Title page for ETD etd-04152011-140601


Type of Document Dissertation
Author Martin, Luke Andrew
URN etd-04152011-140601
Title A Novel Material Modulus Function for Modeling Viscoelastic Materials
Degree PhD
Department Mechanical Engineering
Advisory Committee
Advisor Name Title
Inman, Daniel J. Committee Chair
Ahmadian, Mehdi Committee Member
Kasarda, Mary E. F. Committee Member
Wicks, Alfred L. Committee Member
Yagla, Jon J. Committee Member
Keywords
  • Sorbothane
  • sandwich beam
  • modal
  • viscoelastic
  • complex modulus
  • material modulus function
  • damping
  • GHM
  • MGHM
Date of Defense 2011-04-01
Availability unrestricted
Abstract
Accurately modeling damping in engineering structures has plagued scientist and engineers for decades. The integration of viscoelastic materials into engineering structures can reduce undesired vibrations and serve as an effective passive control mechanism. Various techniques have been developed to model viscoelastic materials. The growing popularity of finite element analysis in the 1980s and 1990s spawned new techniques for modeling damping in complex structures. The technique defined in this dissertation can be incorporated into finite element models.

In metals, the modulus of elasticity can be modeled as a constant. That is, the modulus of elasticity is not treated as a function of frequency in dynamic models. For viscoelastic materials, the modulus of elasticity can be assumed to be constant for static forces and sinusoidal forcing functions. However, when viscoelastic materials undergo excitations from a random or transient forcing function the constant modulus of elasticity assumption may not be valid. This is because the second order equation of motion has non-constant coefficients or coefficients that vary as a function of frequency.

The Golla-Hughes-McTavish (GHM) method is a technique used to incorporate the frequency dependency of viscoelastic materials into finite element models. The GHM method is used as a way to alleviate working with second order differential equations with non-constant coefficients.

This dissertation presents the theory for a new material modulus function suitable for application within the framework of the GHM method. However, the new material modulus function uses different assumptions and is referred to as the Modified GHM method or MGHM method. The MGHM method is shown to improve the curve fit and damping characteristics of the GHM method. Additionally, the MGHM method is shown to reduce to the GHM method when the original GHM assumptions are imposed.

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