ANALYSIS OF NONLINEAR VIBRATION OF COUPLED SYSTEMS WITH CUBIC NONLINEARITY

Siame darbe konservatyvių, sujungtų daugiaspyruoklių sistemų su kubiniu netiesiskumu netiesinių laisvųjų svyravimų analitiniams sprendimams nustatymui gauti taikomi du analitiniai maksimalaus ir minimalaus priartėjimo ir patikslintos amplitudės formavimo metodai. Sprendžiant svarbiausias netiesines diferencialines lygtis, dviejų masių sistemos poslinkius galima nustatyti tiesiogiai naudojant pasiūlytų dviejų metodų tiesines antros eilės diferencialines lygtis, kas ir yra pagrindinis sio tyrimo tikslas. Palyginti su tobulais sprendimais, pirmu svyravimų dažnio priartėjimu gaunama didžiausia abiem metodams toleruotina paklaida 2,220179 %. Tai rodo, kad taikant maksimalaus ir minimalaus priartėjimo ir patikslintos amplitudės ir dažnio formulavimo metodus, netgi vienu priartėjimu pasiekiamas didelis sprendimo tikslumas, kuris galioja placiame svyravimo amplitudžių diapazone, ką rodo ir pateikti pavyzdžiai. http://dx.doi.org/10.5755/j01.mech.17.6.1005

[1]  A. Gilchrist.  The free oscillations of conservative quasilinear systems with two degrees of freedom , 1961 .

[2]  G. Enderlein,et al.  Miller, I., and J. E. Freund: Probability and Statistics for Engineers. Prentice‐Hall, Englewood Cliffs, New Jersey 1965. 432 S., Preis 96. s. , 1968 .

[3]  S. Raynor,et al.  Free vibration of multi-degree-of-freedom non-linear systems , 1972 .

[4]  G. J. Efstathiades.  Combination tones in single mode motion of a class of non-linear systems with two degrees of freedom , 1974 .

[5]  G. Chen.  Applications of a generalized Galerkin's method to non-linear oscillations of two-degree-of-freedom systems , 1987 .

[6]  A. Manevich,et al.  Free oscillations of a non-linear cubic system with two degrees of freedom and close natural frequencies☆ , 1993 .

[7]  L. Cvetićanin.  VIBRATIONS OF A COUPLED TWO-DEGREE-OF-FREEDOM SYSTEM , 2001 .

[8]  L. Cvetićanin.  The Motion of a Two-Mass System with Non-Linear Connection , 2002 .

[9]  Ji-Huan He,et al.  Solution of nonlinear equations by an ancient Chinese algorithm , 2004, Appl. Math. Comput..

[10]  Alexander F. Vakakis,et al.  Non-linear dynamics of a system of coupled oscillators with essential stiffness non-linearities , 2004 .

[11]  Ji-Huan He,et al.  He Chengtian's inequality and its applications , 2004, Appl. Math. Comput..

[12]  Ji-Huan He,et al.  Rebuild of King Fang 40 BC musical scales by He's inequality , 2005, Appl. Math. Comput..

[13]  Osman Kopmaz,et al.  Free vibrations of a mass grounded by linear and nonlinear springs in series , 2006 .

[14]  Xu-Chu Cai,et al.  He's frequency formulation for nonlinear oscillators , 2007 .

[15]  Ji-Huan He,et al.  An Improved Amplitude-frequency Formulation for Nonlinear Oscillators , 2008 .

[16]  Ji-Huan He,et al.  Max-Min Approach to Nonlinear Oscillators , 2008 .

[17]  Amin Barari,et al.  The Approximate Analysis of Nonlinear Behavior of Structure under Harmonic Loading , 2010 .

[18]  Zhonghua Huang,et al.  Cutter Cutting Cobalt-Rich Crusts with Water Jet , 2011, 2011 Second International Conference on Digital Manufacturing & Automation.

[19]  K. Pilkauskas,et al.  FREE VERTICAL OSCILLATIONS IN ROWING , 2011 .

[20]  Mahmoud Bayat,et al.  Analytical solution for strongly nonlinear oscillation systems using energy balance method , 2011 .

[21]  I. Pakar,et al.  Application of Hes energy balance method for nonlinear vibration of thin circular sector cylinder , 2011 .

[22]  Amin Barari,et al.  DYNAMIC RESPONSE OF AXIALLY LOADED EULER-BERNOULLI BEAMS , 2011 .

[23]  Iman Pakar.  Analytical evaluation of the nonlinear vibration of a solid circular sector object , 2011 .

[24]  Amin Barari,et al.  Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems , 2011 .

[25]  Mahdi Bayat,et al.  Application of iteration perturbation method for nonlinear oscillators with discontinuities , 2011 .

[26]  Mahdi Bayat,et al.  Analytical study on the vibration frequencies of tapered beams , 2011 .

[27]  Gholamreza Abdollahzadeh,et al.  Solution of free non-linear vibration of beams , 2011 .

[28]  Mahmoud Bayat,et al.  Mesh-free modeling of two-dimensional heat conduction between eccentric circular cylinders , 2011 .

[29]  Mahdi Bayat,et al.  Visco-elastic MHD flow of Walters liquid B fluid and heat transfer over a non-isothermal stretching sheet , 2011 .

[30]  Mahdi Bayat,et al.  An analytical approach on a mass grounded by linear and nonlinear springs in series , 2011 .

[31]  Mahmoud Bayat,et al.  Analysis of the steel braced frames equipped with ADAS devices under the far field records , 2011 .