vibration control. Several application areas for friction damped systems due to mechanical joints and connections like shells and beams with friction boundaries are presented. This review article includes 134 references. 3. A. Schmidt and L. Gaul: Finite Element Formulation of Viscoelastic Constitutive Equations Using Fractional Time Derivatives Nonlinear Dynamics 29, 37-55, 2002 Fractional time derivatives are used to deduce a generalization of viscoelastic constitutive equations of differential operator type. These so-called fractional constitutive equations result in improved curve-fitting properties, especially when experimental data from long time intervals or spanning several frequency decades need to be fitted. Compared to integer-order time derivative concepts less parameters are required. In addition, fractional constitutive equations lead to causal behavior and the concept of fractional derivatives can be physically justified providing a foundation of fractional constitutive equations. First, threedimensional fractional constitutive equations based on the Gru¨nwaldian formulation are derived and their implementation into an elastic FE code is demonstrated. Then, parameter identifications for the fractional 3-parameter model in the time domain as well as in the frequency domain are carried out and compared to integerorder derivative constitutive equations. As a result the improved performance of fractional constitutive equations becomes obvious. Finally, the identified material model is used to perform an FE time stepping analysis of a viscoelastic structure. 4. L. Gaul and M. Schanz: A comparative study of three boundary element approaches to calculate the transient response of viscoelastic solids with unbounded domains Comput. Methods Appl. Mech. Engrg. 179 (1999), 111-123 As an alternative to domain discretization methods, the boundary element method (BEM) provides a powerful tool for the calculation of dynamic structural response in frequency and time domain. Field equations of motion and boundary conditions are cast into boundary integral equations (BIE), which are discretized only on the boundary. Fundamental solutions are used as weighting functions in the BIE which fulfil the Sommerfeld radiation condition, i.e., the energy radiation into a surrounding medium is modelled correctly. Therefore, infinite and semi-infinite domains can be effectively treated by the method. The soil represents such a semi-infinite domain in soil-structure-interaction problems. The response to vibratory loads superimposed to static pre-loads can often be calculated by linear viscoelastic constitutive equations. Conventional viscoelastic constitutive equations can be generalized by taking fractional order time derivatives into account. In the present paper two time domain BEM approaches including generalized viscoelastic behaviour are compared with the Laplace domain BEM approach and subsequent numerical inverse transformation. One of the presented time domain approaches uses an analytical integration of the elastodynamic BIE in a time step. Viscoelastic constitutive properties are introduced after Laplace transformation by means of an elasticviscoelastic correspondence principle. The transient response is obtained by inverse transformation in each 24
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