Vibration Analysis of Homogeneous Transradially Isotropic Generalized Thermoelastic Spheres

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
J. N. Sharma ◽  
N. Sharma
Keyword(s):  
Vibration Analysis ◽  
Solid Helium ◽  
Formal Solution ◽  
Thermal Relaxation ◽  
Free Vibration Analysis ◽  
Damping Factor ◽  
Special Cases ◽  
Secular Equations ◽  
Generalized Thermoelastic ◽  
Matlab Programming

The exact free vibration analysis of stress free or rigidly fixed, thermally insulated/isothermal, transradially (spherically) isotropic thermoelastic solid sphere has been presented in context of nonclassical thermoelasticity. The transradially isotropic is also frequently referred as spherically isotropic in the literature. The basic governing equations of linear generalized thermoelastic, transradially isotropic, sphere have been uncoupled and simplified with the help of Helmholtz decomposition theorem. The formal solution of the coupled system of partial differential equations has been obtained by employing matrix Fröbenius method of extended series. The secular equations for the existence of possible modes of vibrations in the sphere have been derived by employing boundary conditions. The special cases of spheroidal (S-mode) and toroidal (T-mode) vibrations have also been deduced and discussed. It is found that the toroidal motion gets decoupled from the spheroidal one and remains independent of thermal variations and thermal relaxation time. In order to illustrate the analytical development, the numerical solution of secular equations for spheroidal motion (S-mode) is carried out with respect of magnesium and solid helium spheres. The lowest frequency and damping factor of vibrational modes have been computed with the help of MATLAB programming and the results are presented graphically. The study may find applications in aerospace, navigation, geophysics tribology, and other industries where spherical structures are in frequent use.

Three-Dimensional Free Vibration Analysis of a Homogeneous Transradially Isotropic Thermoelastic Sphere

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
J. N. Sharma ◽  
N. Sharma
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Spherical Wave ◽  
Three Dimensional ◽  
Coupled System ◽  
Solid Sphere ◽  
Radial Coordinate ◽  
Special Cases ◽  
Matlab Programming

In the present paper, an exact three-dimensional vibration analysis of a transradially isotropic, thermoelastic solid sphere subjected to stress-free, thermally insulated, or isothermal boundary conditions has been carried out. Nondimensional basic governing equations of motion and heat conduction for the considered thermoelastic sphere are uncoupled and simplified by using Helmholtz decomposition theorem. By using a spherical wave solution, a system of governing partial differential equations is further reduced to a coupled system of three ordinary differential equations in radial coordinate in addition to uncoupled equation for toroidal motion. Matrix Fröbenious method of extended power series is used to investigate motion along radial coordinate from the coupled system of equations. Secular equations for the existence of various types of possible modes of vibrations in the sphere are derived in the compact form by employing boundary conditions. Special cases of spheroidal and toroidal modes of vibrations of a solid sphere have also been deduced and discussed. It is observed that the toroidal motion remains independent of thermal variations as expected and spheroidal modes are in general affected by thermal variations. Finally, the numerical solution of the secular equation for spheroidal motion (S-modes) is carried out to compute lowest frequency and dissipation factor of different modes with MATLAB programming for zinc and cobalt materials. Computer simulated results have been presented graphically. The analyses may find applications in aerospace, navigation, and other industries where spherical structures are in frequent use.

GENERALIZED THERMOELASTIC WAVES IN MICROSTRETCH PLATES LOADED WITH FLUID OF VARYING TEMPERATURE

2011 ◽  
Vol 03 (03) ◽  
pp. 563-586 ◽  
Author(s):  
S. KUMAR ◽  
J. N. SHARMA ◽  
Y. D. SHARMA
Keyword(s):  
Wave Motion ◽  
Secular Equation ◽  
Long Wavelength ◽  
Inviscid Liquid ◽  
Thermoelastic Plates ◽  
Special Cases ◽  
Secular Equations ◽  
Velocity Attenuation ◽  
Generalized Thermoelastic ◽  
Thermoelastic Waves

In the present paper, the theory of generalized thermo-microstretch elasticity has been employed to study the propagation of straight and circular crested waves in microstretch thermoelastic plates bordered with inviscid liquid layers (or half-spaces), with varying temperature on both sides. The secular equations governing the wave motion in both rectangular and cylindrical plates have been investigated. The results in the case of thin (long wavelength) and thick (short wavelength) plates have also been obtained and discussed as special cases of this work. The secular equation in the case of microstretch coupled with thermoelastic, micropolar thermoelastic and thermoelastic plates can be obtained from the present analysis by an appropriate choice of relevant parameters. The results have been deduced and compared with the relevant publications available in the literature at the appropriate stages of this work. Finally, the analytical developments have been illustrated numerically for aluminum–epoxy-like material sandwiched in the inviscid liquid. The computer simulated results in respect of phase velocity, attenuation coefficient, specific loss factor of energy dissipation and relative frequency shift due to liquid layers on both sides of the plate are presented graphically.

scholarly journals The reflection phenomena ofSV-waves in a generalized thermoelastic medium

2000 ◽  
Vol 23 (8) ◽  
pp. 529-546 ◽  
Author(s):  
Abo-El-Nour N. Abd-Alla ◽  
Amira A. S. Al-Dawy
Keyword(s):  
Thermal Effect ◽  
Elastic Waves ◽  
Plane Waves ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Special Cases ◽  
Thermal Relaxation Times ◽  
Generalized Thermoelastic

We discuss the reflection of thermoelastic plane waves at a solid half-space nearby a vacuum. We use the generalized thermoelastic waves to study the effects of one or two thermal relaxation times on the reflection plane harmonic waves. The study considered the thermal and the elastic waves of small amplitudes in a homogeneous, isotropic, and thermally conducting elastic solid. The expressions for the reflection coefficients, which are the ratio of the amplitudes of the reflected waves to the amplitude of the incident waves are obtained. It has been shown, analytically, that the elastic waves are modified due to the thermal effect. The reflection coefficients of a shear wave that incident from within the solid on its boundary, which depend on the thermoelastic coupling factor and included the thermal relaxation times, have been found in the general case. The numerical values of reflection coefficients against the angle of incidence for different values of thermal relaxation times have been calculated and the results are given in the form of graphs. Some special cases of reflection have also been discussed, for example, in the absence of thermal effect our results reduce to the ordinary pure elastic case.

Free Vibration Analysis of FGM Beams With Different Boundary Conditions Using RKPM Meshless Method

2011 ◽  
Author(s):  
R. Saljooghi ◽  
M. T. Ahmadian
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Meshless Method ◽  
Vibration Analysis ◽  
Reproducing Kernel ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Different Boundary Conditions ◽  
Special Cases

This paper presents free vibration analysis of functionally graded material (FGM) beams with different boundary conditions, using RKPM (Reproducing Kernel Particle Method), which is a meshless method. System of equations of motion is derived by using Lagrange’s method under the assumption of Euler-Bernoulli beam theory. Boundary conditions of beam are taken into account by using Lagrange multipliers. It is assumed that material properties of the beam vary continuously in the thickness direction according to the power-law form. RKPM is applied to obtain eigenvalue equation of vibration and natural frequencies are obtained. It should be noted that for special cases where the beam is uniform, natural frequencies match nicely with theoretical prediction.

Numerical Stability of GFEM Evaluation for Free Vibration Analysis in Trussed Structures

2017 ◽  
Author(s):  
Thamara Petroli ◽  
Marcos Arndt ◽  
Paulo de Oliveira Weinhardt ◽  
ROBERTO Dalledone Machado
Keyword(s):  
Free Vibration ◽  
Numerical Stability ◽  
Vibration Analysis ◽  
Free Vibration Analysis
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