Dynamic topology optimization design of rotating beam cross-section with gyroscopic effects

Topology optimization for eigenfrequencies of a rotating thin plate via moving morphable components

“…18(b). For example, the eigenfrequency loci crossing points locate in the range of γ∈ [3,4] for Fig. 18(a), γ∈ [6,7] for Fig.…”

“…Rotating structures have seen a great variety of applications to industrial products, such as a turbo engine, a helicopter and a spinning solar sail [1][2][3][4]. Previous studies have shown that the dynamic characteristics of a rotating structure are more complicated than non-rotating ones because of the centrifugal stiffening effect [1,3,[5][6][7].…”

“…Recent years have witnessed the efforts to optimize the eigenfrequencies of a rotating beam with the help of topology optimization by Liu et al [4]. They optimized the topology of the cross-section of a rotating beam for two objectives, i.e., maximizing either the fundamental eigenfrequency or the gap between two consecutive eigenfrequencies.…”

“…The other important issue about the topology optimization for eigenfrequencies is the sensitivity analysis of eigenfrequencies, especially of multiply repeated eigenfrequencies, with respect to a design variable. Last decades have witnessed the development of many methods for the sensitivity analysis of eigenfrequencies, for example, the methods by computing the sensitivities of eigenvalues [19,31] and the methods via a smooth approximation [4,[32][33][34].…”

Nonlinear eigenvalue topology optimization for structures with frequency-dependent material properties

“…However, using this simplification cannot accurately evaluate the targeting of nonlinear eigenvalues in the optimization and thus may lead to suboptimal designs. Except for frequency-dependent material, the eigenvalue problems also arise in other science and engineering applications, including control theory 33 , fluidstructure interaction problems 34 , and rotating structure with gyroscopic effects 35 .…”