Symmetry Transformations and Exact Solutions of a Generalized Hyperelastic Rod Equation

• 作者: Hongwu Zhang Jing Zhang Na Lv Ran Wang Xuegang Yuan
• 来源期刊: 计算机、材料和连续体(英文)
• 学科: 数学
• 关键词: GENERALIZED HYPERELASTIC rod EQUATION SYMMETRY transformation Lou’s direct method EXACT solution
• 年，卷（期）: 2018,（5）
• 页码范围: 345-357
• 页数: 13页
• 分类号: O17

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 method1,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.