KELVIN VISCOELASTICITY AND LAGRANGE MULTIPLIERS APPLIED TO THE SIMULATION OF NON-LINEAR STRUCTURAL VIBRATION CONTROL

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RAPHAEL HENRIQUE MADEIRA
HUMBERTO BREVES CODA

Abstract

THIS STUDY PROPOSES A NEW WAY TO MODEL THE MASS / SPRING / DAMPER DEVICES TO CONTROL THE VIBRATION OF TRUSS STRUCTURES DEVELOPING LARGE DISPLACEMENTS. THE STRUCTURE IS MODELED BY THE GEOMETRICALLY EXACT FINITE ELEMENT METHOD BASED ON POSITIONS. THE INTRODUCTION OF THE DEVICE'S MASS IS MADE BY MEANS OF LAGRANGE MULTIPLIERS THAT IMPOSES ITS MOVEMENT ALONG THE STRAIGHT LINE OF A FINITE ELEMENT. A KELVIN/VOIGT LIKE RHEOLOGICAL MODEL CAPABLE OF NON LINEAR LARGE DEFORMATIONS IS ORIGINALLY PROPOSED AND SOLVED ALONG TIME TO ACCOMPLISH THE DAMPING PARAMETERS OF THE DEVICE. EXAMPLES ARE SOLVED TO VALIDATE THE FORMULATION AND TO SHOW THE POSSIBILITIES OF THE PROPOSED TECHNIQUE

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