Natural vibrations of clamped curved nano-beams and nano-arches

Numerical solution of the clamped-clamped (C-C) nanoarches based on the non-local theory of elasticity is analysed. The present study is helpful to understand the mechanical behaviour of the nanostructures. The nanoarch under consideration has constant thickness and dimension of the cross-section and is weakened by crack-like defects. It is assumed that the crack is stationary and the mechanical behaviour of the nanoarch can be modelled by the Eringens non-local theory of elasticity. The influence of cracks on the natural vibration is prescribed with the aid of additional local compliance at the weakened cross-section. An algorithm to determine the eigen frequencies of nanoarches is developed. Present study reveals that there are significant effects of crack length non-local paremeters and radius of the arch on eigen frequency of the nanoarches. The final results are obtained numerically with the help of computer and presented graphically. The results are also compared with those presented by other researchers in the form of a table.