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Research Papers: Design Automation

Optimal Design of Vibrating Systems Through Partial Eigenstructure Assignment

[+] Author and Article Information
Roberto Belotti

Dipartimento di Tecnica e Gestione
dei Sistemi Industriali,
Università degli Studi di Padova,
Stradella S. Nicola 3,
Vicenza 36100, Italy
e-mail: belotti@gest.unipd.it

Dario Richiedei

Dipartimento di Tecnica e Gestione
dei Sistemi Industriali,
Università degli Studi di Padova,
Stradella S. Nicola 3,
Vicenza 36100, Italy
e-mail: dario.richiedei@unipd.it

Alberto Trevisani

Dipartimento di Tecnica e Gestione
dei Sistemi Industriali,
Università degli Studi di Padova,
Stradella S. Nicola 3,
Vicenza 36100, Italy
e-mail: alberto.trevisani@unipd.it

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received October 16, 2015; final manuscript received April 18, 2016; published online May 16, 2016. Assoc. Editor: Kazuhiro Saitou.

J. Mech. Des 138(7), 071402 (May 16, 2016) (8 pages) Paper No: MD-15-1710; doi: 10.1115/1.4033505 History: Received October 16, 2015; Revised April 18, 2016

This paper proposes an inverse structural modification method for eigenstructure assignment (EA), which allows to assign the desired mode shapes only at the parts of interest of the system. The presence of unimposed eigenvector entries leads to a nonconvex problem. Therefore, to boost the convergence to a global optimal solution, a homotopy optimization strategy is implemented based on the convex approximation of the cost function. Such a relaxation is performed through some auxiliary variables and through the McCormick's relaxation of the occurring bilinear terms. The approach handles general assignment tasks, with an arbitrary number of modification parameters and prescribed eigenpairs.

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References

Figures

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Fig. 3

A 39dof model of the vibratory feeder

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Fig. 4

Mode shape at 40 Hz of the modified vibratory feeder

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Fig. 5

Mode shape at 40.135 Hz of the unmodified vibratory feeder

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Fig. 6

Convergence of the method in the second test-case

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Fig. 1

Model of the 5dof test-case

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