The design optimisation of periodic structures to minimise vibration transmission and stress levels

Loasby, Paul Michael (1999) The design optimisation of periodic structures to minimise vibration transmission and stress levels. University of Southampton, Doctoral Thesis.

Abstract

The purpose of this research is to gain an insight into how structural vibration can be minimised by designing a structure which is itself a passive vibration filter. An original periodic structure is modified by altering various parameters, such as bay length, stiffener depth and bay damping, to create an optimal structure, designed to minimise a given objective function. This function is typically the strain or kinetic energy within a structural element, although power input and modal density are also utilised. By altering the design parameters, the optimal structures may remain periodic or have some form of disorder introduced.

Four types of structure have been analysed: a one-dimensional beam, a one-dimensional waveguide, a two-dimensional mass-spring lattice ('squarion'), and a two-dimensional orthogonal beam grillage. An experiment on a waveguide structure has also been performed, demonstrating excellent correlation with the theoretical model.

The modelling of the one-dimensional beam and grillage structures was performed by using the Hierarchical Finite Element Method, the waveguide by the Dynamic Stiffness Method, and the squarion by exact techniques.

For the one-dimensional structures, several different optimal designs were obtained, depending on structure size, design parameters and objective function. Each of these designs demonstrate different ways in which the frequency response can be beneficially altered, with the structures remaining periodic, becoming bi-periodic or being totally disordered.

The mass-connecting springs were the design parameters within the squarion structure with the response of a particular set of masses being the objective function. Here, the squarion was either constrained to remain periodic, or allowed to become disordered as necessary. It was possible to obtain strong localisation of the response, and it was found that the objective function could be reduced to zero, within certain structural and forcing constraints. The reasons behind this are explained. Similarities in the vibration behaviour were observed between the squarion and the orthogonal beam grillage structure.

Overall, this research is able to demonstrate that the introduction of disorder into initially periodic structures can aid passive vibration control. Furthermore, some generic design guidelines are presented to help designers of future aerospace structures introduce passive vibration control.

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