Abstract
The free vibration of multiple-nanobeam system is studied for various edge boundary conditions and number of coupled nanobeams. The size effect is captured using the Eringen's nonlocal elasticity theory. The governing equations of the beams which are coupled in the multiple-nanobeam system are obtained by Timoshenko beam theory. The vibration of multiple-nanobeam system with the number of m coupled nanobeams is described by 2 m coupled partial differential equations. A meshless formulation is presented to discretize the governing equations to a set of ordinary differential equations in time domain. The number of nanobeams of multiple-nanobeam system and the boundary conditions of each nanobeam can be arbitrary. The accuracy of results is examined by comparison of the predictions with available analytical results in the literature for especial cases, and good agreement is seen. In the numerical results the free vibration frequencies and mode shapes of multiple-nanobeam system for various edge boundary conditions are presented and the effects of parameters such as coupling stiffness, nonlocal parameters and number of nanobeams of multiple-nanobeam system are investigate. The presented method can be very useful for analysis of multiple-nanobeam system with arbitrary number of nanobeams, arbitrary boundary conditions, coupling stiffness and length to thickness ratio.
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