Efficient limitation of resonant peaks by topology optimization including modal truncation augmentation

Abstract

In many engineering applications, the dynamic frequency response of systems is of high importance. In this paper, we focus on limiting the extreme values in frequency response functions, which occur at the eigenfrequencies of the system, better known as resonant peaks. Within an optimization, merely sampling the frequency range and limiting the maximum values result in high computational effort. Additionally, the sensitivities of this method are not complete, since only information about the resonance peak amplitude is included. The design dependence with respect to the frequency of the extreme value is missed, thus hampering the convergence. To overcome these difficulties, we propose a constraint which can efficiently and accurately limit resonant peaks in a frequency response function. It has a close relation with eigenfrequency maximization; however, in that case, the amplitudes of the frequency response are unconstrained. In order to keep the computational time low, efficient implementation of this constraint is studied using reduced-order models based on modal truncation and modal truncation augmentation. Furthermore, approximated sensitivities are investigated, resulting in a large computational gain, while still yielding very accurate sensitivities and designs with almost equivalent performance compared with the non-approximated case. Conditions are established for the accuracy and computational efficiency of the proposed methods, depending on the number of peaks to be limited, numbers of inputs and outputs, and whether or not the system input and output are collocated.

Low-Rank Approximation of Frequency Response Analysis of Perforated Cylinders under Uncertainty

“…For the iterative scheme discussed above, it is the largest thickness which is the problematic one, since automatically also the condition number is the largest one. For the computationally most efficient case with only one factorisation over the whole set, the iteration counts for the Krylov basis for t = 1/100 are (33,29,25,23), i.e., constant in relative terms. This is also the worst-case result.…”

“…Wu et al have continued with a series of papers [21,22]. Moreover, Delissen et al [23] have studied this approach in the context of topology optimisation, where also the computational complexity can increase significantly.…”

Dynamic Topology Optimization of Constrained Damping Plates considering Frequency and Temperature Characteristics Based on an Efficient Strategy

“…Takezawa [14] took the complex dynamic compliance as a novel objective function to lessen the resonant response by maximizing the energy dissipation near the resonance. Delissen et al [15] proposed a constraint function based on enhanced modal truncation to limit the frequency response peak at the resonance using an efcient reduced-order model. Furthermore, Kang et al [16,17] adopted the classical Rayleigh damping model to describe the energy dissipation of viscoelastic materials and found that the specifc design confgurations are sensitive to the damping coefcients.…”

Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems

“…the size of the model adopted for state estimation. The use of reduced model is widely proposed in the literature for simplifying both the model-based design (Palomba et al 2015;Xiao et al 2020;Delissen et al 2020) and the control synthesis (Caracciolo et al 2008). The model in (19) is therefore recast in the modal canonical form by using the linear transformation…”