Analysis of low velocity impact on nano-beam using modified couple stress theory

In this paper, low velocity impact on nano-beam using couple stress theory was investigated. Modified couple stress theory was utilized to capture size-dependent effects. Hamilton’s principle was employed to derive governing equations and boundary conditions and then general solution was proposed. The solutions validity was confirmed by comparing present results with that of the literature. Comparing the results shows the present theory is capable to predict low velocity dynamic behavior with acceptable accuracy. The results show as mass ratio increased, natural frequencies decreased and then trend to a constant value. This limit is higher for second and third natural frequencies. Also, the natural frequencies increased when characteristic length to thickness ratio increased. It can be noted higher natural frequencies are more sensitive to variation of this ratio .Furthermore, maximum dynamic deflection raised when mass ratio increased. Moreover, a considerable result from this study is the profound effect of poison ratio on natural frequencies for nano-sized beams. As Poisson’s ratio increased, natural frequencies increased. Also, for low length scale to thickness ratio the size effect is insignificant and response trend to classic solution. Therefore, the couple stress theory can be employed to take into account size effects in low velocity impact on nano-beam problem.