Transient Analysis of Cylindrical Shells via a Numerically Stable Discrete Time State Space Technique

The transient dynamic response analysis of cylindrical shell structures holds paramount importance in areas such as aerospace engineering, structural design exposed to underwater explosions, and sonar signal inversion. While the traditional Transfer Matrix Method (TMM) often encounters numerical instability and computational divergence in time-domain solutions, most existing research primarily emphasizes the frequency domain. This paper introduces an enhanced Discrete-Time State-Space Technique to address these challenges. Grounded in linear Reissner shell theory, this method utilizes the Newmark- integration scheme to convert the partial differential equations governing structural motion into discrete-time first-order state equations. Through the incorporation of similarity transformations and non-dimensionalities, the transfer matrix is recast into Jordan canonical form. This conversion effectively decouples the system's growth and decay modes, mitigating numerical ill-conditioning during extensive recursive computations. The criteria for selecting the time integration step size are determined by considering both the condition number of the system matrix and the sampling theorem, bolstering the algorithm's robustness. Numerical evaluations reveal that our approach offers computational accuracy on par with the Finite Element Method (FEM) when processing Linear Frequency Modulation (LFM) signals and multi-point non-stationary excitations. Moreover, it showcases marked benefits in terms of computational efficiency and convergence rate. Consequently, this study presents a novel theoretical framework for efficiently simulating the transient behavior of cylindrical shell structures under intricate operational scenarios.