Impacts of Length Scale Parameter on Material Dependent Thermoelastic Damping in Micro/nanoplates Applying Modified Coupled Stress Theory

Abstract

Among the different energy dissipation mechanisms, thermoelastic damping plays a vital role and need tobe alleviated in resonators inorder to enhance its performance parameters by improving its thermoelastic dampinglimited qualityfactor, QTED. The maximum energy dissipation is also interrelated with critical length (???????? ) of theplates and by optimizing the dimensions the peaking of energy dissipation can be diminished. As the size of thedevices is scaled down, classical continuum theories are not able to explain the size effect related mechanicalbehavior at micron or submicron levels and as a result non-classical continuum theories are pioneered with theinception of internal length scale parameters. In this paper, analysis of isotropic rectangular micro-plates based onKirchhoff model applying Modified Coupled Stress Theory is used toanalyzethe size-dependent thermoelasticdamping and its impact on quality factor and critical dimensions.Hamilton principle is adapted to derive thegoverning equations of motion and the coupled heat conduction equation is employed to formulate the thermoelasticdamping limited quality factor of the plates. Five different structural materials (PolySi, Diamond,Si, GaAs andSiC)are used for optimizing QTED which depends on the materialperformance index parameters. ThermoelasticDamping Index [TDI] and thermal diffusion length, lT. According to this work, the maximum QTED is attained forPolySi with the lowest TDI and Lcmax is obtained for SiC which is having the lowest lT. The impact of lengthscaleparameters (l), vibration modes, boundary conditions (Clamped–Clamped and Simply Supported), and operatingtemperatures on QTED and Lcare also investigated. It is concluded that QTED is further maximized by selecting lowtemperatures and higher internal length scale parameters (l).The prior knowledge of QTED and Lchelp the designers tocome out with high performance low loss resonators.