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Eman A. N. Al-Lehaibi
Mathematics Department, College of Science and Arts − Sharoura, Najran University, KSA

Hamdy Youssef
Umm Al-Qura University

DOI: 10.1615/TFESC1.mnc.012747
pages 1635-1648

KEY WORDS: Thermoelasticity, lateral vibration, Euler–Bernoulli equation, nano-resonator, heat conduction.


There are two significant effects in the nanoscale resonator; one is the non-Fourier effect on heat conduction, and the other is the coupling effect of temperature and strain rate. In the present study, a problem of vibration of nano- resonator induced by thermal loading is developed. The governing equations will take into account the above two effects when temperature depends on the mechanical and/or the thermal properties. The modulus of elasticity and the thermal conductivity are taken as linear function of the reference temperature. State-space and Laplace transform methods are used to determine the lateral vibration, the temperature, the displacement, the stress and the stress-strain energy of the nano- resonator. The effects of the relaxation time, thermal loading and the reference temperature in all the studied fields will be studied and represented graphically with some comparisons.

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