Development of a viscoelastic spline finite strip formulation for transient analysis of plates

In this study, the forced vibration behavior of viscoelastic plates is investigated using the spline finite strip method (spline FSM). It is assumed that the viscoelastic behavior of materials considered in this research is linear, which means the material constants are independent of load level and are a function of time only. The shear modulus is thus represented as a function of the so-called Prony series. Moreover, it is assumed that the bulk modulus remains constant. For spline FSM, the equilibrium equations are derived using the principle of virtual work and the classical bending plate theory in matrix form. A numerical solution is developed for forced vibration analyses using the Newmark's method. The damping effects corresponding to the viscoelastic nature of materials are incorporated in the analysis by a novel approach that defines a fictitious damping force vector. The convergence of the spline finite strip method for a viscoelastic plate under different loading conditions is studied. Additionally, the fast fourier transform (FFT) of forced vibration responses is applied to evaluate the natural frequencies of plates. The accuracy and efficiency of the proposed spline finite strip model are verified by comparing the simulation outcomes presented in this work with the results obtained from the finite element method using ANSYS. Through a comparison of the results, we found the spline finite strip results to be in good agreement with the finite element results.