Closed-form exact solutions for hysteretically damped longitudinal free and forced vibrations of tapered beams

2018 ◽  
Vol 229 (11) ◽  
pp. 4741-4751
Author(s):  
Yeong-Bin Yang ◽  
Jae-Hoon Kang
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Forced Vibrations ◽  
Free And Forced Vibrations

Closed-Form Exact Solutions for Viscously Damped Free and Forced Vibrations of Longitudinal and Torsional Bars

2017 ◽  
Vol 17 (08) ◽  
pp. 1750093 ◽  
Author(s):  
Jae-Hoon Kang
Keyword(s):  
Free Vibration ◽  
Closed Form ◽  
Closed Form Solution ◽  
Forced Vibrations ◽  
Form Solution ◽  
Forced Response ◽  
Mode Shapes ◽  
Viscous Damping ◽  
Vibration Displacement ◽  
Free And Forced Vibrations

This paper studies the viscously damped free and forced vibrations of longitudinal and torsional bars. The method is exact and yields closed form solution for the vibration displacement in contrast with the well-known eigenfunction superposition (ES) method, which requires expression of the distributed forcing functions and displacement response functions as infinite series sums of free vibration eigenfunctions. The viscously damped natural frequency equation and the critical viscous damping equation are exactly derived for the bars. Then the viscously damped free vibration frequencies and corresponding damped mode shapes are calculated and plotted, aside from the undamped free vibration and corresponding mode shapes typically computed and used in vibration problems. The longitudinal or torsional amplitude versus forcing frequency curves showing the forced response to distributed loadings are plotted for various viscous damping parameters. It is found that the viscous damping affects the natural frequencies and the corresponding mode shapes of longitudinal and torsional bars, especially for the fundamental frequency.

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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