Analytical solution for nonlinear forced response of a viscoelastic piezoelectric cantilever beam resting on a nonlinear elastic foundation to an external harmonic excitation

2014 ◽  
Vol 67 ◽  
pp. 464-471 ◽  
Author(s):  
Seyedeh Marzieh Hosseini ◽  
Hamed Kalhori ◽  
Alireza Shooshtari ◽  
S. Nima Mahmoodi
Keyword(s):  
Analytical Solution ◽  
Elastic Foundation ◽  
Cantilever Beam ◽  
Harmonic Excitation ◽  
Forced Response ◽  
Nonlinear Elastic Foundation ◽  
Piezoelectric Cantilever ◽  
Nonlinear Elastic

Effects of Tuned Mass Damper on Fixed-Fixed 3D Nonlinear String Resting on Nonlinear Elastic Foundation

2017 ◽  
Vol 17 (04) ◽  
pp. 1750047 ◽  
Author(s):  
Yi-Ren Wang ◽  
Li-Ping Wu
Keyword(s):  
Elastic Foundation ◽  
Internal Resonance ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Maximum Amplitude ◽  
Tuned Mass Damper ◽  
Mode Shapes ◽  
Nonlinear Elastic Foundation ◽  
Mass Damper ◽  
Nonlinear Elastic

This paper studies the vibration of a nonlinear 3D-string fixed at both ends and supported by a nonlinear elastic foundation. Newton’s second law is adopted to derive the equations of motion for the string resting on an elastic foundation. Then, the method of multiple scales (MOMS) is employed for the analysis of the nonlinear system. It was found that 1:3 internal resonance exists in the first and fourth modes of the string when the wave speed in the transverse direction is [Formula: see text] and the elasticity coefficient of the foundation is [Formula: see text]. Fixed point plots are used to obtain the frequency responses of the various modes and to identify internal resonance through observation of the amplitudes and mode shapes. To prevent internal resonance and reduce vibration, a tuned mass damper (TMD) is applied to the string. The effects of various TMD masses, locations, damper coefficients ([Formula: see text]), and spring constants ([Formula: see text]) on overall damping were analyzed. The 3D plots of the maximum amplitude (3D POMAs) and 3D maximum amplitude contour plots (3D MACPs) are generated for the various modes to illustrate the amplitudes of the string, while identifying the optimal TMD parameters for vibration reduction. The results were verified numerically. It was concluded that better damping effects can be achieved using a TMD mass ratio [Formula: see text]–0.5 located near the middle of the string. Furthermore, for damper coefficient [Formula: see text], the use of spring constant [Formula: see text]–13 can improve the overall damping.

Free Vibration Analysis for Disconnected Thin Rectangular Plate with Four Free Edges on Nonlinear Elastic Foundation

2011 ◽  
Vol 52-54 ◽  
pp. 1309-1314 ◽  
Author(s):  
Yong Gang Xiao ◽  
Cui Ping Yang
Keyword(s):  
Free Vibration ◽  
Rectangular Plate ◽  
Elastic Foundation ◽  
Vibration Analysis ◽  
Harmonic Balance Method ◽  
Free Vibration Analysis ◽  
Variation Principle ◽  
Thin Rectangular Plate ◽  
Nonlinear Elastic Foundation ◽  
Nonlinear Elastic

In this paper, the free vibration analysis of thin rectangular plate with dowels on nonlinear elastic foundation is investigated. The load transfer on dowels is modeled as vertical springs, whose stiffness depends on the dowel properties and the dowel-plate interaction. Based on Hamilton variation principle, the nonlinear governing equations of thin rectangular plate with discontinuities on nonlinear elastic foundation are established, and the suitable expressions of trial functions satisfying all boundary conditions are proposed. Then, the equations are solved by using Galerkin method and harmonic balance method. The numerical simulation reveals the effects of the dowel parameters and the other ones of the system on free vibration behaves of the disconnected thin rectangular plate.

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