Thermoelastic Vibration of Temperature-Dependent Nanobeams Due to Rectified Sine Wave Heating—A State Space Approach

Document Type : Research Paper


1 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

2 Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh 33516, Egypt

3 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt


In this study, the second type of Green and Naghdi's thermoelasticity theory is applied to present the vibration of a nanobeam subjected to rectified sine wave heating based upon the nonlocal thermoelasticity theory. Both Young's modulus and thermal conductivity are considered to be linear functions of the temperature. The Laplace transform domain is adopted to solve the governing partial differential equations using the state space approach. Numerical computations are carried out using the inverse of Laplace transforms. The effects of nonlocal parameter and angular frequency on the thermal vibration quantities are discussed. The results of all quantities are illustrated graphically and investigated.


Main Subjects

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