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Dynamic stiffness formulation and free vibration analysis of specially orthotropic Mindlin plates with arbitrary boundary conditions

Papkov, S.O. and Banerjee, J. R. (2019). Dynamic stiffness formulation and free vibration analysis of specially orthotropic Mindlin plates with arbitrary boundary conditions. Journal of Sound and Vibration, 458, pp. 522-543. doi: 10.1016/j.jsv.2019.06.028

Abstract

A novel dynamic stiffness formulation which includes the effects of shear deformation and rotatory inertia is proposed to carry out the free vibration analysis of thick rectangular orthotropic plates i.e. the formulation is based on an extension of the Mindlin theory to orthotropic plates in a dynamic stiffness context. The modified trigonometric basis is used to construct the general solution for the free vibration problem of the plate in series form, permitting the derivation of an infinite system of linear algebraic equations which connect the Fourier coefficients of the kinematic boundary conditions of its four edges. The boundary conditions are essentially the deflections and angles of rotations constituting the displacement vector and shear forces and bending moments constituting the force vector. The force-displacement relationship is then obtained by relating the two vectors via the dynamic stiffness matrix. Essentially the ensuing infinite system forms the fundamental basis of the paper, which defines the dynamic stiffness matrix for an orthotropic Mindlin plate in an exact sense. Numerical results are obtained by using the Wittrick-Williams algorithm as solution technique. The theory is first validated using published results and then further illustrated by a series of numerical examples. The paper concludes with significant conclusions.

Publication Type: Article
Additional Information: © Elsevier 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords: Free vibration, Rectangular orthotropic thick plate, Dynamic stiffness method, Infinite system of linear equations, Arbitrary boundary conditions
Subjects: Q Science > QC Physics
T Technology > TA Engineering (General). Civil engineering (General)
Departments: School of Mathematics, Computer Science & Engineering > Engineering > Mechanical Engineering & Aeronautics
URI: https://openaccess.city.ac.uk/id/eprint/22649
[img] Text - Accepted Version
This document is not freely accessible until 4 July 2020 due to copyright restrictions.
Available under License Creative Commons Attribution Non-commercial No Derivatives.

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