An efficient optimization method for transcendental eigenvalue problems based on mode count constraints and heuristic algorithm

Liu, Xiang

doi:10.1007/s00158-024-03807-w

2024-05-27

PRE

Liu, Xiang *

Meijia Song

DOI：10.1007/s00158-024-03807-w

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摘要

En 中文

An efficient, robust, and versatile optimization method (DSM-MCC-HA) is proposed for transcendental eigenvalue problems by combing the advantages of the dynamic stiffness method (DSM), mode count constraint (MCC), and heuristic algorithm (HA). The DSM is used to model free vibration, or buckling or wave propagation eigen problems exactly with very few DoFs leading to efficient computation; moreover, material and geometry are parameters in the analytical DSM models. The monotonically increasing integer-valued mode count based on the Wittrick-Williams algorithm is directly used as the constraint, and there is no need to compute the eigenvalues through dichotomy, which significantly reduces the computational time and meanwhile guarantees the robustness. Heuristic algorithms are adopted as the optimization algorithm resulting in global optima, where the differentiability of the mode count constraint is not required. The proposed method is sufficient general to be applied to different eigenvalue optimization problems, such as lightweight optimization with eigenvalue constraints, band gap constraints or specified eigenvalue(s), maximization of eigenvalue or band gaps with mass constraint, etc.. Difficulties of repeated frequencies, localized modes, and eigenmode switching are not involved. Beam (plane frame) and plate (corrugated sandwich panel) built-up structures are adopted as examples to demonstrate the efficiency, robustness, and versatility of the proposed method.

Keyword:

Structure optimization

Mode count constraint

Dynamic stiffness method

Transcendental eigenvalue problem

Heuristic algorithm