Free vibration of a thermoelastic hollow cylinder with one relaxation time

2015 ◽  
Vol 93 (10) ◽  
pp. 1082-1087 ◽  
Author(s):  
Ibrahim A. Abbas ◽  
Aatef D. Hobiny
Keyword(s):  
Relaxation Time ◽  
Dispersion Relation ◽  
Free Vibration ◽  
Frequency Shift ◽  
Hollow Cylinder ◽  
Analytical Solutions ◽  
Thermoelastic Damping ◽  
Eigenvalue Approach ◽  
Lord And Shulman Theory ◽  
Damping Of Vibrations

The aim of this paper is to study the free vibration problem of a thermoelastic hollow cylinder in the context of the Lord and Shulman theory with one relaxation time. The eigenvalue approach is used to get the analytical solutions. The dispersion relations for the existence of various types of possible modes of vibrations are obtained. The validation of the roots for the dispersion relation is presented. The numerical results of frequency shift, natural frequency, and thermoelastic damping of vibrations have been presented graphically.

scholarly journals Free Vibrations of Nanoscale Beam Under Two-Temperature Green and Naghdi Model

2018 ◽  
Vol 23 (No 3, September 2018) ◽  
pp. 289-293 ◽  
Author(s):  
Ibrahim A. Abbas
Keyword(s):  
Free Vibration ◽  
Strain Rate ◽  
Frequency Shift ◽  
Natural Frequency ◽  
Free Vibrations ◽  
Temperature Model ◽  
Thermoelastic Damping ◽  
Simply Supported ◽  
Two Temperature

The influence of the coupling between strain rate and temperature becomes domineering in the nanoscale beam. In this work, the free vibration of nanoscale beam resonators is analysed using Green and Naghdis theorem under the two-temperature model (2TGNIII). The influence of two-temperature parameters in a nanoscale beam is studied for beams under simply supported conditions. Exact expressions for frequency shift and the thermoelastic damping have been derived in the resonator, and calculation outcomes have been presented graphically with respect to frequency shift, natural frequency, and thermoelastic damping. The scale of length and thickness for a nanobeam equal to 15 × 10−9 m and equal to 1.3 × 10−12 s for time.

Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

Analytical Solutions of Stresses in Functionally Graded Circular Hollow Cylinder with Finite Length

2004 ◽  
Vol 261-263 ◽  
pp. 651-656 ◽  
Author(s):  
Z.S. Shao ◽  
L.F. Fan ◽  
Tie Jun Wang
Keyword(s):  
Young’S Modulus ◽  
Hollow Cylinder ◽  
Finite Length ◽  
Analytical Solutions ◽  
Radial Direction ◽  
Young's Modulus ◽  
Functionally Graded ◽  
Numerical Results ◽  
Stress Fields ◽  
Simply Supported

Analytical solutions of stress fields in functionally graded circular hollow cylinder with finite length subjected to axisymmetric pressure loadings on inner and outer surfaces are presented in this paper. The cylinder is simply supported at its two ends. Young's modulus of the material is assumed to vary continuously in radial direction of the cylinder. Moreover, numerical results of stresses in functionally graded circular hollow cylinder are appeared.

Free vibration analysis of a nonlocal thermoelastic hollow cylinder with diffusion

2020 ◽  
Vol 43 (8) ◽  
pp. 981-997 ◽  
Author(s):  
Dinesh Kumar Sharma ◽  
Dinesh Thakur ◽  
Vishal Walia ◽  
Nantu Sarkar
Keyword(s):  
Free Vibration ◽  
Hollow Cylinder ◽  
Vibration Analysis ◽  
Free Vibration Analysis

A Study on Photothermal Waves in a Semiconductor Material Photogenerated by a Focused Laser Beam

2016 ◽  
Vol 04 (02) ◽  
pp. 1650003 ◽  
Author(s):  
Ibrahim A. Abbas ◽  
K. A. Aly
Keyword(s):  
Wave Propagation ◽  
Laser Beam ◽  
Laplace Transform ◽  
Analytical Solutions ◽  
Elastic Waves ◽  
Carrier Density ◽  
Semiconductor Material ◽  
Eigenvalue Approach ◽  
Intensity Modulated ◽  
Elastic Process

In this work, the theory of coupled plasma, thermal and elastic waves were used to investigate the wave propagation on semiconductor material during photo-thermo-elastic process. A thin slim strip (TSS) medium, elastic semiconductor with isotropic and homogeneous thermal and elastic properties have been considered. The plasma, thermal and elastic waves in a TSS photo generated by a focused and intensity modulated laser beam were analyzed. Laplace transform techniques and eigenvalue approach were used to obtain the analytical solutions for carrier density, displacement, temperature, and stress. Numerical computations have been carried out on silicon-like semiconductor material. The results are presented graphically to show the effect of the coupling between the plasma, thermal, and elastic waves.

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