A dynamic Lagrangian frequency–time method for the vibration of dry-friction-damped systems

• Published in: Journal of sound and vibration Vol. 265; no. 1; pp. 201 - 219
• Main Authors: Nacivet, S, Pierre, C, Thouverez, F, Jezequel, L
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 31.07.2003; Elsevier
• Subjects: Applied sciences; Civil Engineering; Computational techniques; Dynamique, vibrations; Engineering Sciences; Exact sciences and technology; Finite-element and galerkin methods; Friction, wear, lubrication; Fundamental areas of phenomenology (including applications); Machine components; Mathematical methods in physics; Mechanical engineering; Mechanical engineering. Machine design; Mechanics; Physics; Solid mechanics; Structural and continuum mechanics; Structural mechanics; Structures; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations; Vibrations and mechanical waves; Lagrangian; Vibration; Equation of motion; Time frequency domain method; Numerical method; Modeling; Mixed method; Steady state; Dry friction; Finite element method; Vibration damping; Turbine blade; Non linear effect; Structural analysis
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/S0022-460X(02)01447-5

A new frequency–time domain procedure, the dynamic Lagrangian mixed frequency–time method (DLFT), is proposed to calculate the non-linear steady state response to periodic excitation of structural systems subject to dry friction damping. In this formulation, the dynamic Lagrangians are defined as the non-linear contact forces obtained from the equations of motion in the frequency domain, with the adjunction of a penalization on the difference between the interface displacements calculate by the non-linear solver in the frequency domain and those calculated in the time domain from the non-linear contact forces, thus accounting for Coulomb friction and non-penetration conditions. The dynamic Lagrangians allow one to solve for the non-linear forces between two points in contact without using artifacts such as springs. The new DLFT method is thus particularly well suited to handling finite element models of structures in frictional contact, as it does not require a special model for the contact interface. Dynamic Lagrangians are also better suited to frequency-domain friction problems than the traditional time-domain method of augmented Lagrangians. Furthermore, a reduction of the non-linear system to relative interface displacements is introduced to decrease the computation time. The DLFT method is validated for a beam in contact with a flexible dry friction element connected to ground, for frictional constraints that feature two-dimensional relative motion. Results are also obtained for a large-scale structural system with a large number of one-dimensional dry-friction dampers. The DLFT method is shown to be accurate and fast, and it does not suffer from convergence problems, at least in the examples studied.