Free Vibration of Micro- and Nano-Shells Based on Modified Couple Stress Theory

A new theoretical dynamic model is developed, based on the modified couple stress theory, for the vibration analysis of micro- and nano-shells by introducing one internal material length scale parameter. After discretization with the energy approach leading to the Lagrange equation of motion, the natural frequency is analytically solved. The microscale shell exhibits some essential vibration characteristics and it is found using the model that for a microscale shell simply supported at both ends, the natural frequencies are size-dependent. The size dependence is significant when the characteristic radius size is comparable to the material length scale parameter, but decreases with the increase in characteristic size. The size-dependent effect is weaker for the fundamental mode than for other modes.