Nonlinear frequency behaviour of magneto-electromechanical mass nanosensors using vibrating MEE nanoplates with multiple nanoparticles

Nanomechanical mass sensors are promising candidates for low-cost, rapid and sensitive detection of ultrasmall particles such as biomolecules, bacteria and pollutant objects. This advanced mass sensors function based on the change in the vibration behaviour due to the nanoparticle attachment. A nonlinear continuum formulation is developed in this analysis for the large-amplitude vibrations of magneto-electromechanical mass nanosensors. The strain gradient influence and the effect of the nonlocality of stress components are incorporated into the nonlinear analysis via a higher-order scale-dependent theory of elasticity. The nanomechanical sensor makes use of vibrating magneto-electro-elastic (MEE) nanoplates with several possible locations for trapping nanoparticles. The nonlinear equations of the nanosensor are obtained and solved using Hamilton’s principle and perturbation technique, respectively. A verification study is performed by using available finite element results from the literature for graphene-based mechanical nanosensors. The nonlinear frequency shifts are obtained for different scale-dependent theories and various types of compatibility equations. The influences of the mass, position and number of nanoparticles on the frequency shift are studied considering the effects of stress nonlocality, strain gradient, mass moment of inertia, and geometrical nonlinearity.