Nonlinear forced vibration and dynamic buckling of fixed functionally graded graphene platelet-reinforced (FG-GPLRC) porous arches under impulsive loading are investigated. The porosity coefficient varies along the thickness of arch based on a power law distribution with uniform dispersion of graphene platelets (GPLs) in the whole arch. The FG-GPLRC porous arch is made of closed-cell metal foams whose effective materials properties are determined by the volume fraction distribution of materials together with Halpin–Tsai model. The nonlinear motion equations of the FG-GPLRC porous under impulsive loading are derived by employed Hamilton’s principle, and numerically solved by Runge–Kutta (RK) method combined with the differential quadrature method (DQM). Based on the Budiansky–Roth (B-R) criterion of dynamic buckling, the critical dynamic buckling load of the arch is also determined. Two case studies are conducted to show the determination of the dynamic buckling load of the arch, and good accuracy of the developed method in predicting the critical dynamic buckling load of both shallow and deep arches is also verified. Numerical results show that the nonlinear forced vibration and dynamic buckling of arches are quite sensitive to impulsive load duration. In addition, FG-GPLRC porous arches have significantly higher critical dynamic buckling load when undergoing instantaneous impact loading. • Nonlinear forced vibrations of the FG-GPLRC porous arch under impulsive loading are investigated. • Critical nonlinear dynamic buckling load of the arch is determined. • Duration of the impulsive load has significant effect on the dynamic buckling of the arch. • Effects of porosity and its distribution on the nonlinear vibration of the arch are discussed. 

Nonlinear forced vibration and dynamic buckling of FG graphene-reinforced porous arches under impulsive loading

The primary resonance bifurcation problems are discussed for an arch structure with parametric and forced excitation.Based on the first approximate solution obtained by the averaging method,the amplitude-frequency curve and some dynamical behavior have been shown by some researchers for this system.Here,by means of singularity theory,the bifurcation behavior of the amplitude with respect to detuning parameters in the case of primary resonance is further studied.The related transition sets in the parameter plane and the bifurcation diagrams are plotted here,thus providing much more detailed information about bifurcation of the buckled structure.

Bifurcation analysis of an arch structure with parametric and forced excitation in the case of primary resonance

Thermomechanical in-plane dynamic instability of asymmetric restrained functionally graded graphene reinforced composite arches via machine learning-based models

In-plane dynamic instability of functionally graded porous arches reinforced by graphene platelet under a vertical base excitation

A hybrid algorithm for modeling and studying of the effect of material and mechanical uncertainties on stability of sandwich FGM materials under thermal shock

Zhongyang Xie

Papers

Analytical and experimental studies on out-of-plane dynamic parametric instability of a circular arch under a vertical harmonic base excitation