Dynamic stiffness formulation for transverse and in-plane vibration of rectangular plates with arbitrary boundary condit
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Dynamic stiffness formulation for transverse and in-plane vibration of rectangular plates with arbitrary boundary conditions based on a generalized superposition method Zitian Wei
. Xuewen Yin
. Shudong Yu . Wenwei Wu
Received: 27 February 2020 / Accepted: 10 August 2020 Springer Nature B.V. 2020
Abstract Dynamic stiffness formulation is proposed in this paper for both transverse and in-plane vibration of rectangular plates that account for arbitrary boundary conditions. A generalized superposition method is developed to obtain the homogeneous solutions for the governing equations of both transverse and in-plane vibration. Consequently, the dynamic stiffness matrices are formed in a more straightforward way by projection method, the dimensions of which are greatly reduced in comparison with those from the conventional Gorman’s superposition method. The finite element technique is utilized to assemble local stiffness matrix into global coordinates so as to address the dynamics of plate assemblies. Various types of plate-like structures are investigated by the proposed method, through which excellent agreement is found between our results and those from finite
Z. Wei X. Yin (&) W. Wu National Key Laboratory on Ship Vibration and Noise, China Ship Scientific Research Center, Wuxi 214000, People’s Republic of China e-mail: [email protected] Z. Wei e-mail: [email protected] W. Wu e-mail: [email protected] S. Yu Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, ON M5B 2K3, Canada e-mail: [email protected]
element method. The effectiveness, accuracy and convergence of the proposed DSM for both transverse and in-plane vibration are proved in several numerical examples, which demonstrates the proposed DSM is an excellent alternative to the existing DSM. Keywords Dynamic stiffness method Superposition method Transverse and in-plane vibration Plates Projection method
1 Introduction The subject of ship vibration and sound radiation has attracted sustained attention from not only design engineers but research scientists for comprehensive reasons, i.e., acoustic stealth capability, cabin comfort requirement, and marine life conservation. Accordingly, acoustic design strategy including ship vibration analysis is merged into multiple ship design stages. From the view of physical modeling, ship hull can be idealized as an assembly of welded plates with designed interfaces, orientations and stiffening strategies (Yu and Yin 2019). Due to urgent demand for efficient ship vibration analysis in different design stages, analytical solutions for vibrational behaviors of plate-like structures are often preferred instead of cumbersome finite element modelling. However, in order to viably model complex structures, analytical
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methods chosen must be general, versatile and applicable to (i) various types of vibration problems including transverse and in-plane vibration and (ii) arbitrary boundary conditions (BCs) (Yu a
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