Free vibration analysis of rectangular nanoplates based on two-variable refined plate theory using a new strain gradient elasticity theory

In this paper, the free vibration of simply supported rectangular nanoplates based on two-variable refined plate theory using strain gradient elasticity theory is presented. Various formats of gradient elasticity theory are available in the literature. In this work, strain gradient elasticity theory with two gradient constants is used. An analytical method is adopted to find the natural frequencies of rectangular nanoplates. Present results are compared with the results of other works done previously. It is mentioned that it is the first time that two-variable refined theory and strain gradient elasticity theory with two gradient constants are used together for free vibration of nanostructures, so the results of the present work can be used as bench mark for future works.