基于格林函数正交各向异性切口板自由振动特性分析

杨永育1,2,李腾岳2,程长征2,赵航1,葛仁余1

振动与冲击 ›› 2024, Vol. 43 ›› Issue (5) : 182-187.

PDF(1149 KB)
PDF(1149 KB)
振动与冲击 ›› 2024, Vol. 43 ›› Issue (5) : 182-187.
论文

基于格林函数正交各向异性切口板自由振动特性分析

  • 杨永育1,2,李腾岳2,程长征2,赵航1,葛仁余1
作者信息 +

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

  • YANG Yongyu1,2,LI Tengyue2,CHENG Changzheng2,ZHAO Hang1,GE Renyu1
Author information +
文章历史 +

摘要

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。

Abstract

Orthotropic anisotropic plates are widely used in engineering structures due to the light weight and high load-bearing capacity. A method is proposed to analyze the free vibration characteristics of orthotropic anisotropic plates based on the Green's function combining and Peridynamic differential operator (PDDO). Firstly, the displacement function in the vibration control equation is assumed to be the first-order integral form with Green's function. Secondly, the linear fourth-order partial differential equations are discretized into algebraic equations in the radial and circumferential directions of the notched plate, respectively. Finally, the generalized characteristic equation of free vibration is established by constructing PDDO interpolation functions to represent the non-common discrete point displacements, which can obtain the free vibration frequency and shape to prove the accuracy of the proposed method. The influence law of the notch geometry parameters on the vibration characteristics of the structure is analyzed, which can provide support for designing of the plate and shell structure.

关键词

正交各向异性切口板 / 自由振动 / 格林函数 / 近场动力学微分算子

Key words

Orthogonal anisotropic notched plate / Free vibration / Green's function / PDDO

引用本文

导出引用
杨永育1,2,李腾岳2,程长征2,赵航1,葛仁余1. 基于格林函数正交各向异性切口板自由振动特性分析[J]. 振动与冲击, 2024, 43(5): 182-187
YANG Yongyu1,2,LI Tengyue2,CHENG Changzheng2,ZHAO Hang1,GE Renyu1. Free vibration characteristics analysis of orthotropic notched plate based on Green’s function[J]. Journal of Vibration and Shock, 2024, 43(5): 182-187

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