Author(s)

E. Simson & A. Taranukha

Abstract

Shape optimization of large ultrasonic tools E. Simson, A. Taranukha Applied Mathematics Department, Kharkov Polytechnic Institute, Ukraine A method for modal vibration control of large ultrasonic tools whose shapes are adopted in pi astic ,weldi ng usi ng or i gi nal shape optimization technique and special finite element code is proposed. The design problem is to minimize deviation from uniform amplitude distribution at the radiating face of the tool required for fine and uniform finish of weldment while resonance frequency and amplification factor criterions are satisfied. The mathematical analysis of ultrasonic tools is based on the use of three- dimensional finite element model and on the application of the Block Lanczos algorithm to the generalized symmetric eigenproblem. The nodal positions are used as design parameters. The design se

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