Stick-slip and wear phenomena at the contact interface between an elastic beam and a rigid substrate

2020 ◽  
pp. 108128652097167
Author(s):  
Francesco D’Annibale ◽  
Arnaldo Casalotti ◽  
Angelo Luongo
Keyword(s):  
A Priori ◽  
Constitutive Models ◽  
Elastic Beam ◽  
Longitudinal Direction ◽  
Static Problem ◽  
Rigid Substrate ◽  
Equilibrium Equations ◽  
Stick Slip ◽  
Contact Points ◽  
Nonlinear Constitutive Models

In this paper, the static behavior of an elastic beam resting on a rigid substrate is investigated. The structure lies on a rigid substrate and exchanges with it tangential forces, in correspondence with a finite number of contact points. These actions entail extension of the beam in the longitudinal direction together with a negligible bending, owing to the small eccentricity between the beam’s axis line and the rigid substrate. The beam obeys a linear elastic law, while, at the interface, different nonlinear constitutive models are considered to account for stick-slip phenomena due to friction, as well as wear due to abrasion. It is assumed that the contact points are a-priori known, thus entailing that the structural system can be treated as naturally discrete. The static problem is accordingly shown to be governed by a system of nonlinear ordinary differential equations in time, which rules, in incremental form, the equilibrium at the contact points in the longitudinal direction. A numerical solution for the equilibrium equations is carried out, under different imposed time histories of the longitudinal displacement assigned at the boundary. Numerical results are presented to compare and discuss the in-time evolution of the contact interactions between the beam and the substrate.

scholarly journals Friction-induced vibrations in the framework of dynamic substructuring

2020 ◽  
Author(s):  
Jacopo Brunetti ◽  
Walter D’Ambrogio ◽  
Annalisa Fregolent
Keyword(s):  
A Priori ◽  
Element Model ◽  
Friction Forces ◽  
Coupling Conditions ◽  
Contact Points ◽  
Dynamic Substructuring ◽  
Reliable Model ◽  
Time Invariant ◽  
Substructuring Techniques ◽  
Vibrating Systems

AbstractIn complex vibrating systems, contact and friction forces can produce a dynamic response of the system (friction-induced vibrations). They can arise when different parts of the system move one with respect to the other generating friction force at the contact interface. Component mode synthesis and more in general substructuring techniques represent a useful and widespread tool to investigate the dynamic behavior of complex systems, but classical techniques require that the component subsystems and the coupling conditions (compatibility of displacements and equilibrium of forces) are time invariant. In this paper, a substructuring method is proposed that, besides accounting for the macroscopic sliding between substructures, is able to consider also the local vibrations of the contact points and the geometric nonlinearity due to the elastic deformation, by updating the coupling conditions accordingly. This allows to obtain a more reliable model of the contact interaction and to analyze friction-induced vibrations. Therefore, the models of the component substructures are time invariant, while the coupling conditions become time dependent and a priori unknown. The method is applied to the study of a finite element model of two bodies in frictional contact, and the analysis is aimed to the validation of the proposed method for the study of dynamic instabilities due to mode coupling.

Nonlinear Finite Element Analysis for Thermoplastic Pipes

1998 ◽  
Vol 1624 (1) ◽  
pp. 225-230 ◽  
Author(s):  
Chuntao Zhang ◽  
Ian D. Moore
Keyword(s):  
Finite Element ◽  
Geometrical Nonlinearity ◽  
Constitutive Models ◽  
Material Behavior ◽  
Pipe Material ◽  
Limit States ◽  
Element Analysis ◽  
Finite Element Program ◽  
Highly Nonlinear ◽  
Nonlinear Constitutive Models

Thermoplastic pipes are being used increasingly for water supply lines, storm sewers, and leachate collection systems in landfills. To facilitate limit states design for buried polymer pipes, nonlinear constitutive models have recently been developed to characterize the highly nonlinear and time-dependent material behavior of high-density polyethylene (HDPE). These models have been implemented in a finite element program to permit structural analysis for buried HDPE pipes and to provide information regarding performance limits of the structures. Predictions of HDPE pipe response under parallel plate loading and hoop compression in a soil cell are reported and compared with pipe response measured in laboratory tests. Effects on the structural performance of pipe material nonlinearity, geometrical nonlinearity, and backfill soil properties were investigated. Good correlations were found between the finite element predictions and the experimental measurements. The models can be used to predict pipe response under many different load histories (not just relaxation or creep). Work is ongoing to develop nonlinear constitutive models for polyvinylchloride and polypropylene to extend the predictive capability of the finite element model to these materials.

Friction Induced Brake Vibrations at Low Speeds: Experiments, State-Space Reconstruction and Implications on Modeling

2006 ◽  
Author(s):  
Hartmut Hetzler ◽  
Wolfgang Seemann
Keyword(s):  
Classical Model ◽  
A Priori ◽  
Experimental Studies ◽  
Low Frequency ◽  
Disc Brake ◽  
Minimal Models ◽  
Stick Slip ◽  
Cast Doubt ◽  
Vibration Pattern ◽  
Embedding Methods

Today, low frequency disc-brake noises are commonly explained as self-sustained stick-slip oscillations. Although, at a first glance this explanation seems reasonable, there are indices that cast doubt on it. For instance, the basic frequency of the observed oscillations does not scale with the disc-speed as it is with stick-slip oscillations and the classical model does not explain the observed ending of the vibrations beyond a certain speed. Indeed, our experimental studies on groaning noises reveal two different vibration patterns: stick-slip vibrations at almost vanishing relative speed and a second, differing vibration pattern at low to moderate relative speeds. Yet, these two patterns produce a very similar acoustic impression. While the experiment provides a vast amount of data, the dimension and structure of the underlying oscillation is not known a priori – hence, constructing phenomenological minimal models usually must rely on assumptions, e.g. about the number of DOF, etc. Due to noise and complexity, the measured raw data did only allow for a first straight forward insight, rendering further analysis necessary. Hence, time-delay embedding methods together with a principle component analysis were used to reconstruct a pseudo-phase space together with the embedded attractor to analyse for the system's dimension and to separate signal from noise.

scholarly journals Tensile Fracture Mechanism of Masonry Wallettes Parallel to Bed Joints: A Stochastic Discontinuum Analysis

Modelling ◽  
2020 ◽  
Vol 1 (2) ◽  
pp. 78-93
Author(s):  
Bora Pulatsu ◽  
Semih Gonen ◽  
Ece Erdogmus ◽  
Paulo B. Lourenço ◽  
Jose V. Lemos ◽  
...  
Keyword(s):  
Material Properties ◽  
Fracture Mechanism ◽  
Equations Of Motion ◽  
Constitutive Models ◽  
Numerical Approach ◽  
Tensile Fracture ◽  
Fracture Mechanisms ◽  
Contact Points ◽  
Statistical Variations ◽  
Modeling Strategy

Nonhomogeneous material characteristics of masonry lead to complex fracture mechanisms, which require substantial analysis regarding the influence of masonry constituents. In this context, this study presents a discontinuum modeling strategy, based on the discrete element method, developed to investigate the tensile fracture mechanism of masonry wallettes parallel to the bed joints considering the inherent variation in the material properties. The applied numerical approach utilizes polyhedral blocks to represent masonry and integrate the equations of motion explicitly to compute nodal velocities for each block in the system. The mechanical interaction between the adjacent blocks is computed at the active contact points, where the contact stresses are calculated and updated based on the implemented contact constitutive models. In this research, different fracture mechanisms of masonry wallettes under tension are explored developing at the unit–mortar interface and/or within the units. The contact properties are determined based on certain statistical variations. Emphasis is given to the influence of the material properties on the fracture mechanism and capacity of the masonry assemblages. The results of the analysis reveal and quantify the importance of the contact properties for unit and unit–mortar interfaces (e.g., tensile strength, cohesion, and friction coefficient) in terms of capacity and corresponding fracture mechanism for masonry wallettes.

Equations of Nonlinear Motion of Viscoelastic Beams

2005 ◽  
Author(s):  
S. Nima Mahmoodi ◽  
Siamak E. Khadem ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Equations Of Motion ◽  
Elastic Beam ◽  
Longitudinal Direction ◽  
Nonlinear Damping ◽  
Equation Of Motion ◽  
Bending Vibration ◽  
Viscoelastic System ◽  
Nonlinear Beam ◽  
Nonlinear Motion ◽  
Large Amplitude Vibrations

A viscoelastic nonlinear beam with cubic nonlinearities is considered. In order to obtain the equations of nonlinear motion of the beam for large deformation vibrations, the Lagrangian dynamics and Hamilton principle is used. It is considered that the beam vibrates in two directions, one in longitudinal direction and the other in the transverse direction. Large amplitude vibrations cause the nonlinearities in inertia and geometry terms. Also, due to viscoelastic property of the beam, a nonlinear damping term is appeared in the equations of motion. Using the condition of inextensible beams, the equation of motion and boundary conditions of bending vibration of a Kelvin-Voigt viscoelastic beam has been obtained. Finally, if one considers the damping coefficient to be equal to zero in the obtained equation of motion of viscoelastic system then, an equation of motion for the elastic beam will be obtained.

scholarly journals Modelling elastic structures with strong nonlinearities with application to stick–slip friction

2014 ◽  
Vol 470 (2161) ◽  
pp. 20130593 ◽  
Author(s):  
Robert Szalai
Keyword(s):  
Point Contact ◽  
Linear Structure ◽  
Transformation Method ◽  
Friction Model ◽  
Contact Forces ◽  
Stick Slip ◽  
Lipschitz Continuous ◽  
Contact Points ◽  
Dimensional Equation ◽  
Low Dimensional

An exact transformation method is introduced that reduces the governing equations of a continuum structure coupled to strong nonlinearities to a low-dimensional equation with memory. The method is general and well suited to problems with isolated discontinuities such as friction and impact at point contact. It is assumed that the structure is composed of two parts: a continuum but linear structure and finitely many discrete but strong nonlinearities acting at various contact points of the elastic structure. The localized nonlinearities include discontinuities, e.g. the Coulomb friction law. Despite the discontinuities in the model, we demonstrate that contact forces are Lipschitz continuous in time at the onset of sticking for certain classes of structures. The general formalism is illustrated for a continuum elastic body coupled to a Coulomb-like friction model.

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