一般边界条件下矩形叠层板面内振动研究

Inplane vibration research of rectangular laminated plates under general boundary conditions

为研究矩形叠层板的面内振动机理,本文基于能量法求解框架,推导了矩形叠层板面内自由振动的能量方程,分别采用勒让德多项式和人工弹簧技术表示结构位移容许函数与边界条件,进而获得一般边界条件下矩形叠层板面内自由振动特性求解方程。通过与有限元和实验结果进行对比,验证了本文求解模型的正确性。在此基础上,对矩形叠层板的面内振动特性展开参数化研究,分析了纤维铺设角和纤维叠层数等设计参数对面内自由振动特性的影响。结果表明:通过本文所建立的数值分析模型所得结果较为可靠准确,各个设计参数对矩形叠层板结构的面内自由振动特性具有不同的影响规律。

To study the inplane vibration mechanism of the rectangular laminated plate,this paper deduces the energy equation of the inplane free vibration of the rectangular laminated plate on the basis of the energy method to solve the frame and uses the Legendre polynomial and artificial spring technology to represent the structural displacement allowable function and boundary conditions.Then,the free vibration characteristics of the rectangular laminated plate under general boundary conditions are obtained to solve the equation.By comparing with the finite element and experimental results,the accuracy of the model solved in this paper is verified.On this basis,a parametric study of the inplane vibration characteristics of rectangular laminates is carried out,and the effects of design parameters,such as the fiber laying angle and the number of fiber stacks on the inplane free vibration characteristics,are analyzed and compared.Results obtained by the numerical analysis model established in this paper are relatively reliable and accurate,and each design parameter affects the inplane free vibration characteristics of the rectangular laminated plate structure distinctly.