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Dynamic analysis of structures with unilateral constraints: Numerical integration and reduction of structural equations
Author(s) -
Barauskas Rimantas
Publication year - 1994
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620370209
Subject(s) - oblique case , reduction (mathematics) , lagrange multiplier , equations of motion , newmark beta method , mathematics , degrees of freedom (physics and chemistry) , dynamic problem , vibration , numerical integration , bending , modal , work (physics) , dynamic equation , rigid body , mathematical analysis , finite element method , classical mechanics , structural engineering , geometry , mathematical optimization , physics , engineering , nonlinear system , philosophy , linguistics , chemistry , quantum mechanics , polymer chemistry , thermodynamics
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.