Generalized incremental frequency method for topological designof continuum structures for minimum dynamic compliance subject to forced vibration at a prescribed low or high value of the excitation frequency

This paper deals with topological design optimization of elastic, continuum structures without damping that are subjected to time-harmonic, design-independent external dynamic loading with prescribed excitation frequency, amplitude and spatial distribution. The admissible design domain, the boundary conditions, and the available amount(s) of material(s) for single- or bi-material structures are given. An important objective of such a design problem is often to drive the resonance frequencies of the structure as far away as possible from the given excitation frequency in order to avoid resonance and to reduce the vibration level of the structure. In the present paper, the excitation frequency is defined to be 'low' for positive values up to and including the fundamental resonance frequency of the structure, and to be 'high' for values beyond that. Our paper shows that it may be very important to consider different design paths in problems of minimum dynamic compliance in order to obtain desirable solutions for prescribed excitation frequencies, and a so-called 'incremental frequency technique' (IF technique) is applied for this. Subsequently, the IF technique is integrated into an extended, systematic method named as the 'generalized incremental frequency method' (GIF method) that is developed for gradient based dynamic compliance minimization for not only 'low', but also 'high' excitation frequencies of the structure. The GIF method performs search for and determination of the solution to the minimum dynamic compliance design problem, but this is subject to the complexity that problems with prescribed high excitation frequencies exhibit disjointed design sub-spaces. Each of these sub-spaces is associated with a local minimum value of the dynamic compliance, so in general the 'global optimum solution' will have to be selected as the 'best' solution from among a number of local candidate solutions. Illustrative examples of application of the IF technique and the GIF method are presented in the paper.