Modal synthesis when modeling damping by use of fractional derivatives

The fractional derivative damping model and some of its properties are discussed, Small problems involving fractional derivatives may be solved in the Fourier domain. Here modal synthesis is used to solve the equations of motion in the time domain. A state-space vector containing fractional derivatives of the displacements is then introduced, and the system of equations is expanded. The resulting system of equations is decoupled by use of the complex eigenvectors of the system, The solutions of the decoupled equations are superposed, weighted by the eigenmodes, to give the response of the structure, The computational effort can be reduced by taking into account some of the properties of the system.