An Investigation on the Forced Vibration Behavior of Plates Featuring Complex and Arbitrary Geometries Using Isogeometric Analysis

The Isogeometric Method (IGM) has been widely explored in the structural analysis of plates with arbitrary and complex shapes, particularly in the context of free vibration analysis. However, a literature survey highlights the scarcity of research on the application of IGM for forced vibration analysis of such structures. This paper aims to address this research gap by conducting a comprehensive forced vibration analysis on plates with complex and arbitrary shapes using the Isogeometric Method.

The approach employs Non-Uniform Rational B-Spline (NURBS) interpolation functions and the first-order shear deformation theory of plates. The governing equations are derived through the minimization of potential energy, incorporating Rayleigh damping in the analysis. Representative cases, including an L-shaped plate and a square plate with a heart-shaped cutout, are analyzed. Arbitrary-shaped plates are discretized into patches connected using the bending strip method, obtaining the global equation of motion in matrix form. Transient analysis is performed using the Newmark time-stepping approach, with time history responses extracted. Signal processing tools, such as Fast Fourier Transform (FFT) and Wavelet Transform (WT), are employed to extract natural frequencies from the time history responses. Validation is performed using the finite element method (FEM), considering various loading scenarios, including impulse, harmonic, saw shape, and chirp excitations, as well as resonance and beating cases.

Comparative analysis between IGM and FEM reveals that for complicated-shaped plates, IGM provides accurate results in transient analysis with lower degrees of freedom and significantly shorter computation time compared to FEM. Additionally, the frequency spectrum generated by both methods using FFT and WT is found to be fully matched. The results presented in this research contribute significantly to expanding the applicability of IGM in forced vibration analysis.