Abstract
A homogenized modeling technique is developed in this paper to account for viscous damping properties in beam-like lattice structures of repeated patterns. Necessary assumptions regarding the local free deformations, shear deformation beam theory, and compatibility conditions are made to obtain an equivalent continuum model of a three-dimensional lattice. A dissipated energy equivalence approach is then used to relate the energy dissipation for a general case of damping matrix in a lattice element to an equivalent proportionally damped model. As a result, a continuum model with Kelvin–Voigt damping is obtained. Damped bending natural frequencies, frequency response functions, and damping ratios are found using this method and compared to the results of a finite-element analysis for several structures for the purpose of validation.
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