Scale-Dependent MSG Formulations for Vibrational Study of Honeycomb Microplates Covered by Piezoelectric Nanocomposite Patches

Abstract

This study investigates free vibration analysis of a microplate featuring a honeycomb (HC) core and incorporates two nanocomposite piezoelectric (NP) layers. Carbon nanotubes (CNTs) are hired to enhance the electro-mechanical performance of the piezoelectric patches, which are subjected to an externally applied electric voltage. All layers are tightly bonded together and are supported by an elastic substrate according to the Pasternak model, capable of withstanding both normal and shear loads. To establish the kinematic relations, a trigonometric plate theory is employed. The governing equations of motion are deduced through the application of Hamilton’s principle and variational technique. The modified strain gradient theory, which includes three material length-scale parameters (MLSPs), is used to account for the scale effect. An analytical approach based on Fourier series functions is employed to solve the differential equations of motion. Subsequently, the impact of various factors, such as the geometrical characteristics of the HC core, distribution patterns of CNTs, and other significant parameters, on the normalized frequencies of the model is assessed after validating the accuracy of the results. The outcomes of this research have the potential to facilitate the advancement and production of lightweight and intelligent structures and devices, ultimately enhancing their efficiency.