This proposed research aims to develop a general method for the modeling of complex dynamic systems, especially in the critical mid-frequency range. The research builds on the PI's recent work on the vibration and energy flow analyses of elastically restrained beams and plates. The general approach of the research is to divide a complex dynamic system into a number of subsystems or components, based on two innovative ideas: 1) the displacements on each component are expressed as a generalized fast-converging Fourier series expansion; 2) the interactions of various components at junctions are accurately described in the form of force balance or displacement continuity equations.
The research will potentially lead to major advances in numerical methods for the dynamic analysis of complex systems in a broad frequency range. These advances will allow the creation of a unified tool for determining the dynamic properties such as the wave transmission coefficients and modal parameters for various structures or junctions, regardless of boundary conditions, coupling conditions, joint configurations, or the number of components involved. The current model will represent the interactions of the individual components faithfully as under the actual system condition and will overcome the problem of having to calculate or specify, a priori, the joint or component properties. The research will also advance the fundamental understanding and design of complex dynamic systems by focusing on the important uncertainty and sensitivity issues related to the manufacturing and modeling processes.
The research will be focused on the critical mid-frequencies and will lead to solutions of the noise and vibration problems that impact the design of a wide range of dynamic systems from consumer products to aircrafts. The research will develop modeling tools that will free the designers from the often enormous effort in creating models, extracting component modal properties and other model variables, or customizing the formulations and solution procedures to accommodate minor changes or variations in boundary conditions, coupling configurations, or other system or component conditions.
Graduate students will be directly involved with this project. Undergraduate students, especially minority students, will be involved via senior design projects, internship with the industrial partner, and through undergraduate research projects. Through this project, future professionals will be trained with broad backgrounds and strong skills to solve practical engineering problems and to perform advanced researches.
