Thermoelastic damping in rectangular microplate/nanoplate resonators based on modified nonlocal strain gradient theory and nonlocal heat conductive law

Abstract

Size effect is a significant factor for accurate estimation of the thermoelastic damping (TED) in microplate/nanoplate resonators. The actual TED in microstructures/nanostructures is comprehensively affected by various size-dependent mechanisms in the mechanical and thermal field and studying only one of them may lead to one-sided conclusions. In this article, the governing equations of coupled thermoelasticity in a transversely vibrating rectangular plate are derived by the modified nonlocal strain gradient theory and the nonlocal heat conductive law (GK model). Then utilizing the energy approach, a size-dependent TED model for rectangular plates is presented in the form of infinite series. The constitutive boundary conditions are considered to close the nonlocal strain gradient problem in differential form. The silicon material with typical length scale parameters and relaxation time is selected in simulation. The influences of nonlocal elasticity, strain gradient elasticity and nonlocal heat conduction on TED in rectangular plates are investigated under different frequencies, thicknesses and boundary conditions. The simulation results show that the TED expression converges rapidly and the three size-dependent parameters have distinct influences on TED value, critical thickness and critical frequency. By taking advantage of the size effects reasonably, the quality of resonators can be improved.

Keywords:

• Constitutive boundary conditions
• modified nonlocal strain gradient theory
• nonlocal heat conductive law
• rectangular plate resonators
• size effects
• thermoelastic damping

Disclosure statement

No potential conflict of interests was reported by the author(s).

Additional information

Funding

This project is supported by the National Natural Science Foundation of China (Grant No. 51375091).