scholarly journals Vibration of circular micro-ceramic (Si3N4) plate resonators in the context of the generalized viscothermoelastic dual-phase-lagging theory

2019 ◽  
Vol 11 (11) ◽  
pp. 168781401988948 ◽  
Author(s):  
Najat A Alghamdi
Keyword(s):  
Aspect Ratio ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Circular Plate ◽  
Plate Theory ◽  
Relaxation Times ◽  
Mechanical Relaxation ◽  
Dual Phase ◽  
Governing Equations ◽  
Thermally Conducting

In this article, the analysis and numerical results are represented for the thermoelastic of an isotropic homogeneous, thermally conducting, Kelvin–Voigt-type circular micro-plate in the context of Kirchhoff’s Love plate theory of generalized viscothermoelasticity based on the dual-phase-lagging model. The governing equations are obtained for the generalized dual-phase-lagging model and coupled viscothermoelastic plates. The scaled viscothermoelasticity has been illustrated in the case of the circular plate and the axisymmetric circular plate for an aspect ratio for clamped boundary conditions. Laplace transform has been applied, and its inversions have been calculated numerically by using the Tzou method. The results have been carried out for the ceramic (Si3N4). It is noted that the temperature increment and lateral deflection are significantly affected by the time, the width, the thickness, and the mechanical relaxation times of the material.

Damping in thin circular viscothermoelastic plate resonators

2015 ◽  
Vol 93 (12) ◽  
pp. 1597-1605 ◽  
Author(s):  
D. Grover
Keyword(s):  
Circular Plate ◽  
Plate Theory ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Thermomechanical Coupling ◽  
Transverse Motion ◽  
Mechanical Relaxation ◽  
Out Of Plane ◽  
Fixed Radius ◽  
Thermally Conducting

The governing equations of transverse motion and heat conduction of a homogenous, isotropic, thermally conducting, Kelvin–Voigt-type medium, based on Kirchhoff–Love plate theory, are established for out-of-plane vibrations of a generalized viscothermoelastic circular thin plate. The analytical expressions for thermoelastic damping of vibration and frequency shift are obtained for generalized and coupled viscothermoelastic plates. It is noticed that the damping of vibrations significantly depends on mechanical relaxation times and thermal relaxation time in addition to thermomechanical coupling in a circular plate under resonance conditions. The surface conditions also impose significant effects on the vibrations of such resonators. The numerical results may also be illustrated in the case of a circular plate and an axisymmetric circular plate for clamped and simply supported boundary conditions for fixed aspect ratio, fixed radius, and fixed thickness, respectively.

Thermoelastic Damping of the Axisymmetric Vibration of Laminated Trilayered Circular Plate Resonators

2013 ◽  
Vol 313-314 ◽  
pp. 600-603 ◽  
Author(s):  
Yu Xin Sun ◽  
Yan Jiang ◽  
Jia Ling Yang
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Plate Theory ◽  
Axisymmetric Vibration ◽  
Laminated Plate ◽  
Thermoelastic Damping ◽  
Governing Equations ◽  
Out Of Plane ◽  
Laminated Circular Plate ◽  
Thermoelastic Problems

In this paper, thermoelastic damping of the axisymmetric vibration of laminated circular plate resonators will be discussed. Based on the classical laminated plate theory assumptions, the governing equations of coupled thermoelastic problems are established for axisymmetric out-of-plane vibration of trilayered circular plate with fully clamped boundary conditions. The analytical expression for thermoelastic damping is obtained and the accuracy is verified through comparison with FEM results.

Nonlinear vibrations of a thin isotropic circular plate subjected to moving point loads

2020 ◽  
pp. 095440622097615
Author(s):  
Amit K Rai ◽  
Shakti S Gupta
Keyword(s):  
Boundary Conditions ◽  
Frequency Response ◽  
Circular Plate ◽  
Nonlinear Vibrations ◽  
Moving Load ◽  
Harmonic Balance Method ◽  
Angular Speed ◽  
Transverse Displacement ◽  
Governing Equations ◽  
Rotating Load

Here, we have studied the linear and nonlinear vibrations of a thin circular plate subjected to circularly, radially, and spirally moving transverse point loads. We follow Kirchoff’s theory and then incorporate von Kármán nonlinearity and employ Hamilton’s principle to obtain the governing equations and the associated boundary conditions. We solve the governing equations for the simply-supported and clamped boundary conditions using the mode summation method. Using the harmonic balance method for frequency response and Runge-Kutta method for time response, we solve the resulting coupled and cubic nonlinear ordinary differential equations. We show that the resonance instability due to a circularly moving load can be avoided by splitting it into multiple loads rotating at the same radius and angular speed. With the increasing magnitude of the rotating load, the frequency response of the transverse displacement shows jumps and modal interaction. The transverse response collected at the centre of the plate shows subharmonics of the axisymmetric frequencies only. The spectrum of the linear response due to spirally moving load contains axisymmetric frequencies, the angular speed of the load, their combination, and superharmonics of axisymmetric frequencies.

scholarly journals Influence of the Static Pre-Stress in Micro-Viscothermoelastic Resonators Based on Dual-Phase-Lagging Heat Conduction

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Najat A. Alghamdi ◽  
Hamdy M. Youssef
Keyword(s):  
Heat Conduction ◽  
Energy Dissipation ◽  
Thermal Behavior ◽  
Quality Factor ◽  
Analytical Model ◽  
Relaxation Times ◽  
Mechanical Relaxation ◽  
Length Scale ◽  
Dual Phase ◽  
Quality Factors

Thermal and mechanical relaxation times play vital roles in the values of the quality factor of micro/nanoresonators. They can control the energy dissipation across the coupling of mechanical and thermal behavior. In this paper, we introduce an analytical model that considers a pre-stress in a micro-viscothermoelastic resonator to modify the thermal and mechanical relaxation times and thus higher the quality factor. The impacts of length scale and static pre-stress on the quality factor have been discussed. The model expects that significant improvement in terms of quality factors is possible by tuning the pre-stress and the thermal and mechanical relaxation times parameters, and the isothermal value of frequency have significant effects on the thermal quality factor of the resonators.

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.

Exact solution for bending analysis of functionally graded micro-plates based on strain gradient theory

2018 ◽  
Vol 25 (3) ◽  
pp. 439-451
Author(s):  
Meisam Mohammadi ◽  
Afshin Iranmanesh ◽  
Seyed Sadegh Naseralavi ◽  
Hamed Farahmand
Keyword(s):  
Boundary Conditions ◽  
Strain Gradient ◽  
Material Properties ◽  
Plate Theory ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Governing Equations ◽  
Micro Plates ◽  
Micro Structures

Abstract In the present article, static analysis of thin functionally graded micro-plates, based on Kirchhoff plate theory, is investigated. Utilizing the strain gradient theory and principle of minimum total potential energy, governing equations of rectangular micro-plates, subjected to distributed load, are explored. In accordance with functionally graded distribution of material properties through the thickness, higher-order governing equations are coupled in terms of displacement fields. Introducing a novel methodology, governing equations are decoupled, with special privilege of solving analytically. These new equations are solved for micro-plates with Levy boundary conditions. It is shown that neutral plane in functionally graded micro-plate is moved from midplane to a new coordinate in thickness direction. It is shown that considering micro-structures effects affects the governing equations and boundary conditions. Finally, the effects of material properties, micro-structures, boundary conditions and dimensions are expounded on the static response of micro-plate. Results show that increasing the length scale parameter and FGM index increases the rigidity of micro-plate. In addition, it is concluded that using classical theories for study of micro-structures leads to inaccurate results.

Bending of a thin circular plate under hydrostatic pressure over a concentric ellipse

1959 ◽  
Vol 55 (1) ◽  
pp. 110-120 ◽  
Author(s):  
W. A. Bassali
Keyword(s):  
Exact Solution ◽  
Hydrostatic Pressure ◽  
Boundary Conditions ◽  
Circular Plate ◽  
Thin Plate ◽  
Plate Theory ◽  
Simply Supported ◽  
Thin Circular Plate ◽  
Thin Plate Theory

ABSTRACTAn exact solution in finite terms is derived within the limitations of the classical thin-plate theory, for the problem of a thin circular plate acted upon normally by hydrostatic pressure distributed over the area of a concentric ellipse, and subject to boundary conditions covering the usual rigidly clamped and simply supported boundaries.

The polygon-circle paradox and convergence in thin plate theory

1973 ◽  
Vol 73 (1) ◽  
pp. 279-282 ◽  
Author(s):  
N. W. Murray
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Thin Plate ◽  
Plate Theory ◽  
Series Solutions ◽  
Simply Supported ◽  
Convergence Of Series ◽  
Thin Plate Theory ◽  
Polygonal Plate ◽  
Image Position

AbstractThe solution for a simply supported many-sided polygonal plate does not agree with that for the corresponding circular plate. This paper describes the earlier work of Rao and Rajaiah on polygonal plates and then explains why best convergence of series solutions occurs when the boundary conditions are defined as

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.

Length scale-dependent natural frequencies of piezoelectric microplates

2017 ◽  
Vol 24 (13) ◽  
pp. 2749-2759 ◽  
Author(s):  
M Jafari ◽  
E Jomehzadeh ◽  
M Rezaeizadeh
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Free Vibration Analysis ◽  
Length Scale ◽  
Governing Equations ◽  
Classical Plate Theory ◽  
Wide Range ◽  
Piezoelectric Layers

The length-scale free vibration analysis of a rectangular microplate coupled with piezoelectric layers is presented. The modified couple stress theory is used to describe the size effect of the system. The governing equations of motion are obtained using Hamilton’s principle based on the classical plate theory. The transverse part of the electric potential for the piezoelectric layers is considered to satisfy the Maxwell’s equation and the electrical boundary conditions. A new procedure is introduced to decouple the governing equations and then an analytical Levy-type solution is obtained. The exact natural frequencies are established for a wide range of length scales, various plate dimensions, several piezoelectric layer thicknesses, and different boundary conditions. The results show that the effect of length scale parameter is decreased by the piezoelectric electrical field.

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