偏心圆柱薄壳输入功率流特性研究

Input power flow characteristics of thin eccentric cylindrical shells

根据偏心圆柱薄壳截面的几何特性,将偏心圆柱薄壳问题转化为周向变厚度圆柱壳问题。基于Flügge薄壳理论推导出偏心圆柱薄壳的受迫振动方程,采用波传播的思想将偏心柱壳位移以双Fourier级数形式展开,周向变厚度表示为周向角度坐标的函数,通过三角函数变换将变系数的偏微分方程组转换为周向模态阶数相互耦合的有限阶线性方程组,通过对耦合方程进行求解得到偏心柱壳的位移响应,进而计算壳体的输入功率流。通过与文献及FEM结果进行对比,验证了所建立的偏心柱壳振动理论模型及计算方法的准确性。同时,详细计算并分析了激励力位置、偏心率、壳体厚度和材料阻尼等参数对偏心柱壳输入功率流的影响。

According to the geometry characteristics of the cross section of an eccentric cylindrical shell,the eccentric problem was converted into a circumferentially varying thickness problem. The displacements were expanded in double Fourier series in view of the concept of wave propagation and the circumferential thickness was represented as a trigonometric function. Through a series of transformation,the partial differential equations with variable coefficients were converted into a set of linear equations with the circumferential modal parameters coupled with each other. The forced vibration responses of the eccentric cylindrical shell were obtained by solving the coupled equations and then the input power flow was achieved. By comparing with the literature and FEM results, the accuracy of the vibration model established and calculation method for the eccentric cylindrical shell was verified. The influences of the parameters,such as the exciting force position, eccentricity, shell thickness and material damping factor on the input power flow of eccentric cylindrical shell were discussed in detail.