Dynamic stability of power law FG shallow arches: a theoretical approach

One of the remarkable concerns in Shallow arches’ behavior under lateral loading is snap through, a phenomenon which can make the structure collapse or displace to another stable configuration. Introducing functionally graded materials in recent years led to some interesting results, for instance, using functionally graded materials in shallow arches can give structures with favorable stability properties. In this work, we investigate dynamic stability of the pined-pined functionally graded sinusoidal shallow arch under impulsive loading. Material properties vary through the thickness by power law function. Nonlinear governing equations are derived using Euler-Bernoulli beam assumption and equations of motion are expressed by a nonlinear differential-integral equation. The solution utilizes a Fourier form of response. The procedure to analyze dynamic stability followed here uses total energy of the system and Lyapunov function in the phase space. We find the stable region against dynamical snap through under material properties’ variation through the thickness of shallow arch. We also proceed to find the sufficient critical load in order to make the dynamical snap through occur. The results are analyzed in detail and illustrated in some diagrams.