Vibration of structures made of cellular material

Banerjee, Sourish (2004) Vibration of structures made of cellular material. University of Southampton, Doctoral Thesis.

Record type: Thesis (Doctoral)

Abstract

The vibration frequencies of beams made of a variety of microstructures are computed numerically and the change in modal spacing is studied systematically. To compare and contrast the situation with that of continuum, a problem of porosity filled solid with the same external dimensions as those of the cellular beam is undertaken. With the increase in the mode number, a progressive departure in the trend is observed.

A method to reduce the computation involved in the vibration calculations in cellular structures is proposed. Continuum-based assumed modes are used as the basis of the method. It is found that a direct use of the assumed modes in the approximation yields inaccurate results. The source of this error is identified. A sensitivity analysis is presented to show that the small components of modal contribution associated with the exceptionally high frequency modes are responsible for the poor performance of the assumed modes method. The method is improved by pre-conditioning the assumed modes by the use of inverse power iterations. Two examples, a cantilever beam and an L-beam, are presented to demonstrate the working of the method. Further, a reduced order model is developed to estimate the frequency response. The proposed method is shown to result in substantial computation saving for free vibration as well as forced response calculations while the accuracy is not compromised seriously.

The general conclusion that cellular solids cease to behave as continua at moderately high mode numbers may have important implications to the dynamics of structures made of such material at high frequencies.

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