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基于三维弹性理论,采用改进傅里叶级数法(Improved Fourier Series Method,IFSM)对环扇形板三维自由振动进行了数值分析。环扇形板的位移函数表示为一种改进的三角级数形式,而边界条件则通过均匀分布在各边界面的线性弹簧来模拟,通过改变边界约束弹簧的刚度值来实现不同的边界条件。将位移函数的未知级数展开系数看作广义坐标,并采用瑞利-里兹法进行求解,得到一个关于未知系数的标准特征值问题。环扇形板结构的三维自由振动特性可以通过求解标准特征值问题简单获得。数值计算结果充分表明,文中采用改进傅里叶级数法分析环扇形板三维自由振动问题的有效性和正确性。
Based on the three-dimensional elasticity theory, the three-dimensional free vibration of the ring sector plate was numerically analyzed by the Improved Fourier Series Method (IFSM). The displacement function of the ring sector is expressed as an improved form of the trigonometric series and the boundary conditions are modeled by a linear spring uniformly distributed over the boundary surfaces. Different boundary conditions are achieved by changing the stiffness of the boundary constraint spring. The expansion coefficient of unknown function of the shift function is considered as a generalized coordinate and solved by Rayleigh-Leitz method. A standard eigenvalue problem about unknown coefficient is obtained. The three-dimensional free vibration characteristics of the ring sector plate structure can be easily obtained by solving the standard eigenvalue problem. The numerical results show that the validity and correctness of the three-dimensional free vibration of the ring sector plate are analyzed by the improved Fourier series method.