Dynamic analysis of structures with unilateral constraints: Numerical integration and reduction of structural equations. (English) Zbl 0795.73043
Structural dynamic equations with unilateral constraints upon the displacements, velocities and accelerations are employed in order to represent vibrating elastic structures with normal and 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 coordinates of the unconstrained structure and truncating the dynamic contributions of higher modes.
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 coordinates of the unconstrained structure and truncating the dynamic contributions of higher modes.
MSC:
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
elastic vibroconverter; vibrating elastic structures; impact; friction interaction; Lagrange multipliers; minimum work approach; generalized Newmark scheme; modal coordinatesReferences:
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