Size-dependent free vibration analysis of honeycomb sandwich microplates integrated with piezoelectric actuators based on the modified strain gradient theory

Applications of the honeycomb structures due to their lightweight and high stiffness together are developed rapidly in different areas of sciences and technologies. Therefore, in the current study, the vibrational behavior of a sandwich honeycomb rectangular microplate, which is integrated with piezoelectric actuators and is rested on the Pasternak elastic foundation, is investigated. Displacements are defined via the sinusoidal shear deformation theory. The modified strain gradient theory, which suggests three length-scale parameters, is used to predict the results in the micro-scale. Hamilton's principle and variational approach are employed to derive the governing motion equations. A closed-form solution based on the Navier's method is presented to obtain the natural frequencies. After ensuring the reliability of the results in the simpler state, the effect of different parameters on the frequencies is considered. It is seen that the geometrical parameters of the honeycomb cells have a significant effect on the results. Also, as the dimensionless length-scale parameter becomes greater, the frequencies tend to reduce and, increasing the applied voltage to the piezoelectric face sheets lead the frequency to reduce. Since it is the first analysis of honeycomb structures in small dimensions, so the result can be used as benchmarks for further analyses.