Simultaneous optimal design of structural topology, actuator locations and control parameters for a plate structure |
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Authors: | Y Zhu J Qiu H Du J Tani |
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Affiliation: | (1) Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, Japan 980-8577, JP;(2) School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, SG |
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Abstract: | Simultaneous optimization with respect to the structural topology, actuator locations and control parameters of an actively
controlled plate structure is investigated in this paper. The system consists of a clamped-free plate, a H
2 controller and four surface-bonded piezoelectric actuators utilized for suppressing the bending and torsional vibrations
induced by external disturbances. The plate is represented by a rectangular design domain which is discretized by a regular
finite element mesh and for each element the parameter indicating the presence or absence of material is used as a topology
design variable. Due to the unavailability of large-scale 0–1 optimization algorithms, the binary variables of the original
topology design problem are relaxed so that they can take all values between 0 and 1. The popular techniques in the topology
optimization area including penalization, filtering and perimeter restriction are also used to suppress numerical problems
such as intermediate thickness, checkerboards, and mesh dependence. Moreover, since it is not efficient to treat the structural
and control design variables equally within the same framework, a nested solving approach is adopted in which the controller
syntheses are considered as sub processes included in the main optimization process dealing with the structural topology and
actuator locations. The structural and actuator variables are solved in the main optimization by the method of moving asymptotes,
while the control parameters are designed in the sub optimization processes by solving the Ricatti equations. Numerical examples
show that the approach used in this paper can produce systems with clear structural topology and high control performance.
Received 16 November 2001 / Accepted 26 February 2002 |
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Keywords: | Simultaneous optimization Structural topology Vibration control |
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