Nonlinear vibrations of micro-doubly curved shallow shells based on the modified couple stress theory

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• 作者：Amir Veysi ; Rasoul Shabani ; Ghader Rezazadeh
• 关键词：Micro ; doubly curved shallow shells ; Nonlinear vibrations ; Modified couple stress theory ; Frequency response
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：87
• 期：3
• 页码：2051-2065
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：87

文摘

The present study investigates the nonlinear size-dependent behavior of micro-doubly curved shallow shells based on the modified couple stress theory. Assuming von-Karman geometric nonlinearity and the first-order shear deformation theory, the governing equations of the system are derived using variational approach. The governing equations are reduced using the Galerkin method to a system of finite nonlinear ordinary differential equations. Multiple scales method is used to obtain an approximate analytical solution for nonlinear frequency response. Effect of the length scale parameter as well as the shell curvature on the frequency curves is addressed. It is shown that increasing the length scale parameter changes the softening behavior to a hardening one. On the shell curvature plane, it is depicted that for some values of the length scale parameter the system displays totally a hardening behavior. Influence of the length scale on the effective nonlinearity is discussed. It is found that in a flat shell the effective nonlinearity did not change significantly, while the variations are considerable for saddle shells. It is also shown that variation in the shell dimensions for spherical shells had significant effect on the frequency response, while this is not the case for hyperbolic paraboloidal shells. Finally, examining the effects of the damping on the nonlinear dynamics of the system shows wider response region for decreasing damping.