Ashraf Zenkour - Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box ۸۰۲۰۳, Jeddah ۲۱۵۸۹, Saudi Arabia | Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh ۳۳۵۱۶, Egypt
Ahmed Abouelregal - Department of Mathematics, Faculty of Science, Mansoura University, Mansoura ۳۵۵۱۶, 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.

Green and Naghdi s theory, Nanobeam, Nonlocal thermoelasticity theory, State-space formulation, Rectified sine wave heating