On the Design of Bars and Beams for Desired Mode Shapes

Within periodic materials and structures, wave scattering and dispersion occur across constituent material interfaces leading to a banded frequency response. In an earlier paper, the elastodynamics of one-dimensional periodic materials and finite structures comprising these materials were examined with an emphasis on their frequency-dependent characteristics. In this work, a novel design paradigm is presented whereby periodic unit cells are designed for desired frequency band properties, and with appropriate scaling, these cells are used as building blocks for forming fully periodic or partially periodic structures with related dynamical characteristics.Through this multiscale dispersive design methodology, which is hierarchical and integrated, structures can be devised for effective vibration or shock isolation without needing to employ dissipative damping mechanisms. The speed of energy propagation in a designed structure can also be dictated through synthesis of the unit cells. Case studies are presented to demonstrate the effectiveness of the methodology for several applications. Results are given from sensitivity analyses that indicate a high level of robustness to geometric variation.

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“…(15). For the case of isolating a harmonic excitation load, the excitation frequency ω * is specified in non-dimensional form:…”

Section: Approach Imentioning

confidence: 99%

“…Other studies that focused on topology or shape optimization in structural dynamics problems include those of Ma et al [12], Min et al [13], Zhao et al [14], and Lai and Ananthasuresh [15].…”

Section: Introductionmentioning

confidence: 99%

Dispersive elastodynamics of 1D banded materials and structures: Design

Hussein

Hulbert

Scott

2007

Journal of Sound and Vibration

116

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“…Another popular approach is the use of solid isotropic microstructures with penalization (SIMP) (Rozvany 2001). Further topology optimization approaches, such as integral programming, the genetic algorithm and the evolutionary design approach, are also discussed in many articles where structure topologies similar to SIMP have been obtained (Steven et al 2000, Sigmund 2001, Lai and Ananthasuresh 2002.…”

Section: Introductionmentioning

confidence: 99%

Adaptive moving mesh level set method for structure topology optimization

Liu

Korvink

2008

Engineering Optimization

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The level set method is a promising approach to provide flexibility in dealing with topological changes during structural optimization. Normally, the level set surface, which depicts a structure's topology by a level contour set of a continuous scalar function embedded in space, is interpolated on a fixed mesh. The accuracy of the boundary positions is therefore largely dependent on the mesh density, a characteristic of any Eulerian expression when using a fixed mesh. This article combines the adaptive moving mesh method with a level set structure topology optimization method. The finite element mesh automatically maintains a high nodal density around the structural boundaries of the material domain, whereas the mesh topology remains unchanged. Numerical experiments demonstrate the effect of the combination of a Lagrangian expression for a moving mesh and a Eulerian expression for capturing the moving boundaries.

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“…Finally, it should be noted that the methods used in this paper can be applied to the design of elastic bars for desired mode shapes, see Lai and Ananthasuresh [11].…”

Section: Introductionmentioning

confidence: 99%

Resonant hydraulic sloshing in a tank of variable depth

Seymour

Mortell

2007

Z. angew. Math. Phys.

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The forced resonant oscillations of a fluid in a tank of variable depth are considered within the hydraulic approximation. It is shown that for certain bottom topographies a continuous periodic output dominated by the first normal mode is possible. This contrasts with the case of a tank of constant depth, where hydraulic jumps are a feature of the motion. The amplitude and frequency of the output are connected by a cubic equation. The fluid response can act like that of a hard or soft spring, depending on the bottom topography. There is also a critical bottom topography that yields a higher order response amplitude. (2000). 76B15, 74J15, 74J30. Mathematics Subject Classification

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On the Design of Bars and Beams for Desired Mode Shapes

Cited by 23 publications

References 19 publications

Dispersive elastodynamics of 1D banded materials and structures: Design

Dispersive elastodynamics of 1D banded materials and structures: Design

Adaptive moving mesh level set method for structure topology optimization

Resonant hydraulic sloshing in a tank of variable depth

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