Abstract:
By integrating the modified strain gradient theory (MSGT) and the refined higher-order shear deformation theory (RHSDT), this study proposes a dynamic model for a double-layered microbeam connected by a Winkler-Pasternak elastic interlayer. The governing differential equations and boundary conditions were derived. For the case where both upper and lower beams are simply supported at both ends, the analytical solution for the system’s free vibration was obtained using Navier’s method. To efficiently solve complex boundary value problems, a 3-node weak-form quadrature element incorporating the Gauss-Lobatto quadrature rule and the differential quadrature rule was developed, featuring
C2; continuity. Following rigorous validation of the model’s effectiveness, the energy participation criterion (EPC) and the modal assurance criterion (MAC) were introduced to investigate the influence of material scale parameters and elastic interlayer stiffness on the system’s vibration frequencies and mode shapes. It is revealed that: shear deformation effects significantly impact higher-order modes, with this influence diminishing as the slenderness ratio increases; using the EPC revealed that the layer with weaker boundary constraints typically dominates the vibration initially, followed by an alternating dominance pattern with the more constrained layer; the elastic interlayer (particularly the Pasternak layer) plays a critical role specifically during asynchronous vibration modes; changes in its stiffness can induce mode transition phenomena; the MAC quantitatively characterized the mechanisms by which interlayer stiffness and material scale parameters influence system mode localization and transition behavior. The developed model and methodology provide an effective theoretical framework and benchmark data for predicting and analyzing the dynamic behavior of multi-layer microbeam devices in micro-electro-mechanical systems (MEMS), such as sensors, actuators, and resonators, offering valuable insights for their optimized design.