Modal‐slowness analysis of plate vibrations

1992 ◽  
Vol 92 (6) ◽  
pp. 3228-3238 ◽  
Author(s):  
J. Robert Fricke ◽  
Arthur B. Baggeroer
Keyword(s):  
Plate Vibrations ◽  
Slowness Analysis

Comments on “Rectangular finite elements for analysis of plate vibrations”

1968 ◽  
Vol 8 (3) ◽  
pp. 513 ◽  
Author(s):  
G.R. Cowper ◽  
E. Kosko ◽  
G.M. Lindberg ◽  
M.D. Olson
Keyword(s):  
Finite Elements ◽  
Plate Vibrations

Large Amplitude Vibrations of Circular Plate on a Uniform Elastic Foundation

1972 ◽  
Vol 94 (1) ◽  
pp. 43-49 ◽  
Author(s):  
R. Bolton
Keyword(s):  
Circular Plate ◽  
Elastic Foundation ◽  
Normal Modes ◽  
Single Mode ◽  
Linear Mode ◽  
Mode Amplitude ◽  
Plate Vibrations ◽  
Edge Conditions ◽  
Large Amplitude Vibrations ◽  
Mode Response

Herrmann’s equations, the dynamic analogues of the von Karman equations, are solved for a circular plate on a linear elastic foundation by assuming a series solution of the separable form involving unknown time functions. The spatial functions include both regular and modified Bessel functions and are chosen to satisfy the linear mode shape distributions of the plate as well as the usual edge conditions. Total differential equations governing the symmetric plate motions are derived using the Galerkin averaging techniques for a spatially uniform load. By extending the concept of normal modes to nonlinear plate vibrations, comparisons between normal mode response and single mode response, as functions of the first mode amplitude, are shown for different values of the elastic foundation parameter. Results are obtained for plates with simply supported and clamped edges and with both radially moveable and immoveable edges. These results are used to discuss the limitations of single-mode response of circular plates, both with and without an elastic foundation.

scholarly journals GEOMETRIC MODELING OF A SHAPE OF PARALLELOGRAM PLATES IN A PROBLEM OF FREE VIBRATIONS USING CONFORMAL RADII

2021 ◽  
pp. 143-159
Author(s):  
A.A. Chernyaev ◽  
Keyword(s):  
Cross Sections ◽  
Geometric Modeling ◽  
Interpolation Method ◽  
Geometric Characteristic ◽  
Free Vibrations ◽  
Theory Of Elasticity ◽  
Constant Thickness ◽  
Basic Frequency ◽  
Plate Vibrations ◽  
The Subject

The paper considers a method of geometric modeling applied when solving basic twodimensional problems of the theory of elasticity and structural mechanics, in particular the applied problems of engineering. The subject of this study is vibrations of thin elastic parallelogram plates of constant thickness. To determine a basic frequency of vibrations, the interpolation method based on the geometric characteristic of the shape of plates (membrane, cross sections of a rod) is proposed. This characteristic represents a ratio of interior and exterior conformal radii of the plate. As is known from the theory of conformal mappings, conformal radii are those obtained by mapping of a plate onto the interior and exterior of a unit disk. The paper presents basic terms, tables, and formulas related to the considered geometric method with a comparative analysis of the curve diagrams obtained using various interpolation formulas. The original computer program is also developed. The main advantage of the proposed method of determining the basic frequency of plate vibrations is a graphic representation of results that allows one to accurately determine the required solution on the graph among the other solutions corresponding to the considered case of parallelogram plates. Although there are many known approximate approaches, which are used to solve the considered problems, only geometric modeling technique based on the conformal radii ratio gives such an opportunity.

scholarly journals Optimal piezo-electro-mechanical coupling to control plate vibrations

2002 ◽  
Vol 13 (1-4) ◽  
pp. 113-120 ◽  
Author(s):  
Silvio Alessandroni ◽  
Francesco dell'Isola ◽  
Fabrizio Frezza
Keyword(s):  
Mechanical Coupling ◽  
Plate Vibrations ◽  
Control Plate

scholarly journals Destabilizing damping effect on flat-plate vibrations due to flow-induced flutter

2017 ◽  
Vol 199 ◽  
pp. 790-795
Author(s):  
Luca Pigolotti ◽  
Claudio Mannini ◽  
Gianni Bartoli
Keyword(s):  
Flat Plate ◽  
Plate Vibrations ◽  
Damping Effect

A dual regularized method in a control problem of plate vibrations

2007 ◽  
Vol 68 (2) ◽  
pp. 361-368
Author(s):  
A. Z. Ishmukhametov ◽  
R. Makhrous
Keyword(s):  
Control Problem ◽  
Plate Vibrations ◽  
Regularized Method

scholarly journals Single Source Three Dimensional Capture of Full Field Plate Vibrations

2011 ◽  
Vol 52 (7) ◽  
pp. 965-974 ◽  
Author(s):  
A. D. Shaw ◽  
S. A. Neild ◽  
D. J. Wagg ◽  
P. M. Weaver
Keyword(s):  
Three Dimensional ◽  
Single Source ◽  
Full Field ◽  
Plate Vibrations ◽  
Field Plate

Quantum Chaos Methods Applied to High-Frequency Plate Vibrations

1992 ◽  
Vol 18 (2) ◽  
pp. 101-106 ◽  
Author(s):  
O Legrand ◽  
C Schmit ◽  
D Sornette
Keyword(s):  
High Frequency ◽  
Quantum Chaos ◽  
Plate Vibrations

Nonlinear Adaptive Vibration Absorber for the Control of Plate Vibrations

2001 ◽  
Author(s):  
Osama N. Ashour ◽  
Ali H. Nayfeh
Keyword(s):  
Control Strategy ◽  
Flexible Structures ◽  
Digital Signal ◽  
Nonlinear Effects ◽  
Frequency Measurement ◽  
Control Technique ◽  
Vibration Absorber ◽  
Plate Vibrations ◽  
Near Resonance ◽  
Modeling Software

Abstract A nonlinear adaptive vibration absorber to control the vibrations of flexible structures is investigated. The absorber is based on the saturation phenomenon associated with dynamical systems possessing quadratic nonlinearities and a two-to-one internal resonance. The technique is implemented by coupling a second-order controller with the structure’s response through a sensor and an actuator. Energy is exchanged between the structure and the controller and, near resonance, the structure’s response saturates to a small value. Experimental results are presented for the control of a rectangular plate and a cantilever beam using piezoelectric ceramics and magnetostrictive alloys as actuators. The control technique is implemented using a digital signal processing board and a modeling software. The control strategy is made adaptive by incorporating an efficient frequency-measurement technique. This is validated by successfully testing the control strategy for a non-conventional problem, where nonlinear effects hinder the application of the nonadaptive controller.

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