Comparing and optimizing analytical, numerical and experimental vibration models for a simply-supported ribbed plate

Abstract

Ribbed plates are common components in structures, aircrafts, and ships. Owing to safety considerations and proper functioning, it is important to predict the natural frequencies and mode-shapes of such systems efficiently. There are many analytical, numerical, and experimental methods that extract the modal parameters of ribbed plates. However, each present advantages and tradeoffs. The aim of this paper is to implement various modeling and experimental approaches, optimize them, and compare their strengths and weaknesses. Analytical models are based on the assumed-modes method and differ in geometric configuration and trial function selection. Finite element models employ higher-order shear theories. Two experiments are performed to compare theoretical results, and to weigh the benefits of the two common setups. Parallelization and concurrency, mathematical simplifications, and algorithmic improvements are used to optimize the performance of the analytical models so that the benefits of each geometry can be understood. Parallelized programs are then put through algorithmic analysis to estimate local order of growth and study running time. By comparing the performance, accuracy, simplicity, stability, affordability, and parametrization potential of the approaches, vibration scientists and engineers are better able to select methods suitable for their research, application, or design.