Minimizing the acoustic coupling of fluid loaded plates using topology optimization

Title of Document: MINIMIZING THE ACOUSTIC COUPLING OF FLUID LOADED PLATES USING TOPOLOGY OPTIMIZATION Khalid H. Almitani, Doctor of Phelosophy, 2009 Directed By: Professor Amr Baz, Department of Mechanical Engineering, A. James Clark School of Engineering Optimization of the topology of a plate coupled with an acoustic cavity is investigated in an attempt to minimize the fluid-structure interactions at different structural frequencies. A mathematical model is developed to simulate such fluid-structure interactions based on the theory of finite elements. The model is integrated with a topology optimization approach which utilizes the Moving Asymptotes Method. The obtained results demonstrate the effectiveness of the proposed approach in simultaneously attenuating the structural vibration and the sound pressure inside the acoustic domain at several structural frequencies by proper redistribution of the plate material. Prototypes of plates with optimized topologies are manufactured at tested to validate the developed theoretical model. The performance characteristics of plates optimized for different frequency ranges are determined and compared with the theoretical predictions of the developed mathematical model. A close agreement is observed between theory and experiments. The presented topology optimization approach can be an invaluable tool in the design of a wide variety of critical structures which must operate quietly when subjected to fluid loading. MINIMIZING THE ACOUSTIC COUPLING OF FLUID LOADED PLATES USING TOPOLOGY OPTIMIZATION

[1]  M. Bendsøe.  Optimal shape design as a material distribution problem , 1989 .

[2]  J. Fonseca,et al.  Complexity control in the topology optimization of continuum structures , 2003 .

[3]  Ole Sigmund,et al.  A 99 line topology optimization code written in Matlab , 2001 .

[4]  Jakob S. Jensen,et al.  On maximal eigenfrequency separation in two-material structures: the 1D and 2D scalar cases , 2006 .

[5]  Christian Zillober.  A globally convergent version of the method of moving asymptotes , 1993 .

[6]  Jeawon Lee,et al.  Topology optimization for the radiation and scattering of sound from thin-body using genetic algorithms , 2004 .

[7]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[8]  T. W. Wu,et al.  Numerical modeling of acoustic radiation and scattering from thin bodies using a Cauchy principal integral equation , 1992 .

[9]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[10]  C. Jog.  Topology design of structures subjected to periodic loading , 2002 .

[11]  Jakob S. Jensen,et al.  Topology optimization of acoustic–structure interaction problems using a mixed finite element formulation , 2007 .

[12]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[13]  Martin P. Bendsøe,et al.  Optimization of Structural Topology, Shape, And Material , 1995 .

[14]  Dongwoo Sheen,et al.  Checkerboard‐free topology optimization using non‐conforming finite elements , 2003 .

[15]  Malcolm J. Crocker,et al.  Handbook of Acoustics , 1998 .

[16]  M. P. Bendsøe,et al.  Optimization of material properties for improved frequency response , 1994 .

[17]  M. Zhou,et al.  Checkerboard and minimum member size control in topology optimization , 2001 .

[18]  Kai-Uwe Bletzinger,et al.  Extended method of moving asymptotes based on second-order information , 1993 .

[19]  J. Petersson,et al.  Slope constrained topology optimization , 1998 .

[20]  Qin Ni.  A globally convergent method of moving asymptotes with trust region technique , 2003, Optim. Methods Softw..

[21]  Niels Olhoff,et al.  Topology and Reinforcement Layout Optimization of Disk, Plate, and Shell Structures , 1997 .

[22]  C. Fleury.  First and second order convex approximation strategies in structural optimization , 1989 .

[23]  N. Olhoff,et al.  Optimum topology and reinforcement design of disk and plate structures with multiple stiffness and eigenfrequency objectives , 1999 .

[24]  Niels Olhoff,et al.  Minimization of sound radiation from vibrating bi-material structures using topology optimization , 2007 .