An Iterative Numerical Method for Nonlinear Vibrations

1951 ◽  
Vol 18 (1) ◽  
pp. 1-11
Author(s):  
J. E. Brock
Keyword(s):  
Numerical Method ◽  
Nonlinear Elasticity ◽  
Iterative Procedure ◽  
Nonlinear Vibrations ◽  
Initial Approximation ◽  
Forced Vibrations ◽  
Free And Forced Vibrations ◽  
Numerical Integrations

Abstract A simple iterative procedure employing numerical integrations is presented for the analysis of free and forced vibrations of undamped systems having nonlinear elasticity. If the elasticity is symmetrical, it is always possible to make an excellent initial approximation, but the method may also be used in cases of unsymmetrical elasticity. Other applications, such as to systems having parameters which vary with time, are discussed.

Nonlinear Free and Forced Vibrations of Symmetric Laminated Panels

2011 ◽  
Vol 471-472 ◽  
pp. 616-621 ◽  
Author(s):  
Alireza Shooshtari ◽  
Soheil Razavi ◽  
Hadi Ghashochi Bargh ◽  
Mohammad Homayoun Sadr-Lahidjani
Keyword(s):  
Perturbation Method ◽  
External Force ◽  
Laminated Composite ◽  
Composite Plates ◽  
Forced Vibrations ◽  
Numerical Results ◽  
Transverse Displacement ◽  
Laminated Composite Plates ◽  
Free And Forced Vibrations ◽  
Laminated Panels

In this paper, free and forced vibrations of symmetric laminated composite plates are studied analytically by using a perturbation method where the analytical results for transverse displacement are compared with the numerical results. The external force is taken to be harmonic in time and having uniform amplitude.

scholarly journals Nonlinear dynamics of rectangular plates: investigation of modal interaction in free and forced vibrations

2013 ◽  
Vol 225 (1) ◽  
pp. 213-232 ◽  
Author(s):  
Michele Ducceschi ◽  
Cyril Touzé ◽  
Stefan Bilbao ◽  
Craig J. Webb
Keyword(s):  
Nonlinear Dynamics ◽  
Forced Vibrations ◽  
Rectangular Plates ◽  
Modal Interaction ◽  
Free And Forced Vibrations
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