Resonance frequencies of size dependent perforated nonlocal nanobeam

Perforation is a common procedure in fabrication process of micro/nano-electromechanical systems (M/NEMS). Therefore, this paper presents an effort to study the resonance frequencies of size dependent regular square perforated nonlocal nanobeam, which not be discussed before. Equivalent characteristic parameters of perforated beam such as, bending stiffness, shear stiffness, mass, and rotary inertia are presented. The size-scale effect of long-range atomic interaction of nanobeam is described by using nonlocal differential form of Eringen model. Constitutive and governing equations of local and nonlocal perforated Timoshenko and Euler-Bernoulli nanobeam are derived. Analytical solution are exploited to solve the proposed model and derived closed form frequency equations as function of nanoscale and perforation parameters. The verification of current model is presented and compared with published works. Numerical results are illustrated to present the influences of length scale parameter, number of perforated holes, perforation size, and shear effects on the natural frequencies of both nanobeams theories. The obtained results are supportive in mechanical design of high-precision measurement nanobeams sensor and actuators.