Strain Analysis of 3-Dimensional Elastic Large Deformation for a Thick Circular Plate by Convected Coordinates. Comparison with the Classical Plate Theory.

While adaptive tuning of vibration absorbers (ATVA) have been widely studied for vibration control applications, limited studies have been done to explore their potential for noise control applications. This study aims to utilize magnetorheological elastomer (MRE)-based ATVA to control the radiated sound from an elastic plate excited by a plane wave especially at low frequencies. Radiated sound from a clamped circular plate integrated with MRE-based ATVA is analytically studied using classical plate theory. Rayleigh integral approach is, then, used to express the transmitted sound pressure in terms of the plate’s displacement modal amplitude. A MRE-based ATVA under shear mode is investigated. The semi-active Skyhook controller is proposed to attenuate the transverse displacement of the plate and subsequently reduce the radiated sound. The controller determines the current input to the electromagnet and tunes the MRE-based ATVA with the desired stiffness.

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Multiparametric Analytical Solution for the Eigenvalue Problem of FGM Porous Circular Plates

Symmetry ◽

10.3390/sym11030429 ◽

2019 ◽

Vol 11 (3) ◽

pp. 429 ◽

Cited By ~ 2

Author(s):

Krzysztof Żur ◽

Piotr Jankowski

Keyword(s):

Boundary Conditions ◽

Circular Plate ◽

Special Functions ◽

Plate Theory ◽

Equations Of Motion ◽

Free Vibration Analysis ◽

Functionally Graded ◽

Circular Plates ◽

Classical Plate Theory ◽

Coupled Equations

Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory. The three defined coupled equations of motion of the porous functionally graded circular/annular plate were decoupled to one differential equation of free transverse vibrations of plate. The one universal general solution was obtained as a linear combination of the multiparametric special functions for the functionally graded circular and annular plates with even and uneven porosity distributions. The multiparametric frequency equations of functionally graded porous circular plate with diverse boundary conditions were obtained in the exact closed-form. The influences of the even and uneven distributions of porosity, power-law index, diverse boundary conditions and the neglected effect of the coupling in-plane and transverse displacements on the dimensionless frequencies of the circular plate were comprehensively studied for the first time. The formulated boundary value problem, the exact method of solution and the numerical results for the perfect and imperfect functionally graded circular plates have not yet been reported.

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Analytical Solutions To Boundary Value Problem Of Free Vibration Of Sandwich Thin Circular Plates With Discrete Elements

International Journal of Applied Mechanics and Engineering ◽

10.1515/ijame-2015-0040 ◽

2015 ◽

Vol 20 (3) ◽

pp. 617-627

Author(s):

K.K. Żur ◽

J. Jaroszewicz ◽

Ł. Dragun

Keyword(s):

Circular Plate ◽

Plate Theory ◽

Analytical Investigation ◽

Axisymmetric Vibration ◽

Circular Plates ◽

Discrete Elements ◽

Classical Plate Theory ◽

Influence Matrix ◽

The Core ◽

Variable Distribution

Abstract In the paper the influence function and the method of partial discretization in free axisymmetric vibration analysis of multilayered circular plates of constant and linearly variable thickness were presented. The effects of shear deformation and rotary inertia for the core as well as the facings were neglected. An analytical investigation based on the classical plate theory was made for the multilayered plate which satisfies Sokołowski’s condition. Discretization of mass and replacing stiffness of a fixed circular plate were presented. Formulas of influence matrix and Bernstein-Kieropian’s estimators for different steps of discretization were defined. The influence of variable distribution of parameters on the value of double estimators of natural basic and higher frequency of a sandwich circular plate was investigated.

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Surface Crack in a Clamped Circular Plate Subjected to Uniform Lateral Pressure

Journal of Pressure Vessel Technology ◽

10.1115/1.3263307 ◽

1980 ◽

Vol 102 (1) ◽

pp. 8-13

Author(s):

H. Abe´ ◽

M. Ogiwara

Keyword(s):

Stress Intensity Factor ◽

Stress Intensity ◽

Intensity Factor ◽

Circular Plate ◽

Surface Crack ◽

Flexural Rigidity ◽

Plate Theory ◽

Crack Depth ◽

Classical Plate Theory ◽

Bending Stresses

The bending of a clamped circular plate containing a surface crack along its edge is discussed. An approximate method of solution, which is based on the classical plate theory, is proposed to obtain the asymptotic behavior of bending stresses along the tip of the crack. The flexural rigidity of the plate is reduced by the crack. The distribution of bending stresses is therefore changed. A plate of nonuniform thickness is introduced which has the equivalent of the flexural rigidity of the cracked plate under consideration. The bending stress intensity factor is evaluated with the aid of the equivalent plate. It is found that the stress intensity factor increases with the crack depth for shallow cracks, and it decreases when the depth exceeds a certain value.

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Exact Analytical Solution for Free Axisymmetric and Non-Axisymmetric Vibrations of FGM Porous Circular Plates

10.20944/preprints201809.0295.v2 ◽

2018 ◽

Cited By ~ 1

Author(s):

Krzysztof Kamil Żur ◽

Piotr Jankowski

Keyword(s):

Boundary Conditions ◽

Circular Plate ◽

Special Functions ◽

Plate Theory ◽

Exact Analytical Solution ◽

Free Vibration Analysis ◽

Functionally Graded ◽

Circular Plates ◽

Classical Plate Theory ◽

Coupled Equations

Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory. The three defined coupled equations of motion of the porous functionally graded circular/annular plate were decoupled to one differential equation of free transverse vibrations of plate. The one universal general solution was obtained as linear combination of the multiparametric special functions for the functionally graded circular and annular plates with even and uneven porosity distributions. The multiparametric frequency equations of functionally graded porous circular plate with diverse boundary conditions were obtained in the exact closed-form. The influences of the even and uneven distributions of porosity, power-law index, diverse boundary conditions and the negligibled effect of the coupling in-plane and transverse displacements on the dimensionless frequencies of the circular plate were comprehensively studied for the first time. The formulated boundary value problem, the exact method of solution and the numerical results for the perfect and imperfect functionally graded circular plates have not yet been reported.

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Dynamic Response of a Plate With Arbitrary Shape

Journal of Applied Mechanics ◽

10.1115/1.3153743 ◽

1980 ◽

Vol 47 (3) ◽

pp. 620-626 ◽

Cited By ~ 17

Author(s):

K. Nagaya

Keyword(s):

Dynamic Response ◽

Collocation Method ◽

Circular Plate ◽

Present Method ◽

Arbitrary Shape ◽

Fourier Expansion ◽

Impact Load ◽

Plate Theory ◽

Elliptical Plate ◽

Classical Plate Theory

This paper is concerned with a method for solving dynamic response problems of a thin plate with arbitrary shape based on the classical plate theory. The result for an arbitrarily shaped plate subjected to general transient loads is obtained by utilizing the Fourier expansion collocation method. As an example, the dynamic response of a truncated elliptical plate subjected to a uniformly distributed exponentially decaying impact load is investigated. To verify the present method, numerical calculations are also carried out for a circular plate, and the results obtained are compared with the exact ones.

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