scholarly journals Free vibration of a microbeam resting on Pasternak’s foundation via the Green–Naghdi thermoelasticity theory without energy dissipation

2016 ◽  
Vol 35 (4) ◽  
pp. 303-311 ◽  
Author(s):  
Ashraf M Zenkour
Keyword(s):  
Energy Dissipation ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Generalized Thermoelasticity ◽  
Frequency Equation ◽  
Vibration Frequencies ◽  
Simply Supported ◽  
Thermoelasticity Theory ◽  
Foundation Parameters ◽  
Without Energy Dissipation

This article investigates the effect of length-to-thickness ratio and elastic foundation parameters on the natural frequencies of a thermoelastic microbeam resonator. The generalized thermoelasticity theory of Green and Naghdi without energy dissipation is used. The governing frequency equation is given for a simply supported microbeam resting on Winkler–Pasternak elastic foundations. The influences of different parameters are all demonstrated. Natural vibration frequencies are graphically illustrated and some tabulated results are presented for future comparisons.

scholarly journals The effect of an enclosed air cavity on a rectangular drum

1983 ◽  
Vol 24 (3) ◽  
pp. 343-349 ◽  
Author(s):  
H. P. W. Gottlieb
Keyword(s):  
Green’S Function ◽  
Frequency Shift ◽  
Green's Function ◽  
Natural Vibration ◽  
Frequency Equation ◽  
Vibration Frequencies ◽  
Air Cavity ◽  
First Order ◽  
Degenerate Mode ◽  
Function Formulation

AbstractThe effect of an enclosed air cavity on the natural vibration frequencies of a rectangular membrane is investigated. The modes specified by an even integer are not affected. For the odd-odd modes, the frequency equation is found via a Green's function formulation and is solved to first order in a parameter representing the effect of the cavity of the rectangular drum. The frequencies are raised, with the fundamental being most affected. In the case of degeneracies, each degenerate mode contributes to the frequency shift, but the degeneracy itself is not broken to first order.

scholarly journals Eigen Value Approach to Generalized Thermoelastic Interactions in an Unbounded Body with Circular Cylindrical Cavity without Energy Dissipation

2017 ◽  
Vol 22 (4) ◽  
pp. 811-825 ◽  
Author(s):  
S. Chakraborty
Keyword(s):  
Energy Dissipation ◽  
Cylindrical Cavity ◽  
Generalized Thermoelasticity ◽  
Displacement Component ◽  
Eigen Value ◽  
The Laplace Transform ◽  
Circular Cylindrical Cavity ◽  
Matrix Differential ◽  
Vector Matrix ◽  
Without Energy Dissipation

Abstract The theory of generalized thermoelasticity in the context of the Green-Naghdi model -II (thermoelasticity without energy dissipation) is studied for an infinite circular cylindrical cavity subjected to two different cases of thermoelastic interactions when the radial stress is zero for (a) maintaining constant temperature and (b) temperature is varying exponentially with time. The Laplace transform from time variable is used to the governing equations to formulate a vector matrix differential equation which is then solved by the eigen value approach. Numerical computations for the displacement component, temperature distribution and components of thermal stress have been made and presented graphically.

Analysis of the Natural Vibration Properties of a Timoshenko Beam Supported by Springs (by Finite Integral Transform Method)

1999 ◽  
Author(s):  
Zhixiang Xu ◽  
Hideyuki Tamura ◽  
Kunisato Seto
Keyword(s):  
Timoshenko Beam ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Integral Transform ◽  
Frequency Equation ◽  
Transform Method ◽  
Vibration Problem ◽  
Vibration Properties ◽  
Finite Integral ◽  
Integral Transform Technique

Abstract This paper presents analytical results of transverse vibration of a Timoshenko beam supported by spring-spring which stiffness is variable, that is a simplified model of magnetically levitated vehicle body’s vibration problem and magnetic bearings support shaft’s vibration problem. By applying the finite integral transform technique, the analytical solution of this dynamic model is successfully obtained. Especially, by investigating the frequency equation, the effect of the stiffness of two supporting-springs to the natural frequencies is clarified. From the results, it is cleared that the natural frequencies of the beam system can be effectively controlled by changing the supporting-spring’s stiffness.

Rotation of Two-Temperature Generalized Thermoelastic Half-Space Subjected to Thermal Shock and Without Energy Dissipation

2017 ◽  
Vol 14 (1) ◽  
pp. 529-535
Author(s):  
Eman A. N Al-Lehaibi
Keyword(s):  
Mathematical Model ◽  
Energy Dissipation ◽  
Mechanical Load ◽  
Generalized Thermoelasticity ◽  
Laplace Transforms ◽  
Temperature Parameter ◽  
Without Energy Dissipation ◽  
The Impact ◽  
The Mathematical Model ◽  
Two Temperature

In this work, a mathematical model for the thermoelastic medium with constant elastic parameters in the context of two-temperature generalized thermoelasticity without energy dissipation has been constructed. The governing equations of the mathematical model will be taken when the medium is quiescent first. Laplace transforms techniques will be used to get the general solution for any set of boundary conditions. The solution will be obtained for a particular model when the medium is subjected to a thermal load by using stat-space approach. The inversion of the Laplace transforms will be calculated numerically and after that we’ll present the results graphically with some comparisons to study the impact of thermal or mechanical load on the speed of progress of mechanical and thermal waves through the medium. Also, to studying the effect of the two-temperature parameter rotation parameter on all the studied field.

scholarly journals Frequency Analysis for Functionally Graded Material Cylindrical Shells: A Significant Case Study

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Rabia Anwar ◽  
Madiha Ghamkhar ◽  
Muhammad Imran Khan ◽  
Rabia Safdar ◽  
Muhammad Zafar Iqbal ◽  
...  
Keyword(s):  
Functionally Graded Materials ◽  
Natural Frequencies ◽  
Constitutive Relations ◽  
Cylindrical Shells ◽  
Frequency Equation ◽  
Functionally Graded ◽  
Graded Materials ◽  
Simply Supported ◽  
Love’S Shell Theory ◽  
Graded Material

Cylindrical shells play an important role for the construction of functionally graded materials (FGMs). Functionally graded materials are valuable in order to develop durable materials. They are made of two or more materials such as nickel, stainless steel, zirconia, and alumina. They are extremely beneficial for the manufacturing of structural elements. Functionally graded materials are broadly used in several fields such as chemistry, biomedicine, optics, and electronics. In the present research, vibrations of natural frequencies are investigated for different layered cylindrical shells, those constructed from FGMs. The behavior of shell vibration is based on different parameters of geometrical material. The problem of the shell is expressed from the constitutive relations of strain and stress with displacement, as well as it is adopted from Love’s shell theory. Vibrations of natural frequencies (NFs) are calculated for simply supported-simply supported (SS-SS) and clamped-free (C-F) edge conditions. The Rayleigh–Ritz technique is employed to obtain the shell frequency equation. The shell equation is solved by MATLAB software.

BUCKLING AND VIBRATION OF STEPPED, SYMMETRIC CROSS-PLY LAMINATED RECTANGULAR PLATES

2001 ◽  
Vol 01 (03) ◽  
pp. 385-408 ◽  
Author(s):  
Y. XIANG ◽  
J. N. REDDY
Keyword(s):  
Solution Method ◽  
Natural Frequencies ◽  
Laminated Plates ◽  
The Other ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Buckling Loads ◽  
Simply Supported ◽  
Step Thickness ◽  
Thickness Variations

This paper presents the exact buckling loads and vibration frequencies of multi-stepped symmetric cross-ply laminated rectangular plates having two opposite edges simply supported while the other two edges may have any combination of free, simply supported, and clamped conditions. An analytical method that uses the Lévy solution method and the domain decomposition technique is proposed to determine the buckling loads and natural frequencies of stepped laminated plates. Buckling and vibration solutions are obtained for symmetric cross-ply laminated rectangular plates having two-, three- and four-step thickness variations.

scholarly journals On Discontinuties in Thermoelastic Plane Waves without Energy Dissipation Due to a Thermo-Mechanical Shock

2013 ◽  
Vol 18 (2) ◽  
pp. 503-519
Author(s):  
N. Sarkar ◽  
A. Lahiri
Keyword(s):  
Energy Dissipation ◽  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Present Theory ◽  
Mechanical Shock ◽  
Field Equations ◽  
Characteristic Features ◽  
Thermoelastic Solid ◽  
Matrix Differential ◽  
Without Energy Dissipation

The present paper deals with the thermoelastic plane waves due to a thermo-mechanical shock in the form of pulse at the boundary of a homogeneous, isotropic thermoelastic half-space. The field equations of the Green- Naugdhi theory without energy dissipation for an thermoelastic solid in the generalized thermoelasticity theory are written in the form of a vector-matrix differential equation using Laplace transform techniques and then solved by an eigenvalue approach. Exact expressions for the considered field variables are obtained and presented graphically for copper-like material. The characteristic features of the present theory are analyzed by comparing these solutions with their counterparts in other generalized thcrmoelasticity theories.

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