Mathematical Solution for Vibrational Response of Shear and Normal Deformable Advanced Metal Foam CMBS Treated with Nanocomposite Actuators

Abstract

This research focuses on examining the vibrational properties of intelligent curved microbeams (CMBs) that incorporate metal foams and are enhanced with carbon nanotubes-reinforced piezoelectric (CNTRP) actuators. An advanced four-variable theory for shear and normal deformation is applied in the polar coordinate framework to investigate the microstructure, thereby negating the need for a shear correction factor. Additionally, the modified couple stress theory (MCST) is utilized to account for scale effects. The structural attributes exhibit thickness-dependent alterations following predefined functions. The governing equations of motion are deduced using Hamilton’s principle. In instances where the structure has simply supported ends, Fourier series functions are utilized to solve these equations. The outcomes are cross-validated in contradiction with previously documented works with more straightforward setups. The inquiry investigates the effects of critical parameters on the vibrational response of the structure. The results are corroborated in simpler scenarios using existing data in the literature to ensure accuracy.