弹性力学状态变量体系下带有初应力的振动问题

Vibration problem of theory of elasticity in Hamilton system under initial stress

通过在Hellinger-Reissner广义势能中引入应变的非线性项,推导出了弹性力学Hamilton体系下的具有初应力的振动方程,并运用精细积分给出了两端简支的梁、组合梁和四边简支板及组合板在初应力下振动频率。本文结果是严格弹性力学意义(没有引入任何几何变形假设)下的精确解,为衡量各种计入剪切变形的薄板、中厚板理论的准确性提供了一个标准。

In this paper,by considering the nonlinear term in Hellinger-Reissner variational principle,the vibration formulation with initial stress in Hamilton system was derived.As examples,frequencies with initial stress of a beam,composite beam,plate and composite plate were studied in precise integration method.The results were the exact solutions based on the exact elasticity theory（not considering any geometrical hypothesis）.This paper provides a standard for both thin plates and moderately thick plates theory considering the effect of shear deformation.