Nonlinear Static Bending and Forced Vibrations of Single-Layer MoS₂ with Thermal Stress

Single-layer molybdenum disulfide (MoS₂) has been a research focus in recent years owing to its extensive potential applications. However, how to model the mechanical properties of MoS₂ is an open question. In this study, we investigate the nonlinear static bending and forced vibrations of MoS₂, subjected to boundary axial and thermal stresses using modified plate theory with independent in-plane and out-of-plane stiffnesses. First, two nonlinear ordinary differential equations are obtained using the Galerkin method to represent the nonlinear vibrations of the first two symmetrical modes. Second, we analyze nonlinear static bending by neglecting the inertial and damping terms of the two equations. Finally, we explore nonlinear forced vibrations using the method of multiple scales for the first- and third-order modes, and their 1:3 internal resonance. The main results are as follows: (1) The thermal stress and the axial compressive stress reduce the MoS₂ stiffness significantly. (2) The bifurcation points of the load at the low-frequency primary resonance are much smaller than those at high frequency under single-mode vibrations. (3) Temperature has a more remarkable influence on the higher-order mode than the lower-order mode under the 1:3 internal resonance.