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论文类型：期刊论文

发表时间：2018-05-01

发表刊物：CMC-COMPUTERS MATERIALS & CONTINUA

收录刊物：SCIE

卷号：55

期号：2

页面范围：345-357

ISSN号：1546-2218

关键字：Generalized hyperelastic rod equation; symmetry transformation; Lou's direct method; exact solution

摘要：In this paper, a nonlinear wave equation with variable coefficients is studied, interestingly, this equation can be used to describe the travelling waves propagating along the circular rod composed of a general compressible hyperelastic material with variable cross-sections and variable material densities. With the aid of Lou's direct method', the nonlinear wave equation with variable coefficients is reduced and two sets of symmetry transformations and exact solutions of the nonlinear wave equation are obtained. The corresponding numerical examples of exact solutions are presented by using different coefficients. Particularly, while the variable coefficients are taken as some special constants, the nonlinear wave equation with variable coefficients reduces to the one with constant coefficients, which can be used to describe the propagation of the travelling waves in general cylindrical rods composed of generally hyperelastic materials. Using the same method to solve the nonlinear wave equation, the validity and rationality of this method are verified.