Modal superposition of non-classically damped transient problems with position and velocity dependent force

The approach to the solution of transient problems of the semidefinite systems with non-classical damping and force dependent on time, position and velocity is proposed and implemented. It provides reliable, efficient and accurate solution algorithm without blurring the physical meaning. Problem matrix is constant even the problem is nonlinear, its inversion is trivial, and order is controllable. The price is solution of the eignproblem and transformations between natural and principal coordinates. However, in spite of the iterative procedure, modal approach is proved to be highly efficient with maximum two tightening iteration per step for given integration parameters, practically independently on the integration scheme involved. The contribution is illustrated on the theoretical and practical examples. The proposed procedure eliminates nonphysical behaviour of the semidefinite problems under reactive force e.g. as in the ship power propulsion system under ice conditions when simulating long lasting ice impact conditions.