scholarly journals Natural frequencies of elastically supported orthotropic rectangular plates

1975 ◽  
Vol 58 (S1) ◽  
pp. S42-S42 ◽  
Author(s):  
Edward B. Magrab
Keyword(s):  
Natural Frequencies ◽  
Rectangular Plates ◽  
Elastically Supported

Vibration Suppression of an Elastically Supported Beam With Closely Spaced Natural Frequencies

2020 ◽  
Author(s):  
Haizhou Liu ◽  
Hao Gao
Keyword(s):  
Natural Frequencies ◽  
Vibration Suppression ◽  
Fixed Point Theory ◽  
Dynamic Performance ◽  
Point Theory ◽  
Primary System ◽  
Computationally Efficient ◽  
Wide Range ◽  
Univariate Optimization ◽  
Elastically Supported

Abstract Vibration suppression of distributed parameter systems is of great interest and has a wide range of applications. The dynamic performance of a primary system can be improved by adding dynamic vibration absorbers (DVA). Although the relevant topics have been studied for decades, the trade-off between capability of suppressing multiple resonant peaks and complexity of absorbers has not been well addressed. In this paper, the vibration suppression problem of a uniform Euler-Bernoulli beam with closely spaced natural frequencies is investigated. To achieve desired vibration reduction, a two-DOF DVA is connected to the beam through a pair of a spring and a dashpot. By introducing a virtual ground spring, the parameters of the absorber are determined via extended fixed point theory. The proposed method only requires univariate optimization and is computationally efficient. Numerical examples conducted verify the viability of the proposed method and the effectiveness of a two-DOF DVA in suppressing double resonances.

Hydroelastic Vibration of Rectangular Plates

1996 ◽  
Vol 63 (1) ◽  
pp. 110-115 ◽  
Author(s):  
Moon K. Kwak
Keyword(s):  
Boundary Conditions ◽  
Approximate Formula ◽  
Natural Frequencies ◽  
Mass Matrix ◽  
Ritz Method ◽  
Plate Boundary ◽  
Rigid Wall ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Virtual Mass

This paper is concerned with the virtual mass effect on the natural frequencies and mode shapes of rectangular plates due to the presence of the water on one side of the plate. The approximate formula, which mainly depends on the so-called nondimensionalized added virtual mass incremental factor, can be used to estimate natural frequencies in water from natural frequencies in vacuo. However, the approximate formula is valid only when the wet mode shapes are almost the same as the one in vacuo. Moreover, the nondimensionalized added virtual mass incremental factor is in general a function of geometry, material properties of the plate and mostly boundary conditions of the plate and water domain. In this paper, the added virtual mass incremental factors for rectangular plates are obtained using the Rayleigh-Ritz method combined with the Green function method. Two cases of interfacing boundary conditions, which are free-surface and rigid-wall conditions, and two cases of plate boundary conditions, simply supported and clamped cases, are considered in this paper. It is found that the theoretical results match the experimental results. To investigate the validity of the approximate formula, the exact natural frequencies and mode shapes in water are calculated by means of the virtual added mass matrix. It is found that the approximate formula predicts lower natural frequencies in water with a very good accuracy.

Combinations for the Free Vibration Behaviors of Anisotropic Rectangular Plates Under General Edge Conditions

1999 ◽  
Author(s):  
Yoshihiro Narita
Keyword(s):  
Free Vibration ◽  
Structural Design ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Technical Information ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Plate Models ◽  
Edge Conditions ◽  
Anisotropic Rectangular Plates

Abstract The free vibration behavior of rectangular plates provides important technical information in structural design, and the natural frequencies are primarily affected by the boundary conditions as well as aspect and thickness ratios. One of the three classical edge conditions, i.e., free, simple supported and clamped edges, may be used to model the constraint along an edge of the rectangle. Along the entire boundary with four edges, there exist a wide variety of combinations in the edge conditions, each yielding different natural frequencies and mode shapes. For counting the total number of possible combinations, the present paper introduces the Polya counting theory in combinatorial mathematics, and formulas are derived for counting the exact numbers. A modified Ritz method is then developed to calculate natural frequencies of anisotropic rectangular plates under any combination of the three edge conditions and is used to numerically verify the numbers. In numerical experiments, the number of combinations in the free vibration behaviors is determined for some plate models by using the derived formulas, and are corroborated by counting the numbers of different sets of the natural frequencies that are obtained from the Ritz method.

Natural Frequencies of Plate Systems using the Edge Effect Method

1967 ◽  
Vol 9 (4) ◽  
pp. 318-324 ◽  
Author(s):  
S. M. Dickinson ◽  
G. B. Warburton
Keyword(s):  
Natural Frequency ◽  
Edge Effect ◽  
Series Solution ◽  
Natural Frequencies ◽  
Rectangular Plates ◽  
Form Part ◽  
Approximate Frequency ◽  
Flexural Vibrations ◽  
Effect Method ◽  
Partial Success

In this paper the Bolotin edge effect method is used to consider the free flexural vibrations of systems built up from rectangular plates. The constituent plates of the systems are considered either to lie in the same plane and form part of a plate continuous over line supports or to lie in planes at right angles to each other, as in box constructions. The application of the edge effect method to single-and multi-plate systems is described and the approximate frequency equations for two two-plate systems are given. The first 10 natural frequency parameters for these two systems for particular side ratios are compared with those obtained using a series solution and agreement is shown to be good. A few frequency parameters for a closed box computed using the edge effect method and the series solution are also compared. The range of plate systems to which the edge effect method may be applied with complete success and the range to which it may be applied with only partial success are indicated. The sources of errors in the edge effect solutions are indicated.

Vibration of Orthotropic Rectangular Plates With Variable Thickness

1989 ◽  
Vol 111 (1) ◽  
pp. 101-103 ◽  
Author(s):  
Wei-Cheun Liu ◽  
Stanley S. H. Chen
Keyword(s):  
Boundary Conditions ◽  
Computer Program ◽  
Variable Thickness ◽  
Energy Method ◽  
Natural Frequencies ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Orthotropic Properties

The problem vibration of rectangular orthotropic plates with variable thickness and mixed boundary conditions are solved by a modified energy method. A general expression is written for the deflection of the plate without aiming at any particular combination of boundary conditions. Boundary conditions are satisfied approximately by adjusting a set of so-called fixity factors. A computer program has been developed to solve for natural frequencies of plates with variable thicknesses and having different orthotropic properties.

scholarly journals Numerical and Experimental Approach for Identifying Elastic Parameters in Sandwich Plates

2002 ◽  
Vol 9 (4-5) ◽  
pp. 193-201 ◽  
Author(s):  
Sergio Ferreira Bastos ◽  
Lavinia Borges ◽  
Fernando A. Rochinha
Keyword(s):  
Experimental Approach ◽  
Natural Frequencies ◽  
Free Edge ◽  
Free Vibrations ◽  
Elastic Parameter ◽  
Sandwich Plates ◽  
Rectangular Plates ◽  
Elastic Parameters ◽  
Non Destructive ◽  
Parameter Problem

This article deals with the identification of elastic parameters (engineering constants) in sandwich honeycomb orthotropic rectangular plates. A non-destructive method is introduced to identify the elastic parameters through the experimental measurements of natural frequencies of a plate undergoing free vibrations. Four elastic constant are identified. The estimation of the elastic parameter problem is solved by minimizing the differences between the measured and the calculated natural frequencies. The numerical method to calculate the natural frequencies involves the formulation of Rayleigh-Ritz using a series of characteristic orthogonal polynomials to properly model the free edge boundary conditions. The analysis of the results indicates the efficiency of the method.

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