【摘要】 根据大挠度理论建立了正交异性薄膜的非线性动力学方程并对其展开分析。根据薄膜动力学特性建立薄膜振动问题的控制方程组;根据物理和边界条件对方程组进行简化和解算,得出其线性解析解和非线性解析解。利用伽辽金算法得出薄膜非线性振动频率的近似解。通过算例分析验证了近似解的准确性和精度,并对其误差进行了分析。分析结果表明近似解结构简单,且具有较高的精度和较大的适用范围,能够为膜结构工程设计提供理论计算依据。更多还原

【Abstract】 A non-linear kinetic equation of orthotropic membrane was established and analyzed according to the large deflection theory. Firstly,the control equations of the vibration of the membrane were established in line with its dynamic characteristics. Secondly,the equations were simplified based on the physical and boundary conditions,and then,its linear solution and nonlinear solution were obtained. Thirdly,the approximate frequency values of othotropic membrane were obtained by using the Galerkin algorithm. Finally,the approximate solutions were verified by the analysis of an example,and at the same time,the deviation was analyzed. The analysis result show that the approximate solution is simple,and has high precision and large range application. The result could provide theoretical basis for the design of membrane structure.更多还原