Vibrational optimization of a mass-loaded stepped plate

Abstract

In this paper the vibrational characteristics of thin, mass-loaded, stepped plates are investigated. The dimensions of the plates are chosen so that the steps can be thought of as representing the periodically placed stiffeners commonly found in many engineering structures. To achieve this, a classical analytical approach for the analysis of the vibration of a simply supported, stepped plate is first considered. Next, a method for the analysis of such plates carrying concentrated masses is reviewed. The above two analytical methods are then combined to analyse the vibrational behaviour of thin, simply supported and mass-loaded stepped plates. To assess the accuracy of these methods, the resultant frequency responses of the unloaded plate are compared with the Dynamic Stiffness method [1] and those for both the unloaded and mass loaded plates with finite element calculations. For a uniform, mass-loaded plate, there is perfect agreement between the frequency responses obtained from these methods. For the mass-loaded, stepped plate, the agreement is not so complete, the reasons for which are discussed in the paper. The final part of the paper deals with optimisation of the mass positions in order to improve the vibrational behaviour of the plate. In this work, the integral of the frequency response function of the mass-loaded plate over a frequency range containing some 10–15 natural frequencies is regarded as the objective function. The drive and response points are chosen to lie at opposite ends of a plate with high aspect ratio and transverse stiffeners, so that minimizing the frequency response is equivalent to designing vibration isolation characteristics into the plate. The Genetic Algorithm, which is an evolutionary optimization method, is employed to produce the required designs. It is demonstrated that the optimized mass positions significantly improve the vibrational behaviour of the plate.

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ORCID for A.J. Keane: orcid.org/0000-0001-7993-1569

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