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Mini-Oscillator Technique: A Finite Element Method for the Modeling of Linear Viscoelastic Structures

机译：微型振荡技术：线性粘弹性结构建模的有限元方法

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摘要

The use of finite elements to model complex structures has been traditionally effective with regard to mass properties and equilibrium elastic stiffness properties. A practical formulation is presented for the analysis of structures whose constituent materials may be classed as linear viscoelastic. Construction of viscoelastic finite element matrices fully compatible with the usual second order equations of motion is demonstrated, given a knowledge of material properties. The viscoelastic material properties are represented in the Laplace domain by the Golla-Hughes-McTavish (GHM) Analytic Model. The Mini-Oscillator Technique is introduced and developed through the consideration of a single modulus finite element for which the mass and elastic stiffness matrices are known. The simplest case of a single degree of freedom finite element is examined in detail to expose a mechanical analogy from which the Mini-Oscillator Technique derives its name. The procedure is then extended to the case of a general structural model with many elements. Each finite element may be of a different material with stiffness properties ranging between simple elastic and multi modulus viscoelastic.

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