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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Nonlinear Dynamical Modeling and Vibration Responses of An L-Shaped Beam-Mass Structure

Journal of Applied Nonlinear Dynamics 6(1) (2017) 91--104 | DOI:10.5890/JAND.2017.03.007

Jin Wei; Dengqing Cao; Yang Yang; Wenhu Huang

Division of Dynamics and Control, School of Astronautics, Harbin Institute of Technology, Harbin 150001, PR China.

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Abstract

The global modal approach is employed to obtain a set of ordinary differential equations of motion describing the nonlinear dynamics of an L-shaped beam structure in this paper. Firstly, the Lagrangian of nonlinear dynamics for the whole system is formulated. The linear partial differential equations of transverse motion are derived for each beam, along with their boundary and matching conditions. Consequently, the characteristic equation is formulated for the whole system. The natural frequencies and global mode shapes of the system are determined, and orthogonality relations of the global mode shapes are established. Then, the Lagrange's procedure is employed to obtain the nonlinear ODEs of motion for the structure with multiple- DoF. A comparison between the natural frequencies obtained by the proposed method and those from finite element method is given to illustrate the validity of our approach. Through the nonlinear ODEs presented in this article, a study on the variation of dynamic responses for the systems with different number of global modes is performed to give a suggestion of how many modes should be taken for vibration analysis of the structure.

Acknowledgments

We gratefully acknowledge the National Natural Science Foundation of China (Grant Nos. 91216106 and 11472089) for the financial support of this work.

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