scholarly journals Nonsmooth Modal Analysis: Investigation of a 2-DOF Spring-Mass System Subject to an Elastic Impact Law

2015 ◽  
Author(s):  
Anders Thorin ◽  
Mathias Legrand ◽  
Stéphane Junca
Keyword(s):  
Modal Analysis ◽  
Autonomous System ◽  
Unilateral Contact ◽  
Unilateral Constraints ◽  
Mass System ◽  
Elastic Impact ◽  
Nonsmooth Systems ◽  
Community Of Researchers ◽  
Unilateral Contact And Friction ◽  
Nonlinear Smooth

The well-known concept of normal mode for linear systems has been extended to the framework of nonlinear dynamics over the course of the 20th century, initially by Lyapunov, and later by Rosenberg and a growing community of researchers in modal and vibration analysis. This effort has mainly targeted nonlinear smooth systems — the velocity is continuous and differentiable in time — even though systems presenting nonsmooth occurrences have been increasingly studied in the last decades to face the growing industrial need of unilateral contact and friction simulations. Yet, these systems have nearly never been explored from the standpoint of modal analysis. This contribution addresses the notion of modal analysis of nonsmooth systems. Developments are illustrated on a seemingly simple 2-dof autonomous system, subject to unilateral constraints reflected by a perfectly elastic impact law. Even though friction is ignored, its dynamics appears to be extremely rich. Periodic solutions are sought for given numbers of impacts per period and nonsmooth modes are illustrated for one and two impacts per period in the form of two-dimensional manifolds in the phase space. Also, an unexpected bridge between these modes in the frequency-energy plots is observed.

Tykhonov well-posedness of a frictionless unilateral contact problem

2019 ◽  
Vol 25 (6) ◽  
pp. 1294-1311 ◽  
Author(s):  
Zhenhai Liu ◽  
Mircea Sofonea ◽  
Yi-bin Xiao
Keyword(s):  
Contact Problem ◽  
Variational Formulation ◽  
Unilateral Contact ◽  
Well Posedness ◽  
Unilateral Constraints ◽  
The Family ◽  
Contact Models ◽  
Mechanical Interpretation ◽  
Well Posed ◽  
Natural Way

We consider a frictionless contact problem, Problem [Formula: see text], for elastic materials. The process is assumed to be static and the contact is modelled with unilateral constraints. We list the assumptions on the data and derive a variational formulation of the problem, Problem [Formula: see text]. Then we consider a perturbation of Problem [Formula: see text], which could be frictional, governed by a small parameter [Formula: see text]. This perturbation leads in a natural way to a family of sets [Formula: see text]. We prove that Problem [Formula: see text] is well-posed in the sense of Tykhonov with respect to the family [Formula: see text]. The proof is based on arguments of monotonicity, pseudomonotonicity and various estimates. We extend these results to a time-dependent version of Problem [Formula: see text]. Finally, we provide examples and mechanical interpretation of our well-posedness results, which, in particular, allow us to establish the link between the weak solutions of different contact models.

Modal Analysis of Externally Pressurized Air Bearing Workbench Based on Spring-Mass System Method

2011 ◽  
Vol 188 ◽  
pp. 602-607
Author(s):  
Bo Zhang ◽  
Ping Ma ◽  
J.J. Huang
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Nonlinear Modeling ◽  
Experimental Modal Analysis ◽  
Air Bearing ◽  
Mass System ◽  
System Method ◽  
Good Agreement

The stiffness of externally pressurized air bearing is nonlinear, so it is difficult for nonlinear modeling and modal analysis with Finite Element Modal Analysis(FEMA). In this paper, the spring-mass system method which use linear springs in place of nonlinear air bearing has been developed to make FEMA of externally pressurized air bearing workbench more easier and faster. The actual modes of the workbench have also been attained with Experimental Modal Analysis (EMA). The results of EMA have a good agreement with FEAM results ,which verifies the feasibility of spring-mass system method.

scholarly journals Thermomechanical Component Mode Synthesis for Blade Casing Interaction Prediction

2017 ◽  
Author(s):  
Nicolas Guerin ◽  
Fabrice Thouverez ◽  
Claude Gibert ◽  
Mathias Legrand ◽  
Patricio Almeida
Keyword(s):  
Thermal Stresses ◽  
Unilateral Contact ◽  
Synthesis Technique ◽  
Multiphysics Simulations ◽  
Modal Synthesis ◽  
Thermomechanical Behaviour ◽  
Mode Method ◽  
Blade Tip ◽  
Thermal Dilatation ◽  
Unilateral Contact And Friction

Increasing the efficiency of turbomachines is a major concern as it directly translates into lower environmental impact and improved operational costs. One solution is to reduce the blade-casing operating clearance in order to mitigate aerodynamic losses at the unavoidable cost of increased structural unilateral contact and friction occurrences. In centrifugal compressors, the dynamic behaviour of the structures interacting through unilateral contact and friction is not yet fully understood. In fact, the heat generated during such events may affect the dynamics through thermal stresses. This paper presents a complete thermomechanical modelling strategy of impeller rotor and casing, and of blade-tip/casing contact events. A fully coupled thermomechanical modal synthesis technique is introduced and applied to turbomachinery-related models. The blisk is reduced via a hybrid modal synthesis technique combining the Craig-Bampton method and the characteristic constraint mode method. The casing model is reduced using an axisymmetric harmonic modal synthesis. Both strategies involve thermomechanical modes embedding thermal dilatation effects. The contact modelling algorithm is then introduced. It handles unilateral contact and friction occurrences together with heating effects. This algorithm uses the above mentioned reduced-order models as input data to avoid CPU-intensive simulations. The results show that the thermomechanical behaviour of the structures is well preserved by the reduction strategy proposed. Contact simulations on simple cases show qualitative results in accordance with expectations. Further work is needed in order to validate the strategy based on experimental results. However, this methodology opens the way to extended multiphysics simulations of contact events in turbomachinery.

Fractal interfaces with unilateral contact and friction conditions

1992 ◽  
Vol 99 (2-3) ◽  
pp. 395-412 ◽  
Author(s):  
P.D. Panagiotopoulos ◽  
E.S. Mistakidis ◽  
O.K. Panagouli
Keyword(s):  
Unilateral Contact ◽  
Unilateral Contact And Friction
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