On the example of the beams, the dynamics of systems with unilateral constraints are considered. The algorithm for calculating such systems as a combination of the step method of Newmark and the Lemke algorithm that determines the work scheme of the beam in each time step is proposed. Model tasks are considered with a harmonic exciting force, suddenly applied force, impulse exposure. The numerical convergence of the solution was investigated during the thickening of the temporary grid. It is shown that the accuracy of the solution significantly depends on the determination of the moment of changing the working schemes, since the error of the solution increases with an increase in the events “inclusion/off” of unilateral constraints.

Keywords: constructive nonlinearity, unilateral constraints, linear complementary problem, Lemke's algorithm, structural dynamics, Newmark's method