基于格林函数正交各向异性切口板自由振动特性分析

Free vibration characteristics analysis of orthotropic notched plate based on Green’s function

正交异性板因重量轻、承载能力强等优点而被广泛运用于工程结构。基于格林函数,结合新兴的近场动力学微分算子(peridynamic differential operator, PDDO),提出一种分析正交各向异性板自由振动特性的方法。首先,将振动控制方程中的位移函数假设为含格林函数的一阶积分形式;其次,将线性四阶偏微分方程分别在切口板的径向和周向离散成代数方程;最后,通过PDDO构造插值函数表示径向和周向非公共离散点位移,建立自由振动广义特征方程,获得正交各向异性切口板自振频率及振型,证明了该方法的准确性,并分析切口几何参数对结构振动特性的影响规律,为板壳结构设计提供支撑。

Orthotropic plates are widely used in engineering structures due to their advantages of light weight and strong load-bearing capacity.Here,a method to analyze free vibration characteristics of orthotropic notched plate was proposed based on Green’s function and the emerging peridynamic differential operator(PDDO).Firstly,displacement function in the plate’s vibration governing equations was assumed to be a first-order integral form containing Green’s function.Secondly,the plate’s vibration governing equations,i.e.,the linear 4th order partial differential equations were discretized into algebraic equations in radial and circumferential directions of the notched plate,respectively.Finally,interpolation functions were constructed using PDDO to represent radial and circumferential non-common discrete points’displacements,and a generalized characteristic equation for the plate’s free vibration was established to obtain natural frequencies and vibration mode shapes of orthotropic notched plate to prove the correctness of the proposed method.Effects of geometric parameters of notch on the plate’s vibration characteristics were analyzed to provide support for designing plate and shell structures.