螺旋状结构的自由振动分析

Free vibration of helicoidal structures

就工程中应用广泛的螺旋状结构的振动特性进行研究,提出了一个适合分析具有大扭转角的弹性螺旋状结构自由振动特性的数值方法.基于板壳理论和一阶剪切变形理论导出了螺旋状结构模型精确的应变-位移关系,根据虚功原理建立其自由振动的能量方程,运用瑞雷-李兹法建立该螺旋状结构的解析特征方程,并通过有效的计算方法求解其自由振动特性.其中,运用格莱姆-施密特算法生成一族正规化正交多项式作为许可函数,该正交多项式的初始项由该结构边界的几何协调方程而生成.最后,对该数值方法的收敛性、精确性和可行性进行了分析.

Vibration of helicoidal structures widely applied in engineering is studied. A numerical analysis method for free vibration characteristics of elastic helicoidal structures with a great twist is presented. Based on the shell theory and the first order shear deformation theory, an accurate strain-displacement relationship of the helicoidal structure modeled is derived. An energy eqt, ilibrium equation of free vibration is introduced by the principle of virtual work. Applying the Rayleigh-Ritz method an analytical eigenvalue equation is formulated and solved the vibration characteristics of the helicoidal structure are obtained by an efficient computational approach. A set of normalized orthogonal polynomials generated by the Gram Schmidt procedure is presented to the admissible functions. The first polynomial is taken as compliant geometric equations of boundary conditions of the structure. The convergence, the accuracy and the feasibility of the present numerical method are investigated.