Static and Dynamic Stability of Carbon Fiber Reinforced Polymer Cylindrical Shell Subject to Non-Normal Boundary Condition with One Generatrix Clamped

Mathematics

Wei Zhang¹  Lingtao Liu²  Shaowu Yang²  Yuxin Hao²  Wensai Ma³ 

[1] Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China;College of Mechanical Engineering, Beijing Information Science and Technology University, Beijing 100192, China;Department of Mechanics, Inner Mongolia University of Technology, Hohhot 010051, China;

关键词: laminated cylindrical shell;    stability;    unstable region;    boundary condition;    carbon fiber reinforced polymer;   

DOI  :  10.3390/math10091531

来源: DOAJ

【 摘 要 】

In this paper, static and dynamic stability analyses taking axial excitation into account are presented for a laminated carbon fiber reinforced polymer (CFRP) cylindrical shell under a non-normal boundary condition. The non-normal boundary condition is put forward to signify that both ends of the cylindrical shell are free and one generatrix of the shell is clamped. The partial differential motion governing the equations of the laminated CFRP cylindrical shell with a non-normal boundary condition is derived using the Hamilton principle, nonlinear von-Karman relationships and first-order deformation shell theory. Then, nonlinear, two-freedom, ordinary differential equations on the radial displacement of the cylindrical shell are obtained utilizing Galerkin method. The Newton-Raphson method is applied to numerically solve the equilibrium point. The stability of the equilibrium point is determined by analyzing the eigenvalue of the Jacobian matrix. The solution of the Mathieu equation describes the dynamic unstable behavior of the CFRP laminated cylindrical shells. The unstable regions are determined using the Bolotin method. The influences of the radial line load, the ratio of radius to thickness, the ratio of length to thickness, the number of layers and the temperature field of the laminated CFRP cylindrical shell on static and dynamic stability are investigated.

【 授权许可】

Unknown