On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge

On the symplectic superposition method for new analytic free vibration solutions of side-cracked rectangular thin plates

Journal of Sound and Vibration ◽

10.1016/j.jsv.2020.115695 ◽

2020 ◽

Vol 489 ◽

pp. 115695

Author(s):

Zhaoyang Hu ◽

Yushi Yang ◽

Chao Zhou ◽

Xinran Zheng ◽

Rui Li

Keyword(s):

Free Vibration ◽

Thin Plates ◽

Superposition Method

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A General Analytical Solution for Free Vibration of Rectangular Plates Resting on Fixed Supports and With Attached Masses

Journal of Electronic Packaging ◽

10.1115/1.2906424 ◽

1992 ◽

Vol 114 (2) ◽

pp. 239-245 ◽

Cited By ~ 10

Author(s):

R. K. Singal ◽

D. J. Gorman

Keyword(s):

Free Vibration ◽

Analytical Procedure ◽

Thin Plates ◽

Mode Shapes ◽

Experimental Program ◽

Space Vehicles ◽

Superposition Method ◽

Rectangular Plates ◽

Solar Panels ◽

Good Agreement

A comprehensive analytical procedure based on the superposition method is described for establishing the free vibration frequencies and mode shapes of thin plates resting on rigid point supports and with attached masses. Effects of rotary inertia of the attached masses are incorporated into the analysis and are shown to be highly significant. Results of an extensive experimental program are reported and very good agreement is demonstrated between theory and experiment. The analytical procedure has application in numerous contemporary industrial problems, in particular, in the design of solar panels for space vehicles and in the field of electronic packaging.

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Analytical free vibration solutions of fully free orthotropic rectangular thin plates on two-parameter elastic foundations by the symplectic superposition method

Journal of Vibration and Control ◽

10.1177/1077546320967823 ◽

2020 ◽

pp. 107754632096782

Author(s):

Xin Su ◽

Eburilitu Bai

Keyword(s):

Free Vibration ◽

Fundamental Solutions ◽

Thin Plates ◽

Superposition Method ◽

Elastic Foundations ◽

Vibration Problem ◽

Separation Variable ◽

Vibration Problems ◽

Two Parameter ◽

Free Edges

The free vibration of orthotropic rectangular thin plates with four free edges on two-parameter elastic foundations is studied by the symplectic superposition method. Firstly, by analyzing the boundary conditions, the original vibration problem is converted into two sub-vibration problems of the plates slidingly clamped at two opposite edges. Based on slidingly clamped at two opposite edges, the fundamental solutions of these two sub-vibration problems are respectively derived by the separation variable method of the corresponding Hamiltonian system, and then the symplectic superposition solution of the original vibration problem is obtained by superimposing the fundamental solutions of the two sub-problems. Finally, the symplectic superposition solution obtained in this study is verified by calculating the frequencies and mode functions of several concrete rectangular thin plates with four free edges.

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Symplectic Superposition Solution of Free Vibration of Fully Clamped Orthotropic Rectangular Thin Plate on Two-Parameter Elastic Foundation

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455421501224 ◽

2021 ◽

pp. 2150122

Author(s):

Xin Su ◽

Eburilitu Bai ◽

Alatancang Chen

Keyword(s):

Free Vibration ◽

Elastic Foundation ◽

Series Expansion ◽

Separation Of Variables ◽

Solution Process ◽

Thin Plates ◽

Symplectic Space ◽

Superposition Method ◽

Vibration Problem ◽

Two Parameter

Based on the method of separation of variables in Hamiltonian system and superposition method, the series expansion solution of the free vibration problem of orthotropic rectangular thin plates (ORTPs) with four clamped edges (CCCC) on two-parameter elastic foundation is obtained. The original vibration problem is decomposed into two subproblems with two opposite sides simply supported, and the general solution of each subproblem is obtained by using the expansion of symplectic eigenvectors. Then by superposing these two general solutions, the series expansion solution of the original problem is obtained. The advantage of this method is that the solution process is carried out in symplectic space, and the validity of variable separation and symplectic eigenvectors expansion ensures the rationality of the solution process, while avoiding the presetting of the solution form. Finally, the correctness of symplectic superposition solution obtained in this paper is verified by calculating three concrete examples of fully clamped rectangular thin plates.

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On the reflected wave superposition method for a travelling string with mixed boundary supports

Journal of Sound and Vibration ◽

10.1016/j.jsv.2018.10.001 ◽

2019 ◽

Vol 440 ◽

pp. 129-146

Author(s):

E.W. Chen ◽

K. Zhang ◽

N.S. Ferguson ◽

J. Wang ◽

Y.M. Lu

Keyword(s):

Mixed Boundary ◽

Superposition Method ◽

Reflected Wave ◽

Wave Superposition

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Analysis of Clamped Rectangular Plates

Journal of Applied Mechanics ◽

10.1115/1.4009062 ◽

1940 ◽

Vol 7 (4) ◽

pp. A139-A142

Author(s):

Dana Young

Keyword(s):

Middle Surface ◽

Lateral Loading ◽

Thin Plates ◽

Superposition Method ◽

Rectangular Plates ◽

Lagrange’S Equation

Abstract This paper attempts to solve the problem of the bending action of rectangular plates clamped at all four edges and subjected to lateral loading. Analytical in nature, the author’s investigation is based upon the ordinary theory of bending of thin plates as treated in Lagrange’s equation of the middle surface. The superposition method is used and applied to a number of loadings not hitherto studied.

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Numerical Simulation of Distributed Dynamic Systems using Hybrid Tools of Intelligent Computing

Embedded Computing Systems ◽

10.4018/978-1-4666-3922-5.ch018 ◽

2013 ◽

pp. 360-383

Author(s):

Fethi H. Bellamine ◽

Aymen Gdouda

Keyword(s):

Numerical Simulation ◽

Differential Equations ◽

Dynamic Systems ◽

Mixed Boundary ◽

Simulation Models ◽

Control Synthesis ◽

Scaling Analysis ◽

Intelligent Computing ◽

Boundary Constraints ◽

Reduction Techniques

Developing fast and accurate numerical simulation models for predicting, controlling, designing, and optimizing the behavior of distributed dynamic systems is of interest to many researchers in various fields of science and engineering. These systems are described by a set of differential equations with homogenous or mixed boundary constraints. Examples of such systems are found, for example, in many networked industrial systems. The purpose of the present work is to review techniques of hybrid soft computing along with generalized scaling analysis for the solution of a set of differential equations characterizing distributed dynamic systems. The authors also review reduction techniques. This paves the way to control synthesis of real-time robust realizable controllers.

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