Numerical solution based on Rayleigh–Ritz FEM for vibrational analysis of functionally graded MWCNT-reinforced saturated porous annular sector plate on Winkler foundation: waviness and agglomeration effect

Abstract

This study focuses on the vibrational analysis of functionally graded material saturated porous annular sector plate reinforced with multi-walled carbon nanotubes (MWCNTs) on a Winkler foundation. The analysis takes into account the coupled effect of CNT waviness and agglomeration, as well as the influence of pressure in the closed cell on the vibrational properties of the composite plate. In order to assess the mechanical properties of the nanocomposite, a modified Halpin–Tsai micromechanical model incorporating orientation, waviness, and agglomeration factors of MWCNT is utilized. Also, the Biot constitutive law is used instead of the simple Hooke’s law to obtain realistic and practical conclusions. The principle of minimum potential energy and the Rayleigh–Ritz method are employed to solve the governing equations. A comprehensive investigation is conducted considering multiple parameters that can influence the natural frequency of the annular sector plate. These parameters include the CNT weight fraction, CNT distribution pattern, CNT dimension, and porosity parameters such as the porosity coefficient, Skempton coefficient, and porosity distribution. The effect of CNT waviness and agglomeration, as well as the Winkler elastic foundation coefficient, is also taken into consideration. Additionally, the dimension of the sector plate is explored through variations in the inner-to-outer radius ratio, inner-to-thickness ratio, and sector angle.