基于近场动力学算子方法的各向异性板自由振动分析

Free Vibration Analysis for Anisotropic Plates Based on Peridynamic Operator Method

各向异性材料广泛应用于诸多工程领域,研究其振动特性对结构减振与安全设计具有重要意义.本文基于一种新的近场动力学算子方法(Peridynamic operator method,PDOM)构建非局部各向异性模型,并应用于各向异性板的自由振动分析.该模型结合了PDOM将局部微分及其乘积转化为非局部积分的特点,将经典各向异性理论中的应变能密度从局部形式重构为非局部形式.同时,采用变分原理并引入自由振动方程,构建了适用于各向异性自由振动问题的PDOM求解方案.通过三个数值算例:各向异性矩形薄板、各向异性矩形含裂纹板、各向异性矩形含孔板的自由振动,并将计算结果与有限元结果比较,说明了模型在计算含缺陷以及不连续的各向异性板自由振动问题时具有收敛性、稳定性以及高计算精度.

Anisotropic materials find widespread applications across various engineering domains,and the investigation of their vibrational properties holds significant significance for structural vibration mitigation and safety design.This paper introduces a novel approach,peridynamic operator method(PDOM),to construct a non-local anisotropic model and applies it to the analysis of free vibrations in anisotropic plates.This model incorporates the unique feature of PDOM,which transforms local differentials and their products into non-local integrals,thereby reformulating the strain energy density from its local form to a non-local form within classical anisotropic theory.Additionally,by employing a variational principle and introducing the free vibration equation,a PDOM solution is developed for addressing anisotropic free vibration problems.Through three numerical examples:anisotropic rectangular thin plate,anisotropic rectangular plate with cracks,and anisotropic rectangular plate with holes in free vibration,the results are compared with finite element results,demonstrating the convergence,stability,and high computational accuracy of the model when dealing with the free vibration of anisotropic plates with defects and discontinuities.