Vibration analysis of mass nanosensors with considering the axial-flexural coupling based on the two-phase local/nonlocal elasticity

Abstract

The influences of considering coupled axial-flexural vibrations on efficiency of cantilever mass nanosensors, modeled by Rayleigh and Timoshenko beam theories, are investigated in the frame work of a paradox-free nonlocal theory, i.e. two-phase local/nonlocal elasticity. However, the effects of axial-flexural coupling due to eccentricity of attached mass have been ignored in previous studies on mass nanosensors. Governing equations, boundary conditions, and corresponding compatibility conditions are derived by means of Hamilton’s principle and differential law of two-phase elasticity. Next, The Generalized Differential Quadrature Method (GDQM) as well as Generalized Integral Quadrature Method (GIQM) are utilized to attain the discretized two-phase formulation and coupled vibration characteristics of mass nanosensor. Several analogical studies are performed in detail to confirm the credibility of the present formulation and results. Comparisons between the uncoupled and coupled vibrations disclose that there are significant errors in obtaining the natural frequencies of corresponding mass value when the axial and transverse vibrations are considered separately. Therefore, the coupling of axial-lateral displacements resulted from the added mass eccentricity must be considered. This work can be a useful step forward to examine the coupling effects on vibration behavior of mass nanosensors, and it can be helpful to design the nanosensors with higher accuracy.