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
陆炎洲 1李志远 1黄丹 1姚学昊1
作者信息
- 1. 河海大学工程力学系,南京,211100
- 折叠
摘要
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.
Abstract
Anisotropic materials find widespread applications across various engineering domains.The investigation on vibrational properties of anisotropic materials holds significance for structural vibration mitigation and safety design.This paper introduces a novel approach,the peridynamic operator method(PDOM),to construct a non-local anisotropic model and applies it to the analysis of free vibrations in ani-sotropic plates.The 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,the paper employs a variational principle and introduces the free vibration equation to develop a PDOM solution for anisotropic free vibra-tion problems.Three numerical examples are provided,including the free vibrations of a thin anisotropic rectangular plate,an anisotropic rectangular plate with cracks,and an anisotropic rectangular plate with holes.The results are compared with finite element results,showcasing the model's convergence,stabili-ty,and high computational accuracy in dealing with free vibrations of anisotropic plates with defects and discontinuities.
关键词
自由振动/各向异性/近场动力学算子方法/非局部/变分原理Key words
free vibration/anisotropic/PDOM/non-local/variational principle引用本文复制引用
基金项目
中央高校基本科研业务费专项资金(B240201144)
国家自然科学基金项目(12071204)
出版年
2024
NETL
NSTL
万方数据