考虑铺层角的复合材料圆柱壳自由振动三维弹性准确解

为了获得任意角度铺层的多层复合材料圆柱壳的自由振动准确解,在三维弹性理论的基础上,结合分层理论和状态空间法,建立横向位移和应力的传递矩阵,轴向和环向位移采用双螺旋模式的位移函数,对任意角度铺层复合材料圆柱壳简支边界条件下的自由振动进行了理论推导,得到了自由振动方程的精确形式。与文献理论解和有限元计算结果对比,结果表明,关注频率在2倍的环频率以下时,薄壳的固有频率计算精度能控制在1%以内,厚壳的固有频率计算精度能控制在2%以内。对于厚壳的计算可将壳体沿厚度方向划分为多层来处理,这样能有效提高计算精度。计算分析了铺层角对壳体固有频率的影响,环向模态数较低时,固有频率随着铺层角的增加呈抛物线变化趋势;环向模态数较高时,固有频率随着铺层角的增大单调递增。该理论方法同样适用于均质各向同性壳和正交各向异性圆柱壳。 

Three-dimensional elastic exact solution for free vibration of composite cylindrical shells considering ply angle

In order to obtain the exact free vibration solution of laminated cylindrical shell with arbitrary ply angle,the transfer matrix of transverse displacement and stress was established by combining the layer-wise theory with state space method on the basis of three-dimensional elastic theory,the axial and circumferential displacement components were approximated using double helical pattern modes and the free vibration analytic formula of laminated cylindrical shell with arbitrary ply angle under simply supported boundary was derived.The exact form of the free vibration equation was obtained.The validity of the present theoretical method was verified by being compared with the theoretical model from the literature and the finite element methods.The results show that when the considered frequencies are less than two times the ring frequency,the calculation precision for natural frequency of thin shells is less than 1% and that of the thick shells is less than 2%.For the thick shells,the shell can be divided into multi layers along the thickness direction,which can effectively improve the calculation precision.The influence of layer angle on the natural frequency was analyzed based on present method,the results shows that when the circumferential mode is low,the natural frequency is parabolic with the increasing of the layer angle and when the circumferential mode is high,the natural frequency increases monotonically with the increasing of the layer angle.The present method is also suitable for homogeneous isotropic shells and orthotropic cylindrical shells.