VIBRATIONAL OPTIMIZATION OF A MASS-LOADED STEPPED PLATE

In this paper the vibrational characteristics of thin, mass-loaded, st epped 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 ac hieve this, a classical analytical approach for the analysis of the vi bration of a simply supported, stepped plate is first considered. Next , a method for the analysis of such plates carrying concentrated masse s is reviewed. The above two analytical methods are then combined to a nalyse the vibrational behaviour of thin, simply supported and mass-lo aded stepped plates. To assess the accuracy of these methods, the resu ltant 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-lo aded 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 t he paper. The final part of the paper deals with optimisation of the m ass positions in order to improve the vibratioinal behaviour of the pl ate. In this work, the integral of the frequency response function of the mass-loaded plate over a frequency range containing some 10-15 nat ural frequencies is regarded as the objective function. The drive and response points are chosen to lie at opposite ends of a plate with hig h aspect ratio and transverse stiffeners, so that minimizing the frequ ency response is equivalent to designing vibration isolation character istics 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 improv e the vibrational behaviour of the plate. (C) 1998 Academic Press Limi ted.