Optimization of natural frequencies of a slender beam shaped in a linear combination of its mode shapes

Silva, Guilherme Augusto Lopes da; Nicoletti, Rodrigo

doi:10.1016/j.jsv.2017.02.053

Cited by 11 publications

(14 citation statements)

References 16 publications

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“…However, eigenvectors only give relative displacements. Hence, I can adopt the scale defined in [15]: the maximum distance of the beam to the baseline ( max in Fig. 3).…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The effects of shaping the beam according to a given mode shape of the baseline beam and boundary conditions have been reported in [15]. The idea in the present work is to linearize the geometry of the shaped beam and to analyze the effects of such simplified geometry.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The following mathematical formulation is based on that presented in [15]. I consider in the analyses shaped beams (nonstraight beams) with constant cross section, i.e., beams with a certain out-of-plane geometry.…”

Section: Mathematical Model Of the Shaped Beammentioning

confidence: 99%

“…The first ideas of using mode shapes to mold the structure aiming at achieving desired dynamic characteristics were presented in [14]. After that, numerical and experimental results showed the feasibility of the procedure of shaping beams using mode shapes for obtaining desired natural frequencies [15]. In this case, the necessary condition for shifting natural frequencies of the structure is that the beam or the plate be axially constrained (simply supported or clamped).…”

Section: Introductionmentioning

confidence: 99%

“…Another interesting effect is that the shifted natural frequency is always related to the mode shape used to shape the structure. By adopting mode shapes (or a linear combination of mode shapes) to mold the structure, it was possible to shift a given natural frequency without affecting the other frequencies (to increase the fundamental frequency or to create band gaps) and to place the natural frequencies at given desired values [15].…”

Section: Introductionmentioning

confidence: 99%

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Linearization of embedded patterns for optimization of structural natural frequencies

Nicoletti

2019

J Braz. Soc. Mech. Sci. Eng.

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The dynamic characteristics of structures (beams and plates) can be significantly changed by embossing small out-of-plane patterns in these structures. Recent results in literature show, both numerically and experimentally, that shaping a beam in the geometry of its first mode shape significantly increases the value of the first natural frequency of the beam. This phenomenon also occurs when the beam is shaped in the geometry of other mode shapes, and in the case of plates. This work presents new results (numerical and experimental) regarding the linearization of the forms to be imposed to the structure, focusing on shapes composed of straight regions, which would ease the design of stamping tools for example. The results show that the use of straight regions in the geometry of the beams (linear embossed pattern) has a similar effect to that obtained with curved shapes but requiring bigger distances to the baseline (higher shaping deformations). It is also shown that the linearized shapes can be used to optimize the shape of a beam for desired natural frequencies.

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“…However, eigenvectors only give relative displacements. Hence, I can adopt the scale defined in [15]: the maximum distance of the beam to the baseline ( max in Fig. 3).…”

Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Mathematical Model Of the Shaped Beammentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Linearization of embedded patterns for optimization of structural natural frequencies

Nicoletti

2019

J Braz. Soc. Mech. Sci. Eng.

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Isogeometric configuration design optimization of three-dimensional curved beam structures for maximal fundamental frequency

Choi

Kim

Koo

et al. 2021

Struct Multidisc Optim

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This paper presents a configuration design optimization method for three-dimensional curved beam built-up structures having maximized fundamental eigenfrequency. We develop the method of computation of design velocity field and optimal design of beam structures constrained on a curved surface, where both designs of the embedded beams and the curved surface are simultaneously varied during the optimal design process. A shear-deformable beam model is used in the response analyses of structural vibrations within an isogeometric framework using the NURBS basis functions. An analytical design sensitivity expression of repeated eigenvalues is derived. The developed method is demonstrated through several illustrative examples.

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Power Spectral Density of Defect Beams Under a Moving Load

Nguyen

2021

Iran J Sci Technol Trans Civ Eng

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Optimization of natural frequencies of a slender beam shaped in a linear combination of its mode shapes

Cited by 11 publications

References 16 publications

Linearization of embedded patterns for optimization of structural natural frequencies

Linearization of embedded patterns for optimization of structural natural frequencies

Isogeometric configuration design optimization of three-dimensional curved beam structures for maximal fundamental frequency

Power Spectral Density of Defect Beams Under a Moving Load

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