非线性弹性固体中的横波与Milne-Pinney（或Ermakov）方程
Transverse Waves in Nonlinearly Elastic Solids and the Milne-Pinney (or Ermakov) Equation
摘要：
本文建立了非线性弹性动力学一般方程与Pinney非线性常微分方程之间的联系[Proc.Amer.Math.Soc.1（1950）681]。作为一个出发点，我们使用精确的行波解的非线性弹性发现卡罗尔[学报力学3（1967）167]。该连接提供了一种方法，用于寻找新的精确和近似的动态解决方案，新的Hookean和Mooney-Rivlin固体，和一般的第三和第四阶弹性模型的不可压缩固体。
英文摘要：
We establish a connection between the general equations of nonlinear elastodynamics and the nonlinear ordinary differential equation of Pinney [Proc. Amer. Math. Soc. 1 (1950) 681]. As a starting point, we use the exact travelling wave solutions of nonlinear elasticity discovered by Carroll [Acta Mechanica 3 (1967) 167]. The connection provides a method for finding new exact and approximate dynamic solutions for neo-Hookean and Mooney-Rivlin solids, and for the general third- and fourth-order elasticity models of incompressible solids.
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