

[81]  W. Pietraszkiewicz.  On exact expressions of the bending tensor in the nonlinear theory of thin shells , 2012 .

[82]  Jan Awrejcewicz,et al.  Chaotic Vibrations of Closed Cylindrical Shells in a temperature Field , 2008, Int. J. Bifurc. Chaos.

[83]  M. Païdoussis,et al.  Non-linear vibrations and instabilities of orthotropic cylindrical shells with internal flowing fluid , 2010 .

[84]  P. S. Koval’chuk,et al.  Wave Deformation Modes of Fluid-Containing Cylindrical Shells Under Periodic Force , 2005 .

[85]  V. V. Novozhilov,et al.  Foundations of the nonlinear theory of elasticity , 1953 .

[86]  Cyril Touzé,et al.  Non-linear vibrations of free-edge thin spherical shells: modal interaction rules and 1:1:2 internal resonance , 2005 .

[87]  A. Houmat,et al.  Non-linear free vibration of a functionally graded doubly-curved shallow shell of elliptical plan-form , 2010 .

[88]  P. S. Koval'chuk,et al.  On Free Nonlinear Vibrations of Fluid-Filled Cylindrical Shells with Multiple Natural Frequencies , 2005 .

[89]  N. A. Shul’ga,et al.  Forced Vibration of Three-Layered Spherical and Ellipsoidal Shells under Axisymmetric Loads , 2003 .

[90]  Nonlinear vibration of thin shallow conic shells under combined action of peripheral moment and transverse loads , 2003 .

[91]  T. K. Varadan,et al.  Nonlinear free flexural vibration of thin circular cylindrical shells , 1989 .

[92]  K. Avramov,et al.  Dynamics of shallow shells with geometrical nonlinearity interacting with fluid , 2011 .

[93]  V. Lakiza.  Dynamic deformation of a cylindrical composite shell with filler subject to radial two-frequency excitation , 2011 .

[94]  Carme Calderer.  The dynamical behaviour of nonlinear elastic spherical shells , 1983 .

[95]  M. Amabili,et al.  Experiments on Nonlinear Vibrations of Graphite/Epoxy Composite Curved Panels , 2005 .

[96]  David A. Evensen,et al.  Some observations on the nonlinear vibration of thin cylindrical shells , 1963 .

[97]  Qingming Li,et al.  Further study on strain growth in spherical containment vessels subjected to internal blast loading , 2010 .

[98]  Namita Nanda,et al.  Non-linear free and forced vibrations of piezoelectric laminated shells in thermal environments , 2010 .

[99]  Marco Amabili,et al.  Reduced-order models for nonlinear vibrations of fluid-filled circular cylindrical shells: Comparison of POD and asymptotic nonlinear normal modes methods , 2007 .

[100]  H. W. Zhang,et al.  Controllability Conditions of Finite Oscillations of Hyper-Elastic Cylindrical Tubes Composed of a Class of Ogden Material Models , 2008 .

[101]  Pedro Ribeiro,et al.  On the influence of membrane inertia and shear deformation on the geometrically non-linear vibrations of open, cylindrical, laminated clamped shells , 2009 .

[102]  B. Eshmatov.  Dynamic stability of viscoelastic circular cylindrical shells taking into account shear deformation and rotatory inertia , 2007 .

[103]  Method of Green’s function of nonlinear vibration of corrugated shallow shells , 2008 .

[104]  M. Amabili,et al.  Nonlinear Vibrations of Cantilever Circular Cylindrical Shells , 2010 .

[105]  J. H. Ginsberg,et al.  Large Amplitude Forced Vibrations of Simply Supported Thin Cylindrical Shells , 1973 .

[106]  R. Ogden.  Non-Linear Elastic Deformations , 1984 .

[107]  A. Sofiyev,et al.  The non-linear dynamics of FGM truncated conical shells surrounded by an elastic medium , 2013 .

[108]  B. A. Khudayarov,et al.  Numerical investigation of nonlinear vibrations of viscoelastic plates and cylindrical panels in a gas flow , 2007 .

[109]  H Henk Nijmeijer,et al.  Dynamic stability of a base-excited thin orthotropic cylindrical shell with top mass: Simulations and experiments , 2010 .

[110]  J. Awrejcewicz,et al.  Nonlinear coupled problems in dynamics of shells , 2003 .

[111]  Subrata Kumar Panda,et al.  Nonlinear free vibration analysis of thermally post-buckled composite spherical shell panel , 2010 .

[112]  F. Pellicano,et al.  Nonlinear vibrations of functionally graded cylindrical shells , 2013 .

[113]  Erasmo Carrera,et al.  Analysis of laminated doubly-curved shells by a layerwise theory and radial basis functions collocation, accounting for through-the-thickness deformations , 2011 .

[114]  Guy Lemarquand,et al.  Transient modal radiation of axisymmetric sources: Application to loudspeakers , 2010 .

[115]  Xinyun Guo,et al.  Nonlinear Random Response of Cylindrical Panels to Acoustic Excitations Using Finite Element Modal Method , 2003 .

[116]  D. Evensen.  Nonlinear vibrations of an infinitely long cylindrical shell. , 1968 .

[117]  E. Carrera.  Theories and finite elements for multilayered, anisotropic, composite plates and shells , 2002 .

[118]  P. Wriggers,et al.  On the design of energy–momentum integration schemes for arbitrary continuum formulations. Applications to classical and chaotic motion of shells , 2004 .

[119]  Ren Jiu-sheng,et al.  Dynamics and destruction of internally pressurized incompressible hyper-elastic spherical shells , 2009 .

[120]  Marco Amabili,et al.  Nonlinear vibrations of functionally graded doubly curved shallow shells , 2011 .

[121]  Ramin Sedaghati,et al.  Linear and nonlinear vibration analysis of sandwich cylindrical shell with constrained viscoelastic core layer , 2012 .

[122]  Wojciech Pietraszkiewicz,et al.  Intrinsic equations for non-linear deformation and stability of thin elastic shells ? , 2004 .

[123]  Carlo Sansour,et al.  A theory and finite element formulation of shells at finite deformations involving thickness change: Circumventing the use of a rotation tensor , 1995, Archive of Applied Mechanics.

[124]  Youhe Zhou,et al.  Dynamics of a thick-walled dielectric elastomer spherical shell , 2011 .

[125]  L. Kaitai,et al.  The modified model of Koiter’s type for nonlinearly elastic shell , 2010 .

[126]  V. Berdichevsky.  Nonlinear theory of hard-skin plates and shells , 2010 .

[127]  N. A. Shul’ga,et al.  Forced Axisymmetric Nonlinear Vibrations of Reinforced Conical Shells , 2003 .

[128]  Mervyn W. Olson,et al.  Some Experimeiital Observations on the Nonlinear Vibration of Cylindrical Shells , 1965 .

[129]  P. S. Koval’chuk,et al.  Studying the forced vibrations of fluid-filled cylindrical shells with regard to the nonlinear interaction of different flexural modes , 2006 .

[130]  Yong-Gang Wang,et al.  On the nonlinear vibration of heated bimetallic shallow shells of revolution , 2010 .

[131]  V. D. Kubenko,et al.  Nonlinear problems of the vibration of thin shells (review) , 1998 .

[132]  Wei Zhang,et al.  Nonlinear dynamics of FGM circular cylindrical shell with clamped-clamped edges , 2012 .

[133]  N. A. Shul’ga,et al.  On the deformation of a ribbed cylindrical shell with initial deflection under dynamic loading , 2005 .

[134]  Y. Wang,et al.  Nonlinear traveling wave vibration of a circular cylindrical shell subjected to a moving concentrated harmonic force , 2010 .

[135]  L. Librescu,et al.  A nonlinear theory for doubly curved anisotropic sandwich shells with transversely compressible core , 2003 .

[136]  E. L. Jansen,et al.  A perturbation method for nonlinear vibrations of imperfect structures: Application to cylindrical shell vibrations , 2008 .

[137]  David J. Steigmann,et al.  Koiter’s Shell Theory from the Perspective of Three-dimensional Nonlinear Elasticity , 2013 .

[138]  P. S. Koval'chuk,et al.  Circumferential Traveling Waves in Filled Cylindrical Shells , 2003 .

[139]  D. Khodzhaev,et al.  Dynamic stability of a viscoelastic cylindrical panel with concentrated masses , 2008 .

[140]  Paulo B. Gonçalves,et al.  Transient and steady state stability of cylindrical shells under harmonic axial loads , 2007 .

[141]  Effect of Boundary Conditions on Nonlinear Vibrations of Circular Cylindrical Panels , 2007 .

[142]  Francesco Pellicano,et al.  Vibrations of circular cylindrical shells: Theory and experiments , 2007 .

[143]  Anthony N. Palazotto,et al.  Large displacement and rotational formulation for laminated shells including parabolic transverse shear , 1990 .

[144]  S. Panda,et al.  Non-linear free vibration analysis of laminated composite cylindrical/hyperboloid shell panels based on higher-order shear deformation theory using non-linear finite-element method , 2008 .

[145]  Y. Wang,et al.  Nonlinear dynamic response of rotating circular cylindrical shells with precession of vibrating shape—Part II: Approximate analytical solution , 2010 .

[146]  R. Balakrishnan,et al.  Large amplitude oscillations of thick hyperelastic cylindrical shells , 1978 .

[147]  Rüdiger Schmidt,et al.  Geometrically nonlinear finite element simulation of smart piezolaminated plates and shells , 2007 .

[148]  M. Amabili,et al.  Nonlinear vibrations of shallow shells with complex boundary: R-functions method and experiments , 2007 .

[149]  Erasmo Carrera,et al.  Plates and Shells for Smart Structures: Classical and Advanced Theories for Modeling and Analysis , 2011 .

[150]  Dr.-Ing. C. Sansour.  A Theory and finite element formulation of shells at finite deformations involving thickness change , 1995 .

[151]  Christoph Adam.  Moderately large vibrations of doubly curved shallow open shells composed of thick layers , 2007 .

[152]  Francesco Pellicano,et al.  Linear and nonlinear dynamics of a circular cylindrical shell connected to a rigid disk , 2007 .

[153]  M. Amabili.  Reduced-order models for nonlinear vibrations, based on natural modes: the case of the circular cylindrical shell , 2013, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[154]  Pedro Ribeiro,et al.  Forced large amplitude periodic vibrations of cylindrical shallow shells , 2008 .

[155]  K. Liew,et al.  Nonlinear vibration of a coating-FGM-substrate cylindrical panel subjected to a temperature gradient , 2006 .

[156]  Dynamics of reinforced compound shells under nonstationary loads , 2006 .

[157]  H. M. Navazi,et al.  An analytical study of the non-linear vibrations of cylindrical shells , 2011 .

[158]  T. V. Karnaukhova,et al.  Numerical modeling of the active damping of forced thermomechanical resonance vibrations of viscoelastic shells of revolution with the help of piezoelectric inclusions , 2010 .

[159]  Jan Awrejcewicz,et al.  Routes to chaos in continuous mechanical systems: Part 2. Modelling transitions from regular to chaotic dynamics , 2012 .

[160]  Nguyen Dinh Duc,et al.  Nonlinear dynamic response of imperfect eccentrically stiffened FGM double curved shallow shells on elastic foundation , 2013 .

[161]  M. P. Païdoussis,et al.  Nonlinear dynamics and stability of cantilevered circular cylindrical shells conveying fluid , 2013 .

[162]  Marco Amabili,et al.  Nonlinear normal modes for damped geometrically nonlinear systems: Application to reduced-order modelling of harmonically forced structures , 2006 .

[163]  J. Awrejcewicz,et al.  Chaotic vibrations of spherical and conical axially symmetric shells , 2005 .

[164]  X. Wang,et al.  An analytical study of the non-linear vibrations of functionally graded cylindrical shells subjected to thermal and axial loads , 2013 .

[165]  M. P. Païdoussis,et al.  NON-LINEAR DYNAMICS AND STABILITY OF CIRCULAR CYLINDRICAL SHELLS CONTAINING FLOWING FLUID, PART II: LARGE-AMPLITUDE VIBRATIONS WITHOUT FLOW , 1999 .

[166]  Fulei Chu,et al.  Nonlinear vibrations of rotating thin circular cylindrical shell , 2012 .

[167]  M. Païdoussis,et al.  Effect of geometric imperfections on non-linear stability of circular cylindrical shells conveying fluid , 2009 .

[168]  K. V. Avramov,et al.  Nonlinear modes and traveling waves of parametrically excited cylindrical shells , 2010 .

[169]  A. Leissa,et al.  Vibration of shells , 1973 .

[170]  P. S. Koval'chuk,et al.  On Multimode Nonlinear Vibrations of Filled Cylindrical Shells , 2003 .

[171]  K. Avramov,et al.  Free vibrations of a shallow shell in fluid under geometrically nonlinear deformation , 2011 .

[172]  M. Shariyat.  Non-linear dynamic thermo-mechanical buckling analysis of the imperfect laminated and sandwich cylindrical shells based on a global-local theory inherently suitable for non-linear analyses , 2011 .

[173]  Yang Xiang,et al.  Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments , 2012 .

[174]  Marco Amabili,et al.  Experiments on large-amplitude vibrations of a circular cylindrical panel , 2003 .

[175]  P. S. Koval’chuk,et al.  Forced nonlinear oscillations of cylindrical shells interacting with fluid flow , 2006 .

[176]  Namita Nanda,et al.  Nonlinear dynamic response of laminated shells with imperfections in hygrothermal environments , 2011 .

[177]  Frederico M. A. Silva,et al.  Transient stability of empty and fluid-filled cylindrical shells , 2006 .

[178]  Bhanu Singh,et al.  Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel using nonlinear FEM , 2011 .

[179]  K. Avramov.  Multidimensional models of traveling waves and nonlinear modes in cylindrical shells , 2011 .

[180]  V. Lakiza.  Dynamics of an elastic cylindrical shell with a gas–liquid medium subject to two-frequency vibrational excitation , 2008 .

[181]  M. Shariyat.  NONLINEAR THERMOMECHANICAL DYNAMIC BUCKLING ANALYSIS OF IMPERFECT VISCOELASTIC COMPOSITE/SANDWICH SHELLS BY A DOUBLE-SUPERPOSITION GLOBAL-LOCAL THEORY AND VARIOUS CONSTITUTIVE MODELS , 2011 .

[182]  Jiu-sheng Ren.  Dynamical response of hyper-elastic cylindrical shells under periodic load , 2008 .

[183]  K. Avramov,et al.  On effect of initial imperfections on parametric vibrations of cylindrical shells with geometrical non-linearity , 2012 .

[184]  P. S. Koval’chuk.  Nonlinear Vibrations of a Cylindrical Shell Containing a Flowing Fluid , 2005 .

[185]  P. S. Koval’chuk,et al.  Chaotic Modes of Forced Nonlinear Vibrations of Fluid-Filled Cylindrical Shells , 2003 .

[186]  Qingming Li,et al.  Instability in the transformation between extensional and flexural modes in thin-walled cylindrical shells , 2011 .

[187]  R. Ogden,et al.  Asymmetric bifurcations of thick-walled circular cylindrical elastic tubes under axial loading and external pressure , 2008 .

[188]  J. Turner,et al.  Nonlinear vibrations of electroelastic shells with relatively large shear deformations , 2006 .

[189]  V. H. Nam,et al.  Nonlinear dynamical analysis of eccentrically stiffened functionally graded cylindrical panels , 2012 .

[190]  Marco Amabili,et al.  Nonlinear Vibrations and Stability of Shells and Plates , 2008 .

[191]  J. Bandyopadhyay,et al.  Nonlinear Free Vibration Analysis of Laminated Composite Cylindrical Shells with Cutouts , 2007 .

[192]  M. C. Ray,et al.  Active control of geometrically nonlinear transient vibrations of laminated composite cylindrical panels using piezoelectric fiber reinforced composite , 2013 .

[193]  Ramin Sedaghati,et al.  Nonlinear free vibration analysis of sandwich shell structures with a constrained electrorheological fluid layer , 2012 .

[194]  Cyril Touzé,et al.  Non-linear vibrations of free-edge thin spherical shells: Experiments on a 1:1:2 internal resonance , 2007 .

[195]  On numerical solution of dynamic problems in the theory of reinforced shells , 2006 .

[196]  Changping Chen.  Nonlinear Dynamic of a Rotating Truncated Conical Shell , 2012 .

[197]  Yiming Fu,et al.  Analysis of nonlinear dynamic response and dynamic buckling for laminated shallow spherical thick shells with damage , 2008 .

[198]  W. Pietraszkiewicz,et al.  Local Symmetry Group in the General Theory of Elastic Shells , 2006 .

[199]  P. S. Koval'chuk,et al.  Influence of Initial Geometric Imperfections on the Vibrations and Dynamic Stability of Elastic Shells , 2004 .

[200]  J. Awrejcewicz,et al.  Large amplitude free vibration of orthotropic shallow shells of complex shapes with variable thickness , 2013 .

[201]  B. Kh. Eshmatov,et al.  Non-linear vibration and dynamic stability of a viscoelastic cylindrical panel with concentrated mass , 2007 .

[202]  Peter Wriggers,et al.  A finite element post-processed Galerkin method for dimensional reduction in the non-linear dynamics of solids. Applications to shells , 2003 .

[203]  Marco Amabili,et al.  Theory and experiments for large-amplitude vibrations of empty and fluid-filled circular cylindrical shells with imperfections , 2003 .

[204]  Zhou Youhe,et al.  THE DYNAMICS RESPONSE AND STABILITY OF A DIELECTRIC ELASTOMER CYLINDRICAL SHELL UNDER STATIC AND PERIODIC VOTAGE , 2012 .

[205]  Marco Amabili,et al.  Nonlinear stability of cylindrical shells subjected to axial flow : Theory and experiments , 2008 .

[206]  J. N. Bandyopadhyay,et al.  Large amplitude free vibration of laminated composite shells with cutout , 2008 .

[207]  Francesco Pellicano,et al.  Dynamic stability and sensitivity to geometric imperfections of strongly compressed circular cylindrical shells under dynamic axial loads , 2009 .

[208]  Paulo B. Gonçalves,et al.  CHAOTIC BEHAVIOR RESULTING IN TRANSIENT AND STEADY STATE INSTABILITIES OF PRESSURE-LOADED SHALLOW SPHERICAL SHELLS , 2003 .

[209]  Marco Amabili.  Theory and experiments for large-amplitude vibrations of circular cylindrical panels with geometric imperfections , 2006 .

[210]  M. Salim Azzouz,et al.  Finite Element Multiple-Mode Approach to Nonlinear Free Vibrations of Shallow Shells , 2004 .

[211]  Mansour Darvizeh,et al.  Non-linear analysis of dynamic stability for functionally graded cylindrical shells under periodic axial loading , 2008 .

[212]  Ugurhan Akyuz,et al.  Stability and asymmetric vibrations of pressurized compressible hyperelastic cylindrical shells , 1999 .

[213]  Paulo B. Gonçalves,et al.  Low-Dimensional Galerkin Models for Nonlinear Vibration and Instability Analysis of Cylindrical Shells , 2005 .

[214]  V. G. Filin,et al.  On Modes of Flexural Vibrations of Initially Bent Cylindrical Shells Partially Filled with a Liquid , 2003 .

[215]  R. Chaudhuri.  A nonlinear zigzag theory for finite element analysis of highly shear-deformable laminated anisotropic shells , 2008 .

[216]  Hui-Shen Shen,et al.  Nonlinear vibration of shear deformable FGM cylindrical shells surrounded by an elastic medium , 2012 .

[217]  C. Adam.  Nonlinear flexural vibrations of layered panels with initial imperfections , 2006 .

[218]  Marco Amabili,et al.  Parametric instability of a circular cylindrical shell with geometric imperfections , 2004 .

[219]  Marco Amabili,et al.  Nonlinear vibrations of circular cylindrical panels , 2005 .

[220]  J. Altenbach,et al.  On generalized Cosserat-type theories of plates and shells: a short review and bibliography , 2010 .

[221]  Victor A. Eremeyev,et al.  On the shell theory on the nanoscale with surface stresses , 2011 .

[222]  D. A. Evensen,et al.  Nonlinear flexural vibrations of thin-walled circular cylinders , 1967 .

[223]  Jan Awrejcewicz,et al.  Routes to chaos in continuous mechanical systems. Part 1: Mathematical models and solution methods , 2012 .

[224]  Marco Amabili,et al.  A comparison of shell theories for large-amplitude vibrations of circular cylindrical shells: Lagrangian approach , 2003 .

[225]  Pedro Ribeiro,et al.  A hierarchical finite element for geometrically non‐linear vibration of doubly curved, moderately thick isotropic shallow shells , 2003 .

[226]  M. Païdoussis,et al.  Nonlinear vibrations and imperfection sensitivity of a cylindrical shell containing axial fluid flow , 2009 .

[227]  K. V. Avramov,et al.  Vibrations of a complex-shaped panel , 2010 .

[228]  M. P. Païdoussis,et al.  Reduced-order models for nonlinear vibrations of cylindrical shells via the proper orthogonal decomposition method , 2003 .

[229]  M. Païdoussis,et al.  Nonlinear dynamics of harmonically excited circular cylindrical shells containing fluid flow , 2010 .

[230]  A. R. de Faria.  Finite element analysis of the dynamic response of cylindrical panels under traversing loads , 2004 .

[231]  A. Deniz,et al.  The nonlinear dynamic buckling response of functionally graded truncated conical shells , 2013 .

[232]  Zafer Gürdal,et al.  Dynamic buckling analysis of composite cylindrical shells using a finite element based perturbation method , 2011 .

[233]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

[234]  James K. Knowles,et al.  Large amplitude oscillations of a tube of incompressible elastic material , 1960 .

[235]  J. N. Reddy,et al.  Tensor-based finite element formulation for geometrically nonlinear analysis of shell structures , 2007 .

[236]  Marco Amabili,et al.  Nonlinear Supersonic Flutter of Circular Cylindrical Shells , 2001 .

[237]  T. V. Karnaukhova,et al.  Influence of dissipative heating on active damping of forced resonance vibrations of a flexible viscoelastic cylindrical panel by piezoelectric actuators , 2012 .

[238]  R. Benamar,et al.  NON-LINEAR VIBRATIONS OF SHELL-TYPE STRUCTURES: A REVIEW WITH BIBLIOGRAPHY , 2002 .

[239]  Marco Amabili,et al.  Internal resonances in non-linear vibrations of a laminated circular cylindrical shell , 2012 .

[240]  R. Ogden,et al.  Nonlinear axisymmetric deformations of an elastic tube under external pressure , 2010 .

[241]  R. Vaicaitis,et al.  Nonlinear Response of Double-Wall Cylindrical Shell Vibrations under Random Excitation , 2006 .

[242]  M. P. Païdoussis,et al.  NON-LINEAR DYNAMICS AND STABILITY OF CIRCULAR CYLINDRICAL SHELLS CONTAINING FLOWING FLUID. PART III: TRUNCATION EFFECT WITHOUT FLOW AND EXPERIMENTS , 2000 .

[243]  P. Sinha,et al.  Nonlinear free vibration analysis of laminated composite shells in hygrothermal environments , 2007 .

[244]  Marco Amabili,et al.  Nonlinear vibrations of clamped-free circular cylindrical shells , 2011 .

[245]  Atanas A. Popov,et al.  Parametric resonance in cylindrical shells: a case study in the nonlinear vibration of structural shells , 2003 .

[246]  B. Eshmatov.  Nonlinear vibrations of viscoelastic cylindrical shells taking into account shear deformation and rotatory inertia , 2007 .

[247]  O. Thomas,et al.  Non-linear vibrations of imperfect free-edge circular plates and shells , 2009 .

[248]  Xinling Wang,et al.  Influences of large deformation and rotary inertia on wave propagation in piezoelectric cylindrically laminated shells in thermal environment , 2006 .

[249]  A. Popov.  Auto-parametric resonance in thin cylindrical shells using the slow fluctuation method , 2004 .

[250]  Marco Amabili,et al.  A new nonlinear higher-order shear deformation theory with thickness variation for large-amplitude vibrations of laminated doubly curved shells , 2012 .

[251]  Takao Yamaguchi,et al.  Chaotic oscillations of a shallow cylindrical shell with a concentrated mass under periodic excitation , 2004 .

[252]  Eelco Jansen.  Analytical-numerical models for flutter of cylindrical shells in supersonic flow , 2003 .

[253]  Paolo Tiso,et al.  A finite element-based perturbation method for nonlinear free vibration analysis of composite cylindrical shells , 2011 .

[254]  Namita Nanda,et al.  Geometrically Nonlinear Transient Response of Functionally Graded Shell Panels with Initial Geometric Imperfection , 2013 .

[255]  V. Karnaukhov,et al.  Studying the harmonic vibrations of a cylindrical shell made of a nonlinear elastic piezoelectric material , 2008 .

[256]  K. Dong,et al.  Wave propagation characteristics in piezoelectric cylindrical laminated shells under large deformation , 2007 .

[257]  Marco Amabili,et al.  Chaotic vibrations of circular cylindrical shells: Galerkin versus reduced-order models via the proper orthogonal decomposition method , 2006 .

[258]  Wei Zhang,et al.  Dynamic Response of Cantilever FGM Cylindrical Shell , 2011 .

[259]  V. A. Zarutskii,et al.  Dynamic problems for and stress–strain state of inhomogeneous shell structures under stationary and nonstationary loads , 2009 .

[260]  Marco Amabili,et al.  Multimode Approach to Nonlinear Supersonic Flutter of Imperfect Circular Cylindrical Shells , 2002 .

[261]  Marco Amabili,et al.  Dynamic instability and chaos of empty and fluid-filled circular cylindrical shells under periodic axial loads , 2006 .

[262]  Eelco Jansen,et al.  The effect of static loading and imperfections on the nonlinear vibrations of laminated cylindrical shells , 2008 .

[263]  Yeh Kai-yuan,et al.  Nonlinear natural frequency of shallow conical shells with variable thickness , 2005 .

[264]  P. S. Koval’chuk,et al.  Application of asymptotic methods to the investigation of one-frequency nonlinear oscillations of cylindrical shells interacting with moving fluid , 2007 .

[265]  M. Amabili.  A non-linear higher-order thickness stretching and shear deformation theory for large-amplitude vibrations of laminated doubly curved shells , 2014 .

[266]  P. S. Koval’chuk,et al.  Nonlinear problems of the dynamics of elastic shells partialiy filled with a liquid , 2000 .

[267]  P. Lugovoi,et al.  Forced Nonstationary Vibrations of a Sandwich Cylindrical Shell with Cross-Ribbed Core , 2005 .

[268]  H. Parisch.  A continuum‐based shell theory for non‐linear applications , 1995 .

[269]  Firooz Bakhtiari-Nejad,et al.  Nonlinear free vibration analysis of prestressed circular cylindrical shells on the Winkler/Pasternak foundation , 2012 .

[270]  Haitao Gao,et al.  Multi-objective global optimal parafoil homing trajectory optimization via Gauss pseudospectral method , 2013 .

[271]  F. Alijani,et al.  CHAOTIC VIBRATIONS IN FUNCTIONALLY GRADED DOUBLY CURVED SHELLS WITH INTERNAL RESONANCE , 2012 .

[272]  Hessameddin Yaghoobi,et al.  NONLINEAR FREE AND FORCED THERMO-ELECTRO-AERO-ELASTIC VIBRATION AND DYNAMIC RESPONSE OF PIEZOELECTRIC FUNCTIONALLY GRADED LAMINATED COMPOSITE SHELLS , 2013 .

[273]  R. Benamar,et al.  Geometrically non-linear free and forced vibrations of simply supported circular cylindrical shells: A semi-analytical approach , 2007 .

[274]  Ali Aminyazdi.  Applicability of homotopy perturbation method to study the nonlinear vibration of doubly curved cross-ply shells , 2013 .

[275]  Anthony N. Palazotto,et al.  Nonlinear Analysis of Shell Structures , 1992 .

[276]  H. Akay,et al.  Radial oscillations of nonhomogeneous, thick-walled cylindrical and spherical shells subjected to finite deformations , 1976 .

[277]  P. S. Koval’chuk,et al.  Nonlinear vibrations of cylindrical shells filled with a fluid and subjected to longitudinal and transverse periodic excitation , 2010 .

[278]  Asd Wang,et al.  Stability and vibrations of elastic thick-walled cylindrical and spherical shells subjected to pressure , 1972 .

[279]  M. Païdoussis,et al.  Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction , 2003 .

[280]  In-Won Lee,et al.  Supersonic flutter suppression of piezolaminated cylindrical panels based on multifield layerwise theory , 2006 .

[281]  V. F. Meish.  Numerical Solution of Dynamic Problems for Reinforced Ellipsoidal Shells under Nonstationary Loads , 2005 .

[282]  K. Avramov,et al.  Nonlinear modes of cylindrical panels with complex boundaries. R-function method , 2011 .

[283]  V. Lakiza.  Features of the Motion of a Gas-Liquid Medium in a Compound Shell (Sphere and Truncated Cone) Subject to Vibration , 2005 .

[284]  M. Amabili.  Nonlinear vibrations of angle-ply laminated circular cylindrical shells: Skewed modes , 2012 .

[285]  J. L. Sanders,et al.  NONLINEAR THEORIES FOR THIN SHELLS , 1963 .

[286]  Marco Amabili,et al.  Nonlinear Dynamics and Stability of Circular Cylindrical Shells , 2004 .

[287]  W. Pietraszkiewicz,et al.  On modified displacement version of the non-linear theory of thin shells , 2009 .

[288]  K. V. Avramov.  Nonlinear forced vibrations of a cylindrical shell with two internal resonances , 2006 .

[289]  E. Jansen.  Dynamic Stability Problems of Anisotropic Cylindrical Shells via a Simplified Analysis , 2005 .

[290]  Liviu Librescu,et al.  Refined geometrically nonlinear theories of anisotropic laminated shells , 1987 .

[291]  S. Pradyumna,et al.  Geometrically nonlinear transient analysis of functionally graded shell panels using a higher-order finite element formulation , 2014 .

[292]  M. Toorani,et al.  Dynamics of the geometrically non-linear analysis of anisotropic laminated cylindrical shells , 2003 .

[293]  M. Amabili,et al.  Non-linear vibrations of shallow circular cylindrical panels with complex geometry. Meshless discretization with the R-functions method , 2012 .

[294]  Renfu Li,et al.  Nonlinear Response of a Shallow Sandwich Shell With Compressible Core to Blast Loading , 2008 .

[295]  P. Ribeiro.  Non-linear free periodic vibrations of open cylindrical shallow shells , 2008 .

[296]  Francesco Pellicano,et al.  Dynamic instability of a circular cylindrical shell carrying a top mass under base excitation: Experiments and theory , 2011 .

[297]  Hessameddin Yaghoobi,et al.  Nonlinear free and forced thermo-electro-aero-elastic vibration and dynamic response of piezoelectric functionally graded laminated composite shells, Part I: Theory and analytical solutions , 2013 .

[298]  Eelco Jansen.  The effect of geometric imperfections on the vibrations of anisotropic cylindrical shells , 2007 .

[299]  Jean W. Zu,et al.  Nonlinear vibrations of a shell-shaped workpiece during high-speed milling process , 2013 .

[300]  Marco Amabili,et al.  Non-linear vibrations of doubly curved shallow shells , 2005 .

[301]  J. Awrejcewicz,et al.  Stability, bifurcation and chaos of closed flexible cylindrical shells , 2008 .

[302]  Jan Awrejcewicz,et al.  Chaotic vibrations of flexible infinite length cylindrical panels using the Kirchhoff–Love model , 2007 .

[303]  Frederico M. A. Silva,et al.  Global stability analysis of parametrically excited cylindrical shells through the evolution of basin boundaries , 2007 .

[304]  Eelco Jansen,et al.  A comparison of analytical–numerical models for nonlinear vibrations of cylindrical shells , 2004 .

[305]  P. S. Koval’chuk,et al.  On the spectrum of natural frequencies of circular cylindrical shells completely filled with a fluid , 2006 .

[306]  M. Païdoussis,et al.  Effect of geometry on the stability of cylindrical clamped shells subjected to internal fluid flow , 2007 .

[307]  V. Meish,et al.  Analysis of the nonaxisymmetric vibrations of flexible ellipsoidal shells discretely reinforced with transverse ribs under nonstationary loads , 2008 .

[308]  E. Carrera.  Historical review of Zig-Zag theories for multilayered plates and shells , 2003 .

[309]  S. Panda,et al.  Nonlinear free vibration of spherical shell panel using higher order shear deformation theory – A finite element approach , 2009 .

[310]  Aouni A. Lakis,et al.  Large amplitude vibrations of anisotropic cylindrical shells , 2004 .

[311]  Marco Amabili,et al.  On the accuracy of the multiple scales method for non-linear vibrations of doubly curved shallow shells , 2011 .

[312]  Paulo B. Gonçalves,et al.  Low-dimensional models for the nonlinear vibration analysis of cylindrical shells based on a perturbation procedure and proper orthogonal decomposition , 2008 .

[313]  Marco Amabili,et al.  Stability and vibration of empty and fluid-filled circular cylindrical shells under static and periodic axial loads , 2003 .

[314]  V. F. Meish,et al.  Vibrations of Reinforced Cylindrical Shells with Initial Deflections under Nonstationary Loads , 2005 .