THE SOLITARY WAVE SOLUTIONS OF A ONE-DIMENSIONAL NONLINEAR EQUATION OF WAVE PROPAGATION IN FUNCTIONALLY GRADED BEAMS

PDF(1505 KB)

Journal of Vibration and Shock ›› 2009, Vol. 28 ›› Issue (9) : 188-191.

论文

THE SOLITARY WAVE SOLUTIONS OF A ONE-DIMENSIONAL NONLINEAR EQUATION OF WAVE PROPAGATION IN FUNCTIONALLY GRADED BEAMS

Sun Dan Luo Songnan

Author information +

History +

Abstract

Considering finite deformation and cross Poisson effects, a new nonlinear wave equation in a functionally graded beam was derived by means of Hamilton principle. By using travelling wave reduced form method, the nonlinear partial differential equation of wave propagation in a functionally graded beam was transformed ordinary differential equation. The solitary wave solutions of displacement are obtained by using method of undetermined coefficient of displacement functions and solving the nonlinear differential equation of wave propagation. Two cases of functionally graded materials, elastic modulus and mass density along the depth varying with exponentially and parabolic type, were analyzed by examples. The curves of displacement are presented and the influence of parameters of the functionally graded materials and velocity of wave propagation on amplitude and width of solitary wave are analyzed．

Key words

functionally graded beams / finite deformation / nonlinear wave / travelling wave reduced form method / solitary wave solution

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

Sun Dan Luo Songnan . THE SOLITARY WAVE SOLUTIONS OF A ONE-DIMENSIONAL NONLINEAR EQUATION OF WAVE PROPAGATION IN FUNCTIONALLY GRADED BEAMS [J]. Journal of Vibration and Shock, 2009, 28(9): 188-191