Prof. Dr. Ibrahim A. Abbas

Professor - Department of Mathematics

Faculty of science

Address: Sohag University, Egypt.



Publications Which contain the keyword: Exact solution

2018-10-18 08:32:27 Keywords Exact solution, two-temperature model, nanoscale resonator,
The influence of thermal and conductive temperatures in a nanoscale resonator
In this work, the thermoelastic interaction in a nano-scale resonator based on two-temperature Green-Naghdi model is established. The nanoscale resonator ends were simply supported. In the Laplace’s domain, the analytical solution of conductivity temperature and thermodynamic temperature, the displacement and the stress components are obtained. The eigenvalue approach resorted to for solutions. In the vector-matrix differential equations form, the essential ... Read more

2018-10-06 09:36:11 Keywords free vibration, Thermoelasticity, Exact solution, GNIII model,
Exact solution for a free vibration of thermoelastic hollow cylinder under GNIII model
The exact analytic solutions are obtained with the use of the eigenvalue approach for a free vibration problem of a thermoelastic hollow cylinder in the context of Green and Naghdi theory (GNIII). The dispersion relations for the existence of various types of possible modes of vibrations in the considered hollow cylinder are derived in a compact form and the validation ... Read more

Exact Solution of Thermoelastic Damping and Frequency Shifts in a Nano-Beam Resonator
In this study, we consider the problem of a generalized thermoelastic vibration of a bounded nano-beam resonator in the context of Green and Naghdi theory (GNIII). The first four modes of vibration in the nano-beam resonator are investigated for the beam under clamped and simply supported conditions. Analytical expressions for the deflection, temperature change, frequency shifts, and thermoelastic damping in ... Read more