We can find the application of plated structures in the different fields of engineering like mechanical, civil, naval, and aerospace. These structures may be sometimes subjected to time-dependent loads like air-blast. In this paper, we use a superparametric element to analyze the thin plates of arbitrary geometries. We use cubic serendipity shape function to represent the plate geometry and an ACM plate bending element along with in-plane displacements to define the displacement field. The element can accommodate different arbitrary geometries, and there is no shearlocking problems as observed in isoparametric elements. We apply Newmark $$\beta$$ scheme with Newton–Raphson iteration technique to solve the nonlinear governing equation. We present different examples for linear and nonlinear transient vibration analyses to prove the efficacy of the numerical formulation.