Wave Propagation and Vibration of Spring-Mass Systems

Author

Jonathan Wayne Langenfeld, Southern Illinois University CarbondaleFollow

Date of Award

12-1-2010

Degree Name

Master of Science

Department

Mechanical Engineering

First Advisor

Abrate, Serge

Abstract

AN ABSTRACT OF THE THESIS OF JONATHAN WAYNE LANGENFELD, for the Master of Science degree in Mechanical Engineering and Energy Processes, presented on 28 October 2010, at Southern Illinois University Carbondale. TITLE: WAVE PROPAGATION AND VIBRATION OF SPRING-MASS SYSTEMS MAJOR PROFESSOR: Dr. Serge Abrate The main focus of this research was to study wave propagation and modeling techniques of spring-mass systems. The purpose is to show that by engineering a materials microstructure, the material can have wave filtering capabilities. Numerical solutions were obtained for the steady-state response of a uniform, alternating, and branched spring-mass chain. The spring-mass chains studied were excited by harmonic forces; it is shown how gaps exist in the frequency ranges which can be applied to the chain, to filter wave propagation. The spring-mass chains were modeled as a continuum being governed by the wave equation or higher order models such as Love's rod theory. It was concluded that the best agreement was found between the spring-mass chain and the continuum models when excited by very low frequencies. Transient response problems are addressed for uniform materials, sandwiched materials, laminates, and graded materials. Analytical solutions for the response to these problems are presented along with numerical solutions using the finite element method. Step and impulse loading cases are studied to monitor if and how the initial wave pulse distorts upon propagation through a material. Underwater blast loading cases are studied which model water as a uniform bar transmitting waves into the hull of a sea going vessel. Results are presented for one-dimensional cloaking scenarios. Cloaking models are created from basic two component models and increased to four component models. Analytical and numerical solutions are obtained proving that the magnitude of reflected waves can be reduced by gradually decreasing the wave speed with each added layer. All of the results obtained throughout this research agree that the microstructure of a material can be engineered to control wave propagation.