Variable-thickness higher-order sandwich beams with FG cellular core and CNT-RC patches: vibrational analysis in thermal environment

Abstract

This research presents an in-depth exploration of the vibrational performance exhibited by sandwich beams with variable thickness profiles. These beams undergo a gradual reduction in thickness along their length. The core material of these sandwich beams is constructed from FG cellular materials, while the facesheets are reinforced with carbon nanotubes. Due to the varying distribution patterns of these reinforcements concerning the beam’s height, it becomes essential to apply stress transformations at specific angles to accurately compute the equivalent material properties. The study employs both Hamilton’s principle and variational approach to derive the governing equations for motion, as well as the associated boundary conditions. To comprehensively assess the effects of various parameters such as geometry, porosity coefficient, diverse distribution patterns of porosity and carbon nanotubes, as well as the transformation angle on the natural frequencies, a robust numerical technique known as the differential quadrature method is employed to solve the derived equations. It is found that compared to beams with a constant thickness, tapered beams typically display lower frequencies. Also, if the reinforcements are not arranged in the upper and lower layers in the direction of changing the thickness, the results will have noticeable changes.