Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps

By Jianbin Du, N. Olhoff. 2007

298 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/7c108cc5d0698207e4dc8aa1bec70721bec7071f

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Optimum design of band-gap beam structures (2012, methodology): “(6)–(8) are not valid for multiple eigenfrequencies, and the derivation of design sensitivities of such eigenvalues is much more cumbersome, see, e.g. (Zhong and Cheng, 1986; Seyranian et al., 1994; Du and Olhoff, 2007a,b) and papers cited therein.”
Minimization of sound radiation from vibrating bi-material structures using topology optimization (2007, methodology): “Maximization of intrinsic properties of the structures like fundamental and higher order eigenfrequencies, gaps between two consecutive eigenfrequencies, and phononic band gaps (see, e.g., Diaz and Kikuchi 1992; Bendsøe and Diaz 1994; Kosaka and Swan 1999; Krog and Olhoff 1999; Pedersen 2000; Sigmun”
Isogeometric Shape Optimization of Vibrating Membranes (2011, methodology): “…+1 are given as b b b b b From (9) and (15), it follows that if the partial derivative of a function f with respect to ρ has been calculated as above, its sensitivities with respect to the design variables ρ b are given by Other methods of dealing with multiple eigenvalues are discussed in [37–40].”
Bi-directional Evolutionary Structural Optimization on Advanced Structures and Materials: A Comprehensive Review (2016, background): “This is mainly due to artificial localized modes in low density regions [24, 98].”
A critical review of established methods of structural topology optimization (2009, background): “Olhoff has also been extremely active in applying SIMP to reliability-based problems (Kharmanda and Olhoff 2004), vibrating continua (Olhoff and Du 2006; Du and Olhoff 2007a and b), and design-dependent loads (Hammer and Olhoff 1999, 2000; Du and Olhoff 2004a and b).”
Topology optimization of continuum structures under buckling constraints (2015, background): “Other methods for dealing with multiple eigenvalues can be found in the research literature [8,10,23,31].”
Level Set Based Structural Topology Optimization for Minimizing Frequency Response (2011, methodology): “At the same time, some interpolation schemes [6,8,28] were proposed to prevent and eliminate the localized modes in the SIMP method.”
GA topology optimization using random keys for tree encoding of structures (2009, methodology): “Figures 29, 30 and 31 depicts a topology similar to the one obtained in Du and Olhoff (2007) (Fig. 11, b).”