DYNAMIC ANALYSIS OF STRUCTURES WITH UNILATERAL CONSTRAINTS - NUMERICAL-INTEGRATION AND REDUCTION OF STRUCTURAL EQUATIONS

Structural dynamic equations with unilateral constraints upon the displacements, velocities and accelerations are employed in order to represent vibrating elastic structures with normal, oblique impact and friction interaction points. For obtaining a numerical integration scheme the Lagrange multipliers and a minimum work approach are employed at each time step. The algorithm is presented as an extension of the generalized Newmark scheme. It seems to retain the asymptotic features of the original one. The reduction of the number of dynamic degrees of freedom of the unilaterally constrained structures is carried out by representing the equations of motion in modal co-ordinates of the unconstrained structure and truncating the dynamic contributions of higher modes. The presented techniques have been verified by investigating free longitudinal vibroimpact motion laws of an elastic vibroconverter and free longitudinal and bending vibration of a vibroconverter interacting with a moving rigid body by oblique impact and friction forces.