Método de otimização topológica aplicado ao projeto de sonotrodos para transdutores piezelétricos. / Topology optimization method applied to the design of transducers sonotrodos piezoelectric.

AUTOR(ES)

César Yukishigue Kiyono

DATA DE PUBLICAÇÃO

2008

RESUMO

This work aims at the development of a method based on Topology Optimization to design a mechanical structure, called sonotrode, which is a device usually connected to a high power piezoelectric transducer (mechanical device capable of converting electric energy into mechanical displacement or vice-versa). A sonotrode transmits mechanical vibrations of a piezoelectric transducer, adjusting the amplitude and the distribution of these vibrations to fit the design needs of the transducer. Among applications of piezoelectric transducers using sonotrodes, we can cite navigation sonars, ultrasonic cleaning and melting, acoustic tomography, ultrasonic drilling, ultrasonic fabric cutting, etc. The design needs of the sonotrode differs for each application, ranging from obtaining maximum displacement in one single point of its structure, to obtaining uniform displacements on a whole face of the sonotrode. To improve the attainment of the optimum result, in this work "Topology Optimization" (TO) is applied to design the sonotrode. TO is a procedure to design the optimal layout of structures by distributing material within a fixed domain. The objective of the developed TO formulation is to find the best topology of the sonotrode that produces maximum and uniform displacements at one of its face. The TO method is implemented using the "Sequential Linear Programming" (SLP) as the optimization algorithm, and it is based on the "Simple Isotropic Material with Penalization" (SIMP) interpolation for material model formulation. Its also presented a study about the material model "Rational Approximation of Material Properties" (RAMP), in an attempt to reduce numerical instabilities like localized modes. "Finite Element Method" (FEM) is applied to model the sonotrode considering piezoelectric four-node axisymmetric elements. A node-based design variable implementation for continuum structural topology optimization is presented to minimize numerical instabilities such as "checkerboard pattern". The ressonance frequencies and modes are computed through Lanczos Method. A "Modal Assurance Criterion" (MAC) based formulation is used to track a certain mode, so that, the ressonance frequency related to this mode can be optimized. Examples are presented to verify the efficiency and the generality of the proposed method, and also, a study about the influence of the optimization parameters used in the method. Finally, results that meets all the design requirements are presented, as well as their post-processed topology, and the analysis in the commercial software ANSYS®.

ASSUNTO(S)

método de lanczos simp sonotrodos para ultrassom simp método de elementos finitos piezelétrico sonotrodes for ultrasonics otimização topológica lanczos eigensolver piezoeletric finite element method ramp ramp topology optimization

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