Journal Article

Nonlinear Stability Analysis of Multi-Stiffened Laminated Composite Plates Under Uniform In-plane Harmonic Loading

Patel, S. N., Fayaz, Danish

2025

Overview

Purpose When an in-plane harmonic loading is applied to a plate, the linear dynamic instability region (DIR) formed, gives only the range of frequencies where the plate becomes unstable, however, it doesn’t give any information about the transverse deformations. Hence, a nonlinear time history analysis is required to capture the actual time-varying deformations along with the nonlinear frequency response analyses to capture the actual frequency-varying deformations in the dynamic instability zone. Method In this study, a nonlinear mathematical model is developed within the finite element framework to analyze both the nonlinear frequency response and the time-history behavior of laminated composite plates attached with composite laminated stiffeners. The plates are subjected to time-dependent (harmonic) in-plane edge loading. An isoparametric finite element formulation is used to model the plate and stiffener components. To gain a comprehensive understanding of the instability characteristics of the stiffened plates, the Newmark-β method is employed for solving the linear and nonlinear dynamic equilibrium equations. Furthermore, the Incremental Harmonic Balance (IHB) method is utilized to trace the nonlinear frequency response path of the stiffened system. Results and Conclusions The results show that the dynamic responses under linear theory become unbounded within the DIR due to the lack of stabilizing mechanisms. Nonlinear theory introduces displacement-dependent restoring forces and geometric nonlinearities, which produce stabilizing effects and result in bounded periodic responses. Increasing the stiffener count enhances plate stiffness, causing the dynamic instability region to shrink and shift toward higher frequencies. This leads to reduced vibration amplitudes and improved stability across a wider frequency range. Overall, the nonlinear dynamic responses remain bounded and stable, demonstrating the system’s increased resilience to dynamic excitations.

• Publisher: Springer Nature Singapore,Springer Nature B.V
• Subject: Acoustics / Composite structures / Control / Dynamic stability / Dynamical Systems / Edge loading / Engineering / Engineering Acoustics / Equilibrium equations / Finite element method / Frequency ranges / Frequency response / Geometric nonlinearity / Isoparametric finite elements / Laminar composites / Mathematical models / Nonlinear dynamics / Nonlinear response / Original Paper / Stability analysis / Stiffeners / Time dependence / Vibration / Vibration control