Free vibration analysis of Timoshenko beams by DSC method

Free vibration analysis of Timoshenko beams has been presented. Discrete singular convolution method is used for numerical solution of equation of motion of Timoshenko beam. Clamped, pinned and sliding boundary conditions and their combinations are taken into account. Typical results are presented for different parameters and boundary conditions. Numerical results are presented and compared with that available in the literature. It is shown that very good results are obtained. This method is very effective for the study of vibration problems of Timoshenko beam. Copyright © 2009 John Wiley & Sons, Ltd.

[1]  Ömer Civalek,et al.  An efficient method for free vibration analysis of rotating truncated conical shells , 2006 .

[2]  Josip Brnić,et al.  Finite-element model for creep buckling analysis of beam-type structures , 2007 .

[3]  S. Timoshenko,et al.  LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars , 1921 .

[4]  Jeong-Seo Koo,et al.  Variational formulation for Timoshenko beam element by separation of deformation mode , 1994 .

[5]  Moshe Eisenberger,et al.  Dynamic stiffness vibration analysis using a high‐order beam model , 2003 .

[6]  Y. Cheung,et al.  Vibration of tapered Mindlin plates in terms of static Timoshenko beam functions , 2003 .

[7]  A. Ferreira,et al.  Radial basis functions and higher-order shear deformation theories in the analysis of laminated composite beams and plates , 2004 .

[8]  Andrew Y. T. Leung,et al.  FOURIERp-ELEMENT FOR THE ANALYSIS OF BEAMS AND PLATES , 1998 .

[9]  Shan Zhao,et al.  On the spurious solutions in the high-order finite difference methods for eigenvalue problems , 2007 .

[10]  Y. Xiang,et al.  On the missing modes when using the exact frequency relationship between Kirchhoff and Mindlin plates , 2005 .

[11]  Ömer Civalek,et al.  Three-dimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method , 2007 .

[12]  Ömer Civalek,et al.  Free vibration and buckling analyses of composite plates with straight-sided quadrilateral domain based on DSC approach , 2007 .

[13]  G. Wei,et al.  DSC ANALYSIS OF RECTANGULAR PLATES WITH NON-UNIFORM BOUNDARY CONDITIONS , 2002 .

[14]  Ömer Civalek,et al.  Nonlinear analysis of thin rectangular plates on Winkler–Pasternak elastic foundations by DSC–HDQ methods , 2007 .

[15]  Guo-Wei Wei,et al.  A new algorithm for solving some mechanical problems , 2001 .

[16]  M. Endo,et al.  An alternative formulation of the boundary value problem for the Timoshenko beam and Mindlin plate , 2007 .

[17]  Moshe Eisenberger,et al.  An exact high order beam element , 2003 .

[18]  A. Ferreira.  FREE VIBRATION ANALYSIS OF TIMOSHENKO BEAMS AND MINDLIN PLATES BY RADIAL BASIS FUNCTIONS , 2005 .

[19]  Chang-New Chen,et al.  DQEM analysis of out-of-plane deflection of non-prismatic curved beam structures considering the effect of shear deformation , 2006 .

[20]  Y. Xiang,et al.  DSC analysis of free-edged beams by an iteratively matched boundary method , 2005 .

[21]  Chien Ming Wang,et al.  Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes , 2006 .

[22]  Moshe Eisenberger,et al.  Dynamic stiffness matrix for variable cross-section Timoshenko beams , 1995 .

[23]  Yang Xiang,et al.  Discrete singular convolution and its application to the analysis of plates with internal supports. Part 2: Applications , 2002 .

[24]  Guo-Wei Wei,et al.  VIBRATION ANALYSIS BY DISCRETE SINGULAR CONVOLUTION , 2001 .

[25]  C. Wang,et al.  Shear deformable bending solutions for nonuniform beams and plates with elastic end restraints from classical solutions , 1998 .

[26]  Guo-Wei Wei.  Wavelets generated by using discrete singular convolution kernels , 2000 .

[27]  Ö. Civalek.  A parametric study of the free vibration analysis of rotating laminated cylindrical shells using the method of discrete singular convolution , 2007 .

[28]  Turgut Kocatürk,et al.  Free vibration analysis of beams by using a third-order shear deformation theory , 2007 .

[29]  J. Reddy.  On the dynamic behaviour of the Timoshenko beam finite elements , 1999 .

[30]  Yang Xiang,et al.  Discrete singular convolution for the prediction of high frequency vibration of plates , 2002 .

[31]  G. Wei.  Discrete singular convolution for beam analysis , 2001 .

[32]  C. Dolph.  On the Timoshenko theory of transverse beam vibrations , 1954 .

[33]  Janet M. Lees,et al.  Modelling crack propagation in structures: Comparison of numerical methods , 2007 .

[34]  D. Zhou,et al.  Vibrations of Mindlin rectangular plates with elastically restrained edges using static Timoshenko beam functions with the Rayleigh-Ritz method , 2001 .

[35]  C. Wang.  Timoshenko Beam-Bending Solutions in Terms of Euler-Bernoulli Solutions , 1995 .

[36]  P.A.A. Laura,et al.  Analysis of Vibrating Timoshenko Beams Using the Method of Differential Quadrature , 1993 .

[37]  Michael A. Sprague,et al.  Legendre spectral finite elements for structural dynamics analysis , 2007 .

[38]  Hui Chen,et al.  Charge distribution on narrow MEMS beams of nearly square cross-section , 2007 .

[39]  J. N. Reddy,et al.  Unified finite elements based on the classical and shear deformation theories of beams and axisymmetric circular plates , 1997 .

[40]  Stuart C. Althorpe,et al.  Wavelet-distributed approximating functional method for solving the Navier-Stokes equation , 1998 .

[41]  A. Matzenmiller,et al.  On the resolution of transverse stresses in solid-shells with a multi-layer formulation , 2006 .

[42]  B.A.H. Abbas,et al.  Finite element model for dynamic analysis of Timoshenko beam , 1975 .

[43]  Yang Xiang,et al.  A NOVEL APPROACH FOR THE ANALYSIS OF HIGH-FREQUENCY VIBRATIONS , 2002 .

[44]  Vincent Denoël,et al.  Advantages of a semi-analytical approach for the analysis of an evolving structure with contacts , 2007 .

[45]  Shan Zhao,et al.  On the validity of "A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximation function (LDAF) method is inferior to high order finite differences" , 2007, J. Comput. Phys..

[46]  Jinhee Lee,et al.  Eigenvalue analysis of Timoshenko beams and axisymmetric Mindlin plates by the pseudospectral method , 2004 .

[47]  Guo-Wei Wei,et al.  Comparison of discrete singular convolution and generalized differential quadrature for the vibration analysis of rectangular plates , 2004 .

[48]  Yang Xiang,et al.  The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution , 2001 .

[49]  Gregory E. Fasshauer,et al.  Computation of natural frequencies of shear deformable beams and plates by an RBF-pseudospectral method , 2006 .

[50]  T. Kocatürk,et al.  Vibration of viscoelastic beams subjected to an eccentric compressive force and a concentrated moving harmonic force , 2006 .

[51]  Ming-Hung Hsu,et al.  Electromechanical analysis of electrostatic nano‐actuators using the differential quadrature method , 2007 .

[52]  D. Zhou,et al.  Vibrations of point-supported rectangular plates with variable thickness using a set of static tapered beam functions , 2002 .

[53]  Yang Xiang,et al.  Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm , 2002 .

[54]  Guo-Wei Wei,et al.  Discrete singular convolution for the solution of the Fokker–Planck equation , 1999 .

[55]  J. N. Reddy,et al.  Relationships between bending solutions of classical and shear deformation beam theories , 1997 .

[56]  H. Benaroya,et al.  DYNAMICS OF TRANSVERSELY VIBRATING BEAMS USING FOUR ENGINEERING THEORIES , 1999 .

[57]  G. Wei,et al.  Local spectral time splitting method for first- and second-order partial differential equations , 2005 .

[58]  T. Kocatürk.  Determination of the steady-state response of viscoelastically supported cantilever beam under sinusoidal base excitation , 2005 .

[59]  Yang Xiang,et al.  Plate vibration under irregular internal supports , 2002 .

[60]  Guo-Wei Wei,et al.  Discrete singular convolution for the sine-Gordon equation , 2000 .

[61]  Guo-Wei Wei,et al.  DSC‐Ritz method for high‐mode frequency analysis of thick shallow shells , 2005 .

[62]  T. Kocatürk,et al.  Dynamic analysis of eccentrically prestressed viscoelastic Timoshenko beams under a moving harmonic load , 2006 .

[63]  T. Huang,et al.  The Effect of Rotatory Inertia and of Shear Deformation on the Frequency and Normal Mode Equations of Uniform Beams With Simple End Conditions , 1961 .

[64]  S. H. Lo,et al.  Vibration analysis of rectangular Mindlin plates with internal line supports using static Timoshenko beam functions , 2002 .

[65]  Y. Xiang,et al.  Local adaptive differential quadrature for free vibration analysis of cylindrical shells with various boundary conditions , 2006 .

[66]  Arul S Jayachandran,et al.  Variable order secant matrix technique applied to the elastic postbuckling of arches , 2007 .

[67]  Shan Zhao,et al.  Option valuation by using discrete singular convolution , 2005, Appl. Math. Comput..

[68]  Moshe Eisenberger,et al.  Exact Static and Dynamic Stiffness Matrices for General Variable Cross Section Members , 1989 .

[69]  U. Lee.  Spectral Element Method in Structural Dynamics , 2009 .

[70]  Yang Xiang,et al.  Matched interface and boundary (MIB) method for the vibration analysis of plates , 2009 .

[71]  F. Schoefs,et al.  A cracked beam finite element for through-cracked tube , 2007 .