The equations of motion of structures with elastic and linear viscoelastic materials in the time domain are derived. The approach leads to a system of equations where the matrices are symmetric, real, and composed of constant coefficients. A four-parameter fractional derivative model is used to model the frequency dependence of the linear viscoelastic material since experimental data can be fitted successfully over a wide frequency range. The resulting equations of motion are the fractional order elastic-viscoelastic equations of motion. The closed-form, steady state solution of a single degree of freedom system is obtained in the frequency domain and is used to compare the results obtained by using numerical procedures. The proper selection of the stiffness for viscoelastic dampers placed in elastic structural systems is discussed in order to ensure that the damper is effective in reducing dynamic amplification of the structure.
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