ENERGY DISSIPATION IN VIBRATING STRUCTURES

by Sondipon Adhikari
First Year Report abstract, Cambridge University Engineering Department
May 14, 1998.
Supervisor: Jim Woodhouse

Characterization of damping forces in vibrating structures has always been an active area of research in structural dynamics. Although the topic of damping is an old problem, it has gained momentum in the recent years due to modern engineering developments such as composite materials and structural control. In-spite of a large amount of research, knowledge of damping mechanisms and generic methodologies for handling them in the equations of motion have not been developed yet. The present report is aimed at contributing new methodologies in achieving solution of damped equations of motion, and developing procedures for identification of damping in the context of general vibrating structures. The analysis is limited to linear structural behaviour. The report is divided into three chapters and is appended with a list of references.

A review of the literature on damping within the scope of modal analysis is presented in Chapter 1. Different models of damping used in the context of linear structural vibrations and currently available analysis methods for non-classically damped structures and experimental determination of damping parameters have been reviewed. Limitations of the presently available techniques for dynamic analysis of damped structures and some of the open questions requiring further research are brought out. The motivation for focusing attention on use of complex modes is highlighted.

In Chapter 2, the conventional modal analysis method for linear continuous system is extended to handle general locally reacting damping models. On the account of non-proportional nature of the damping the natural frequencies and mode shapes become complex. Based on the small damping assumption, simple expressions of the natural frequencies and mode shapes have been obtained in terms of undamped system natural frequencies and mode shapes. In conjunction with the above formulation, a method has been proposed to detect the spatial distribution of damping in vibrating structures. The approach is fairly straight-forward and easily amenable to the conventional modal testing procedures. Information of the complex modes and natural frequencies appears to be sufficient to carry out the proposed method. Validity of the suggested procedure is verified by applying it to two commonly occurred problems in structural dynamics: an axially vibrating rod and an N spring-mass oscillator. For most of the test cases considered the developed method predicts the location of the damping with a sufficient accuracy.

Finally, in Chapter 3 a research proposal has been sketched which hopefully will lead us towards a better understanding of the models of damping and its effect on the vibrational response of engineering structures.

@mastersthesis{rp3,
    author={S. Adhikari},
    title={Energy Dissipation in Vibrating Structures},
    school={Cambridge University Engineering Department},
    year={1998},
    month={May},
    address={Cambridge, UK},
    note={First Year Report}
}