Space–time topology optimization for one-dimensional wave propagation

Jensen, Jakob Søndergaard

doi:10.1016/j.cma.2008.10.008

Cited by 31 publications

(17 citation statements)

References 30 publications

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“…So, we have restated the original equation (9) in the form of four equations (12)- (15), with 11 B , 12 B , 21 B , 22 B as the dependent variables instead of 1 A ; no approximations are involved so far. Now we introduce approximations by neglecting the right-hand side of (15), so that:…”

Section: Solution By the Methods Of Varying Amplitudesmentioning

confidence: 99%

“…The corresponding expressions for these constants are lengthy, and thus not given here. So, the solution 1 1 ( ) A x of the considered problem is composed in the form (11), where amplitudes 11 B , 12 B are defined by (30), and amplitudes 21 B , 22 B by (24).…”

Section: Solution By the Methods Of Varying Amplitudesmentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8]). The approaches proposed for treating such problems may be divided in two groups: active control, when structural parameters are varied in time [3,[8][9][10][11][12], and passive control, when these parameters are changing only in space [2,5,7,[13][14][15]. In most cases behavior is considered in presence of a point load or an excitation source, and boundary conditions are not taken into account [2-6, 12-14, 16-17].…”

Section: Introductionmentioning

confidence: 99%

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Vibration suppression for strings with distributed loading using spatial cross-section modulation

Sorokin

Thomsen

2015

Journal of Sound and Vibration

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Document VersionPeer reviewed version Link back to DTU Orbit Citation (APA): Sorokin, V., & Thomsen, J. J. (2015). Vibration suppression for strings with distributed loading using spatial cross-section modulation. Journal of Sound and Vibration, 335, 66-77. DOI: 10.1016/j.jsv.2014.09.028 Vibration suppression for strings with distributed loading using spatial cross-section modulation Abstract A problem of vibration suppression in any preassigned region of a bounded structure subjected to action of an external time-periodic load which is distributed over its domain is considered. A passive control is applied, in that continuous spatially periodic modulations of structural parameters are used as a means for vibration suppression. As an example, stationary vibrations of a string under action of a distributed time-periodic load are studied. This system in a simplified form models such processes as interaction between membranes and colloids, oscillations of transmission lines under action of rain and wind, and dynamics of suspension bridges and stay cables. Suppression of vibration in predefined regions of the string is performed by continuous spatial modulation of its cross-section. For analyzing the problem considered a novel approach named the method of varying amplitudes is employed. This approach is applicable for solving differential equations without a small parameter, and may be considered as a natural continuation of the classical methods of harmonic balance and averaging. As a result, optimal parameters for the string cross-sectional area modulation are determined for the cases of harmonically, uniformly and arbitrarily distributed load, which allows for completely suppressing or considerably reducing vibration in the prescribed part of the string (compared to the case without modulation). vibration suppression; bounded structure; distributed loading; continuous spatially periodic modulation; the method of varying amplitudes.

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Section: Solution By the Methods Of Varying Amplitudesmentioning

confidence: 99%

Section: Solution By the Methods Of Varying Amplitudesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vibration suppression for strings with distributed loading using spatial cross-section modulation

Sorokin

Thomsen

2015

Journal of Sound and Vibration

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“…Among the techniques and tools used to deal with this type of problems, homogenization and variational formulations have played an important role (see also [1,3,15,18]). More recently, optimal design problems for time-dependent designs and time-dependent state equations -mainly of hyperbolic type -have been also considered ( [5,8,9,10]). In particular, in [8] a class of spatialtemporal composite materials (rank-1 and rank-2 spatial-temporal laminates) were introduced.…”

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confidence: 99%

Long Time Behavior of a Two-Phase Optimal Design for the Heat Equation

Allaire¹,

Münch²,

Periago³

2010

SIAM J. Control Optim.

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Abstract. We consider a two-phase isotropic optimal design problem within the context of the transient heat equation. The objective is to minimize the average of the dissipated thermal energy during a fixed time interval [0, T ] . The time-independent material properties are taken as design variables. A full relaxation for this problem was established in [Relaxation of an optimal design problem for the heat equation, JMPA 89 (2008)] by using the homogenization method. In this paper, we study the asymptotic behavior as T goes to infinity of the solutions of the relaxed problem and prove that they converge to an optimal relaxed design of the corresponding two-phase optimization problem for the stationary heat equation. Next, we study necessary optimality conditions for the relaxed optimization problem under the transient heat equation and use those to characterize the micro-structure of the optimal designs, which appears in the form of a sequential laminate of rank at most N , the spatial dimension. An asymptotic analysis of the optimality conditions let us prove that, for T large enough, the order of lamination is in fact of at most N − 1. Several numerical experiments in 2D complete our study.

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“…Time-domain methods have the advantage of computing the response of a linear system at many frequencies with a single time-domain analysis. This idea has been used for antenna design using the finite-difference time-domain method [13], onedimensional filter and pulse modulator designs [14,15], and simultaneous space-time optimization [16] in the setting of the FETD method. Additionally, time-domain methods can accommodate strongly nonlinear or active (time-varying) media, whereas frequency methods have difficulties with these physical regimes because the frequency is no longer preserved.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization for transient response of photonic crystal structures

2010

Self Cite

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An optimization scheme based on topology optimization for transient response of photonic crystal structures is developed. The system response is obtained by a finite-element time-domain analysis employing perfectly matched layers as an absorbing boundary condition. As an example a waveguide-side-coupled microcavity is designed. The gradient-based optimization technique is applied to redistribute the material inside the microcavity such that the Q factors of a monopole and a dipole mode are improved by 375% and 285%, respectively, while maintaining strong coupling. This is obtained by maximizing the stored energy inside the microcavity in the decaying regime of the transient response. Manufacturable designs are achieved by filtering techniques capable of controlling minimum length scales of the design features.

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Space–time topology optimization for one-dimensional wave propagation

Cited by 31 publications

References 30 publications

Vibration suppression for strings with distributed loading using spatial cross-section modulation

Vibration suppression for strings with distributed loading using spatial cross-section modulation

Long Time Behavior of a Two-Phase Optimal Design for the Heat Equation

Topology optimization for transient response of photonic crystal structures

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