Nonlinear waves and periodic solution in finite deformation elastic rod

作者：Liu ZF^*; Zhang SY

来源：Acta Mechanica Solida Sinica, 2006, 19(1): 1-8.

DOI：10.1007/s10338-006-0601-0

• nonlinear wave
• finite deformation
• Poisson effect
• Jacobi elliptic function

A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.

• 出版日期2006-3
• 单位太原理工大学