Exact Free Vibration Analysis for Plate Built-Up Structures under Comprehensive Combinations of Boundary Conditions

Author:

Liu Xiang1234,Xie Chen123,Dan Han-cheng5ORCID

Affiliation:

1. Key Laboratory of Traffic Safety on Track (Central South University), Ministry of Education, Central South University, Hunan, Changsha 410075, China

2. Joint International Research Laboratory of Key Technology for Rail Traffic Safety, Hunan, Changsha 410075, China

3. School of Traffic & Transportation Engineering, Central South University, Hunan, Changsha 410075, China

4. State Key Laboratory of High Performance Complex Manufacturing, Central South University, Hunan, Changsha 410075, China

5. School of Civil Engineering, Central South University, Hunan, Changsha 410075, China

Abstract

In this research, an exact dynamic stiffness model for spatial plate built-up structures under comprehensive combinations of different boundary conditions is newly proposed. Dynamic stiffness formulations for plate elements with 16 different types of supported opposite edges and arbitrarily supported boundary conditions along other edges are developed, which makes the dynamic stiffness method (DSM) more applicable to engineering problems compared to existing works. The Wittrick–Williams algorithm of the DSM is applied with the explicit expressions of the J0 count for plate elements under all above support conditions. In return, there is no need to refine the element in the DSM, and thus, it becomes immensely efficient. Moreover, the present theory is applied for exact free vibration analysis within the whole frequency range of three built-up structures which are commonly encountered in engineering. The results show that the DSM gives exact results with as much as 100-fold computational efficiency advantage over the commercial finite element method. Besides, benchmark results are also provided.

Funder

National Key R&D Program of China

Publisher

Hindawi Limited

Subject

Mechanical Engineering,Mechanics of Materials,Geotechnical Engineering and Engineering Geology,Condensed Matter Physics,Civil and Structural Engineering

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