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Precise energy decay rates for some viscoelastic and thermo-viscoelastic rods.

机译：某些粘弹性和热粘弹性棒的精确能量衰减率。

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摘要

Energy dissipation in systems with linear viscoelastic damping is examined. It is shown that in such viscoelastically damped systems the use of additional dissipation mechanisms (such as boundary velocity feedback or thermal coupling) may not improve the rate of energy decay. The situation where the viscoelastic stress relaxation modulus decreases to its (positive) equilibrium modulus at a subexponential rate, e.g., like {dollar}(1+t)sp{lcub}-alpha{rcub}+E,{dollar} where {dollar}alpha>0, E>0{dollar} is examined. In this case, the nonoscillatory modes (the so-called creep modes) dominate the energy decay rate. The results are in two parts.; In the first part, a linear viscoelastic wave equation with infinite memory is examined. It is shown that under appropriate conditions on the kernel and initial history, the total energy is integrable against a particular weight if the kinetic energy component of the total energy is integrable against the same weight. The proof uses energy methods in an induction argument. Precise energy decay rates have recently been obtained using boundary velocity feedback. It is shown that the same decay rates hold for history value problems with conservative boundary conditions provided that an a priori knowledge of the decay rate of the kinetic energy term is assumed.; In the second part, a simple linear thermo-viscoelastic system, namely, a viscoelastic wave equation coupled to a heat equation, is examined. Using Laplace transform methods, an integral representation formula for W(x,s), the transform of the displacement w(x,t), is obtained. After analyzing the location of the zeros of the appropriate characteristic equation, an asymptotic expansion for the displacement w(0,t) is obtained which is valid for large t and the specific kernel {dollar}g(t)=g(infty)+{lcub}delta tsp{lcub}eta-1{rcub}overGamma(eta){rcub}, 0
机译：研究了具有线性粘弹性阻尼的系统中的能量耗散。结果表明，在这种粘弹性阻尼系统中，使用其他耗散机制（例如边界速度反馈或热耦合）可能不会提高能量衰减率。粘弹性应力松弛模量以次指数速率降低至其（正）平衡模量的情况，例如{dollar}（1 + t）sp {lcub} -alpha {rcub} + E，{dollar} } alpha> 0，E> 0 {dollar}被检查。在这种情况下，非振荡模式（所谓的蠕变模式）主导着能量衰减率。结果分为两部分。在第一部分中，研究了具有无限记忆力的线性粘弹性波动方程。结果表明，在适当的条件下，在籽粒和初始历史记录下，如果总能量的动能分量对于相同的重量是可积分的，则总能量对于特定的重量是可积分的。该证明在归纳论证中使用能量方法。最近已经使用边界速度反馈获得了精确的能量衰减率。结果表明，对于具有保守边界条件的历史值问题，只要假设对动能项的衰减率具有先验知识，则衰减率相同。在第二部分中，研究了简单的线性热粘弹性系统，即与热方程耦合的粘弹性波动方程。使用拉普拉斯变换方法，获得了W（x，s）的积分表示公式，即位移w（x，t）的变换。在分析了适当的特征方程零点的位置之后，获得了位移w（0，t）的渐近展开式，该展开式对于大t和特定核{dol} g（t）= g（infty）+有效{lcub} delta tsp {lcub} eta-1 {rcub} overGamma（eta）{rcub}，0

著录项

  • 作者

    Inch, Scott Eugene.;

  • 作者单位

    Virginia Polytechnic Institute and State University.;

  • 授予单位 Virginia Polytechnic Institute and State University.;
  • 学科 Mathematics.; Physics General.; Applied Mechanics.
  • 学位 Ph.D.
  • 年度 1992
  • 页码 76 p.
  • 总页数 76
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 数学;物理学;应用力学;
  • 关键词

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