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.

研究了多纳米束系统在不同边缘边界条件和耦合纳米束数量下的自由振动。使用 Eringen 的非局部弹性理论来捕捉尺寸效应。利用Timoshenko梁理论得到了多纳米束系统中耦合梁的控制方程。米数多纳米束系统的振动耦合纳米束由 2 m 耦合偏微分方程描述。提出了一种无网格公式，将控制方程离散为时域中的一组常微分方程。多纳米束系统的纳米束数量和每个纳米束的边界条件可以是任意的。通过将预测与文献中针对特殊情况的可用分析结果进行比较来检查结果的准确性，并且可以看到良好的一致性。在数值结果中，给出了多纳米束系统在各种边缘边界条件下的自由振动频率和振型，并研究了多纳米束系统的耦合刚度、非局部参数和纳米束数量等参数的影响。