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New developments in a method of modeling frequency-dependent material damping and modulus in structural dynamics analysis are reported. The fundamental feature of the general method is the introduction of augmenting thermodynamic fields (ATF) to interact with the mechanical displacement field of continuum mechanics. These ATF are directly motivated by the “internal state variables” of materials science. The coupled partial differential equations that govern the dynamic behavior of a uniaxial rod are numerically solved within the computational framework of the finite element method, resulting in “ATF-damped” finite elements. Previous work in the development of this modeling technique is characterized by the use of a single augmenting field, with application to lightly-damped rods, beams, and truss structures. New developments include: (1) demonstration of the ability to model the behavior of high-damping materials; and (2) the use of multiple augmenting fields to model materials whose behavior departs significantly from that of standard anelastic solids.
frequency-dependent material damping, uniaxial finite element analysis, anelasticity, internal state variables, viscoelasticity, complex modulus, material damping, internal friction, mechanical properties
Assistant professor of Aerospace Engineering, The Pennsylvania State University, University Park, PA