Nonlinear vibrations of a rotating sandwich functionally graded porous plate reinforced by graphene nanoplatelets

Abstract

The blade-disk rotor structure is widely utilized in rotating machinery such as turbines and generators. In this study, the disk is considered perfectly rigid, and the blade is modeled as a rectangular plate. Addressing the large deformations and chaotic phenomena exhibited by rotating blades in complex environments, a geometrically nonlinear model is developed for a rotating sandwich functionally graded porous plate (SFGPP) reinforced with graphene nanoplatelets (GPLs) subjected to sinusoidal pulse excitation. Based on the von-Kármán large deformation assumptions and Kirchhoff plate theory, the energy expression for the forced vibration of the SFGPP is derived. The governing equations of the structure are established using Hamilton's principle and the assumed mode method, and the dynamic response is solved employing the fourth-order Runge-Kutta method. Bifurcation and chaotic phenomena induced by rubbing are analyzed through systematic bifurcation diagrams and maximum Lyapunov exponent plots under varying material parameters. This study details how various material parameters affect the nonlinear vibration characteristics of the SFGPP, specifically analyzing plate thickness, porosity coefficient and distribution, GPL distribution and content, as well as GPL length-to-thickness and length-to-width ratios. The methodology and findings presented herein provide significant guidance for the in-depth analysis of the vibrational response of SFGPPs reinforced with GPLs, particularly their complex dynamic characteristics under critical partial rubbing conditions. More importantly, the revealed dependencies of dynamic behavior on material parameters offer crucial insights and quantitative data for the design optimization of such advanced composite blades, ultimately contributing to enhanced reliability and longevity of high-performance rotating machinery.