Study On In-plane Dynamic Stability Of Functionally Graded Porous Material Arches

Functionally graded porous materials(FGP)arches hold vast prospects in engineering applications.However,in the face of harsh engineering environments and complex external loads,the structural instability mechanism remains unclear,and the correspongding design criteria are still lacking behind.To refine the instability theory of FGM arches and explore their instability mechanism,urgent research efforts should be put forward.This thesis undertakes a series of innovative studies on the dynamic stability of FGP arches under various dynamic loads,the main content includes:(1)A comprehensive study on the dynamic stability of FGM circular arches under a localized distributed radial loading is conducted.Based on the principle of Hamilton,the motion equation of FGP arches is established.Utilizing a Galerkin procedure,the equation of motion is discretized and further arranged into a standard Mathiu-Hill form.The Bolotin method is employed to determine the dynamic unstable region of circular arches.Effects of porosity distribution patterns,porosity coefficients,Graphere Platelets(GPL)weight fractions,slenderness ratio,and distribution range of external loads on the dynamic unstable regions are explored,providing guidance for engineering design.It is found that under the same dynamic load amplitude,the width of dynamic unstable region for FGP-GPLRC arches subjected to a full span loading is the largest,followed by the mid-span loading S/2,and the minimum width of unstable region belongs to the case of mid-span loading S/4.It is also found that the FGPGPLRC circular arch having a uniform pore distribution mode has the widest dynamic unstable region,followed by the asymmetric pore distribution mode,and the symmetric pore distribution mode arch has the narrowest dynamic unstable region.(2)The in-plane parametric resonance of FGP circular arches under a vertical base excitation are studied,condisering damping effects.The modal displacement is approximated by trigonometric function.By combining the Galerkin method and Bolotin method,the dynamic unstable regions corresponding to periods T and 2T are obtained.The coupled vibration behaviors of the FGP arches are further discussed.Then FE model is established for transient analysis to validate the analytical results of the dynamic unstable regions.The variations of dynamic unstable regions for FGP circular arches under different structural parameters are studied in detail,and the corresponding optimal design parameters are given.Research results show that GPL fraction can improve the dynamic stability of FGP-GPLRC circular arch.The higher GPL fraction is,the more obvious the dynamic stability enhancement effect will be shown.When the dimensionless excitation amplitude is less than the minimum excitation amplitude,the dynamic instability behavior of FGP-GPLRC arches may not exist.(3)The in-plane dynamic stability of the fixed-fixed,pinned-pinned,and fixed-pinned FGP circular arches subjected to a half-span radial load are investigated.By using a differential quadrature algorithm,the dynamic unstable regions of arches are determined.Then FE model is built,and transient analysis is carried out to verify the accuracy of DQM calculated results.The variation law of dynamic unstable regions under the different material and geometric parameters are analyzed to reveal the dynamic instability mechanism of FGP circular arches.It is found that the bandwidth of the dynamic instability region of FGP-GPLRC circular arch becomes narrower when the constraints at both ends gradually grow.In returns,the dynamic instability phenomenon of the FGP-GPLRC arch having stronger constraints is difficult to occur.Increasing the porosity coefficient may reduce the mass density and weaken the bending and axial compression stiffness of the cross section.As a result,the FGP-GPLRC circular arch with a higher porosity coefficient is easier to buckle.(4)The nonlinear vibration of the FGP sinusoidal shallow arches under vertical harmonic uniform load is analyzed.According to the internal force balance condition,the vibration equation is built.An incremental harmonic balance technique(IHB)is utilized to obtain the time history curve and frequency response characteristics of arches.To verify the stability of the algorithm,the Floquet theory is adopted.Numerical simulation is then carried out to verify the correctness of the algorithm.Finally,the influence of material parameters and geometric characteristics on the nonlinear vibration behavior of the sinusoidal arch is clarified.The research results show that the fourth-order Runge–Kutta method can only track the stable segment of the frequency response curve,and the corresponding dynamic time history gradually approaches the steady-state solution from the initial value.Compared with that,the IHB method can obtain the complete frequency response curve and directly display the steady-state solution.When the geometric dimensions and dynamic characteristics of the arch are given,the increase of porosity coefficient significantly exacerbates the leftward softening behavior of the frequency response curve.The increase in GPL mass fraction,however,may weaken the softening behavior of the frequency response curve.