厚板弯曲与拉伸振动精化理论及其求解新途径

利用弹性动力学中Boussinesq—Galerkin一般解，基于微分算子谱和算子代数理论，采用了适当的规范条件，建立了推演厚板结构动力学方程的新途径．首次给出了考虑横向荷载作用的平板弯曲和拉压振动的两类动力学方程具体形式．为推导动力学方程方便和利用微分算子谱分解理论，引进了虚微分算子（i ）的概念．并将本文得到的平板结构振动方程与各种平板结构的弯曲方程作了对比分析．由于本文推导时没有采用任何工程假设，因此本文提出的平板动力学方程是精确的，可用于求解厚壁平板的振动和设计平板振动主动控制策略．本文为不采用几何方法，而是采用分析和代数的方法精确推导低维结构的动力学支配方程提供了一种统一规范的方法．

Refined dynamic theory of thick plates in extension-bending and its new formulism

In this paper, based on the theory of elastodynarnics, applied the general solution proposed by Boussinesq-Galerkin and the operator theory of partial differential equations, the refined equations of elastodynamics of the thick plate including the effect of the transverse loading was obtained by using appropriate gauge conditions. The imaginary differential operator was firstly introduced in order to apply the spectrum decomposition theory of differential operators. The refined dynamic equations of plate bend and stretch were given, respectively. And the refined dynamic theory of thick plates was compared with the different classical theory of plates. Derivation of the dynamic equation was conducted without any priory assumption, so the proposed dynamic equation of plates is exact. The governing equation proposed by this paper can be used to analyze vibration of thick plates, evaluate the applicable condition of the engineering plate theory and exactly to design the active vibration control of thick plates.