Semi-Active Control of Sound Radiated From an Elastic Circular Plate Integrated With Adaptive Tuned Vibration Absorbers

2016 ◽  
Author(s):  
Masoud Hemmatian ◽  
Ramin Sedaghati
Keyword(s):  
Circular Plate ◽  
Plate Theory ◽  
Integral Approach ◽  
Shear Mode ◽  
Transverse Displacement ◽  
Vibration Absorbers ◽  
Classical Plate Theory ◽  
Low Frequencies ◽  
Control Applications ◽  
Radiated Sound

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.

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

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 429 ◽  
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.

Transverse bending of infinite and semi-infinite thin elastic plates. III

1958 ◽  
Vol 54 (2) ◽  
pp. 288-299 ◽  
Author(s):  
W. A. Bassali ◽  
M. Nassif ◽  
H. P. F. Swinnerton-Dyer
Keyword(s):  
Isotropic Plate ◽  
Plate Theory ◽  
Outer Boundary ◽  
Exact Expression ◽  
Transverse Displacement ◽  
Elastic Plates ◽  
Classical Plate Theory ◽  
Transverse Bending ◽  
Elastically Restrained ◽  
Limiting Case

ABSTRACTWithin the restrictions of the classical plate theory, complex variable methods are used in this paper to develop an exact expression for the transverse displacement of an infinitely large isotropic plate having a free outer boundary and elastically restrained at an inner circular boundary, the plate being subjected to a general type of loading distributed over the area of a circle. The limiting case of a half-plane clamped along the straight edge and acted upon normally by the same loading is also considered.

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

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.

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

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.

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

2018 ◽  
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.

Dynamic Response of a Plate With Arbitrary Shape

1980 ◽  
Vol 47 (3) ◽  
pp. 620-626 ◽  
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.

scholarly journals Antiplane–inplane shear mode delamination between two second-order shear deformable composite plates

2016 ◽  
Vol 22 (3) ◽  
pp. 259-282 ◽  
Author(s):  
András Szekrényes
Keyword(s):  
Plate Theory ◽  
Plate Thickness ◽  
State Space Model ◽  
Boundary Surface ◽  
Plate Boundary ◽  
Composite Plates ◽  
Second Order ◽  
Shear Mode ◽  
Mode Iii ◽  
Double Plate System

The second-order laminated plate theory is utilized in this work to analyze orthotropic composite plates with asymmetric delamination. First, a displacement field satisfying the system of exact kinematic conditions is presented by developing a double-plate system in the uncracked plate portion. The basic equations of linear elasticity and Hamilton’s principle are utilized to derive the system of equilibrium and governing equations. As an example, a delaminated simply supported plate is analyzed using Lévy plate formulation and the state-space model by varying the position of the delamination along the plate thickness. The displacements, strains, stresses and the J-integral are calculated by the plate theory solution and compared with those by linear finite-element calculations. The comparison of the numerical and analytical results shows that the second-order plate theory captures very well the mechanical fields. However, if the delamination is separated by only a relatively thin layer from the plate boundary surface, then the second-order plate theory approximates badly the stress resultants and so the mode-II and mode-III J-integrals and thus leads to erroneous results.

Dynamical Behaviors of Sinusoidal Nanocomposite Plates Subjected to Thermomechanical Loads

2021 ◽  
Author(s):  
Vu Ngoc Viet Hoang ◽  
Dinh Gia Ninh
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Rectangular Plates ◽  
Sine Function ◽  
Classical Plate Theory ◽  
Wolfram Mathematica ◽  
Number Of Cycles

In this paper, a new plate structure has been found with the change of profile according to the sine function which we temporarily call as the sinusoidal plate. The classical plate theory and Galerkin’s technique have been utilized in estimating the nonlinear vibration behavior of the new non-rectangular plates reinforced by functionally graded (FG) graphene nanoplatelets (GNPs) resting on the Kerr foundation. The FG-GNP plates were assumed to have two horizontal variable edges according to the sine function. Four different configurations of the FG-GNP plates based on the number of cycles of sine function were analyzed. The material characteristics of the GNPs were evaluated in terms of two models called the Halpin–Tsai micromechanical model and the rule of mixtures. First, to verify this method, the natural frequencies of new non-rectangular plates made of metal were compared with those obtained by the Finite Element Method (FEM). Then, the numerical outcomes are validated by comparing with the previous papers for rectangular FGM/GNP plates — a special case of this structure. Furthermore, the impacts of the thermal environment, geometrical parameters, and the elastic foundation on the dynamical responses are scrutinized by the 2D/3D graphical results and coded in Wolfram-Mathematica. The results of this work proved that the introduced approach has the advantages of being fast, having high accuracy, and involving uncomplicated calculation.

scholarly journals Nonlinear Dynamic Analysis for Rectangular FGM Plates with Variable Thickness Subjected to Mechanical Load

2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Khuc Van Phu ◽  
Le Xuan Doan ◽  
Nguyen Van Thanh
Keyword(s):  
Variable Thickness ◽  
Nonlinear Dynamic ◽  
Volume Fraction ◽  
Mechanical Load ◽  
Plate Theory ◽  
Geometrical Nonlinearity ◽  
Nonlinear Dynamic Analysis ◽  
Dynamic Responses ◽  
Rectangular Plates ◽  
Classical Plate Theory

 In this paper, the governing equations of rectangular plates with variable thickness subjected to mechanical load are established by using the classical plate theory, the geometrical nonlinearity in von Karman-Donnell sense. Solutions of the problem are derived according to Galerkin method. Nonlinear dynamic responses, critical dynamic loads are obtained by using Runge-Kutta method and the Budiansky–Roth criterion. Effect of volume-fraction index k and some geometric factors are considered and presented in numerical results.

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