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.
Optimal Design of Vibrating Systems Through Partial Eigenstructure Assignment
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.
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Belotti, R., Richiedei, D., and Trevisani, A. (May 16, 2016). "Optimal Design of Vibrating Systems Through Partial Eigenstructure Assignment." ASME. J. Mech. Des. July 2016; 138(7): 071402. https://doi.org/10.1115/1.4033505
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