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# Vibration suppression of a moving beam subjected to an active-control electrostatic force

Shueei-Muh Lin1

Mechanical Engineering Department, Kun Shan University, Tainan, Taiwan 710-03, Republic of China. E-Mail: smlin@mail.ksu.edu.tw

Computer Modeling in Engineering & Sciences 2009, 43(1), 73-90. https://doi.org/10.3970/cmes.2009.043.073

## Abstract

In this study, the mathematical model of a moving beam is established. This model is composed of a governing differential equation and three homogenous boundary conditions and one non-homogenous boundary condition including a time-dependent inertia force and a nonlinear active control force. Obviously, a moving mass problem with nonlinear and time dependent boundary condition is very complicated. One solution method is here developed to derive the exact solution for this system. By taking a change of dependent variable with a shifting function the original system is transformed to be a system composed of one non-homogeneous governing differential equation and four homogeneous boundary conditions. Further, based on an orthogonality condition of the eigenfunctions the mode superposition method is used to derive the exact solution for the transformed system. It should be noted that the transformed system is proved to be non-self-adjoint. Its orthogonality condition of eigenfunctions is different to the conventional one. Based on this orthogonality condition, the mode superposition method can be used to solve the transformed problem. The effects of different accelerations of a moving beam on the dynamic positioning and vibration of beam are significant. For suppressing vibration, two simple designs of active control of electrostatic force against the vibration are presented here. These are verified to be very effective.

## Keywords

APA Style
Lin, S. (2009). Vibration suppression of a moving beam subjected to an active-control electrostatic force. Computer Modeling in Engineering & Sciences, 43(1), 73-90. https://doi.org/10.3970/cmes.2009.043.073
Vancouver Style
Lin S. Vibration suppression of a moving beam subjected to an active-control electrostatic force. Comput Model Eng Sci. 2009;43(1):73-90 https://doi.org/10.3970/cmes.2009.043.073
IEEE Style
S. Lin, "Vibration suppression of a moving beam subjected to an active-control electrostatic force," Comput. Model. Eng. Sci., vol. 43, no. 1, pp. 73-90. 2009. https://doi.org/10.3970/cmes.2009.043.073

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