title: Structural optimization for nonlinear dynamic response.
abstract: Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped-clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order of magnitude by relatively simple changes in the shape of these elements. We expect the proposed approach, and its extensions, to be useful for the design of systems used for fundamental studies of nonlinear behaviour as well as for the development of commercial devices that exploit nonlinear behaviour.
authors: Department of Mechanical Engineering, Technical University of Denmark, Kgs. Lyngby, Denmark.
authors: Suguang
authors: http://orcid.org/0000-0002-8136-9437
authors: S
authors: Dou
authors: Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI, USA.
authors: B Scott
authors: http://orcid.org/0000-0002-9168-369X
authors: BS
authors: Strachan
authors: Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA shawsw@msu.edu.
authors: Steven W
authors: http://orcid.org/0000-0002-3874-4828
authors: SW
authors: Shaw
authors: Department of Mechanical Engineering, Technical University of Denmark, Kgs. Lyngby, Denmark Department of Electrical Engineering, Technical University of Denmark, Kgs. Lyngby, Denmark.
authors: Jakob S
authors: http://orcid.org/0000-0001-9962-6166
authors: JS
authors: Jensen
keywords: adjoint method; internal resonance; nonlinear normal mode; normal form; shape optimization