Theoretical analysis and experimental measurement of coupling dynamic characteristics for transversely isotropic rectang
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O R I G I NA L PA P E R
Yi-Chuang Wu · Chien-Ching Ma · Hong-Cin Liou
Theoretical analysis and experimental measurement of coupling dynamic characteristics for transversely isotropic rectangular plate based on modified FSDT assumption
Received: 9 February 2020 / Revised: 17 May 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract The theoretical analysis of thick plate vibration behavior has been investigated in the literature, but most of the studies were focused on flexural dynamic characteristics and lack experimental verification. In this study, the analytical solutions based on the superposition method for both the flexural and extensional vibrations are presented to obtain resonant frequencies and associated mode shapes for a transversely isotropic thick rectangular plate. The displacement equilibrium equations and boundary conditions of the modified firstorder shear deformation theory (FSDT) are derived by utilizing Hamilton’s principle and the variation method. To verify the validity of the theoretical model, the finite-element method (FEM) and impact experiment results for thick plates are employed in this work. Excellent agreement of resonant frequencies and associated mode shapes is obtained for FEM calculation and theoretical analysis. To excite vibrations of a thick rectangular plate, a steel ball controlled by an electromagnet is utilized. A steel ball is dropped freely from a height of 231 mm on the top of the plate surface, and a transient wave will be generated after the ball impact on the specimen. The frequency spectrum of the thick rectangular plate is constructed by using the fast Fourier transform of the time-domain transient response. The excited resonant frequencies obtained from experimental measurement are compared with theoretical results. The comparisons show that the modified FSDT provides an excellent prediction of the resonant frequencies and mode shapes for the dynamic characteristics of thick rectangular plates.
1 Introduction Today, the analysis of transversely isotropic materials is a very important branch of applied mathematics and engineering sciences. With the rapid development of modern industry, the theory of transversely isotropic elasticity is given more and more attention. These materials are associated with many technological fields, such as civil engineering and material engineering, and many emerging technologies have demand the development of transversely isotropic materials. In addition, transversely isotropic plates are also used in many Y.-C. Wu Department of Mechanical Engineering, National Chung Cheng University, No.168, Sec. 1, University Rd., Minhsiung, Chiayi 62102, Taiwan, Republic of China E-mail: [email protected] C.-C. Ma (B) Department of Mechanical Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan, Republic of China E-mail: [email protected] H.-C. Liou Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA E-mail: [email protected]
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