环状粘弹层合悬臂薄壁圆柱壳的振动特性研究

文章采用传递矩阵法分析了悬臂边界条件下环状局部覆盖粘弹层合薄壁圆柱壳的振动特性。基于乐甫薄壳理论,结合粘弹性阻尼的变形协调关系和层间作用力关系,建立了基层和约束层薄壁圆柱壳的一阶状态微分方程,利用传递矩阵法推导了结构的整体传递矩阵,并通过高精度的精细积分方法进行求解,得到了固有频率、损耗因子和三维振型,探讨了约束阻尼层位置变化时对振动特性的影响,并通过有限元法进行了比较,通过算例验证了传递矩阵法对模态特性分析的有效性,前25阶模态以周向振动为主,最低阶固有频率对应的三维模态振型为(1,5),并且在悬臂端的振动位移最大,约束阻尼层覆盖位置对薄壁圆柱壳振动特性的影响较大。

Study on vibration characteristics of a ring covered viscoelastic laminated cantilever thin cylindrical shell

Vibration characteristics of a ring covered viscoelastic laminated cantilever thin cylindrical shell are studied by transfer matrix method. A first-order ordinary differential equations for the host shell and the constraining layer are established based on Love's shell theory combining with deformation coordination of viscoelastic damping layer and interactional forces, and an integrated transfer matrix of the whole component is derived by transfer matrix method. Then, the natural frequencies, loss factors and three-dimensional shapes are derived by high-precise integration method, and its vibration characteristics are discussed when the cov-ered position is different. Finally, the results are compared with results of finite element method. The ex-ample results show that transfer matrix method is effective to solve the vibration characteristics of the ring covered viscoelastic laminated cantilever thin cylindrical shell, and the main modal vibration occurs in the circumferential direction. The three-dimensional modal shape corresponding to the lowest order natural fre-quency is (1, 5), and the cantilever's vibration displacement is maximum. At the same time, the covered location of constrained damping layer has obvious impact on modal characteristics of the thin cylindrical shell.