Nonlinear dynamical responses of forced carbon nanotube-based mass sensors under the influence of thermal loadings

This study presents an analytical solution for the nonlinear forced vibration response of bridged carbon nanotube (CNT)-based mass sensors subjected to different types of thermal loading and external harmonic excitations. The structure undergoes a temperature change through its thickness when considering three different distribution patterns of the temperature, namely uniform, linear, and nonlinear. The CNT is modeled as a nonlocal doubly clamped beam that complies with Euler–Bernoulli beam theory and Eringen’s nonlocal elasticity theory. The von Kármán geometric nonlinearity is adopted to account for the mid-plane stretching of end-constrained beams. The extended Hamilton’s principle is used to derive the nonlinear governing equations of motion, boundary conditions, and continuity conditions accounting for the location of the deposited particle. The method of multiple scales (MMS) is employed to perform the nonlinear dynamical analysis of the nanobeam. Analytical expressions of the nonlinear dynamic response of the system exposed to thermal loadings in the case of primary resonance are presented. An important contribution of this work is the provision for closed-form expressions of the resonance frequency and the critical amplitude of the considered system. Simultaneously, validation of the results by MMS is achieved by Galerkin’s procedure and Runge–Kutta method. Then, the effects of the thermal loads and some key parameters on the nonlinear resonance frequency and amplitude shifts are discussed, and some meaningful conclusions are drawn.