一类非线性弹性梁方程解的存在性

研究了一类非线性弹性梁方程的初边值问题,考虑了材料的粘性效应及非线性外阻尼,建立了一类轴向载荷作用下的非线性弹性支承梁方程,并利用Faedo-Galerkin方法,证明了该方程在一定的初边值条件下解的存在性,为力学中弯曲与扭转联合作用下具有结构阻尼的振动问题的研究与计算提供了数学依据。

Existence of Solutions for a Class of Equation of Nonlinear Elastic Beam

In this paper,we considered the abstract initial value problem associated with a kind of nonlinear system of partial differential equations,established a kind of equation of nonlinear elastic beam subjected to axial force load by considering both viscosity effect and nonlinear external damping,and the existence of solutions for the equation by the Galerkin method,which casts the basis for the reseach and calculation on the coupled flexural and tensional oscillations with structural damping.