Summary
Mechanical models for non-linear dynamic systems are defined by differential equations of second order where frequently also first order differential equations are present. Differential equations of first order occur if some degrees of freedom have no corresponding mass, if the stiffness parameters vanish in some of the equations or if a controller is implemented in the system. For linear systems of first and second order various numerical procedures for solving the differential equations are available. A semi- analytical method is presented which is exact for the linear dynamic and decoupled systems of first and second order. A modal transformation of the partitioned system equations is necessary for each part. After a discretization in the time-domain the relevant equations for a suitable and effective time-integration algorithm are defined taking non-linearity and the variable mass into account. The resulting procedure is derived and it turns out that the formulation is analogous to a BEM-formulation in time as Green functions are used. The method is extended to coupled non-linear differential equations of first and second order and is applied to a system with two degrees of freedom having time-periodic mass.
