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RESEARCH PAPERS

# A Topology Optimization Problem in Control of Structures Using Modal Disparity

[+] Author and Article Information
A. R. Diaz1

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226diaz@egr.msu.edu

R. Mukherjee

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226mukherji@egr.msu.edu

For simplicity of exposition, bending in only one plane is shown here. The model, however, accounts for bending in two planes.

1

Corresponding author.

J. Mech. Des 128(3), 536-541 (Jul 20, 2005) (6 pages) doi:10.1115/1.2181603 History: Received February 22, 2005; Revised July 20, 2005

## Abstract

Modal disparity and a topology optimization problem seeking to maximize this disparity are introduced, with the goal of developing a new methodology for control of vibration in flexible structures. Modal disparity is generated in a structure by the application of external forces that vary the stiffness of the structure. When the forces are switched on and off and, as a result, the structure is switched between two stiffness states, modal disparity results in vibration energy being transferred from a set of not-controlled modes to a set of controlled modes. This allows the vibration of the structure to be completely attenuated by removing energy only from a small set of controlled modes. A topology optimization problem determines the best locations for application of the external forces. Simulation results are presented to demonstrate control of vibration exploiting modal disparity in two three-dimensional (3D) frame structures.

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## Figures

Figure 1

Structure and potential locations for cable system. Cables are shown as thick lines.

Figure 2

Structure and cable system solution of Example 1

Figure 3

Decay of energy in not-controlled modes in Example 1 after 20 on/off cable tension switches

Figure 4

Another local optimum solution of Example 1

Figure 5

Structure (a), ground cable structure (b), and optimal cable system (c) of Example 2

Figure 6

Decay of energy in not-controlled modes in Example 2 after 20 on/off cable tension switches

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