A New Method to Find the Forced Response of Nonlinear Systems with Dry Friction

2021 ◽  
Author(s):  
Gregory L. Altamirano ◽  
Meng-Hsuan Tien ◽  
Kiran D'Souza
Keyword(s):  
Dry Friction ◽  
Coulomb Friction ◽  
Nonlinear Response ◽  
Piecewise Linear ◽  
Time Integration ◽  
Nonlinear Behavior ◽  
Forced Response ◽  
New Method ◽  
Analysis Tools ◽  
Compatibility Constraint

Abstract Coulomb friction has an influence on the behavior of numerous mechanical systems. Coulomb friction systems or dry friction systems are nonlinear in nature. This nonlinear behavior requires complex and time demanding analysis tools to capture the dynamics of these systems. Recently, efforts have been made to develop efficient analysis tools able to approximate the forced response of systems with dry friction. The objective of this paper is to introduce a methodology that assists in these efforts. In this method, the piecewise-linear nonlinear response is separated into individual linear responses that are coupled together through compatibility constraint equations. The new method is demonstrated on a number of systems of varying complexity. The results obtained by the new method are validated through the comparison with results obtained by time integration. The computational savings of the new method is also discussed.

Modeling Contact Dynamics of Vanes With Adjustable Upstream Flow Angles

2012 ◽  
Author(s):  
Daniel Schurzig ◽  
Sebastian Tatzko ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Coulomb Friction ◽  
Nonlinear Behavior ◽  
Simulation Method ◽  
Forced Response ◽  
Contact Forces ◽  
Contact Dynamics ◽  
Flow Angle ◽  
Complementarity Conditions ◽  
Time Stepping ◽  
Upstream Flow

In this paper, a simulation method is proposed for a sub-category of compressor vanes showing nonlinear behavior due to an adjustable upstream flow angle. The proposed algorithm computes the forced response of a single vane based on the New-mark time stepping scheme after reducing the structural matrices using the Craig-Bampton method. The contacts are modeled by Coulomb friction and Newton impact constraints. Contact forces are determined using linear complementarity conditions with decoupled orthogonal friction force directions. Different discretization methods for the cylindrical contact partners are proposed. Finally, numerical results are shown in order to validate the proposed algorithms.

Forced Response Analysis of Shrouded Blades by an Alternating Frequency/Time Domain Method

2006 ◽  
Author(s):  
Shi Yajie ◽  
Hong Jie ◽  
Shan Yingchun ◽  
Zhu Zigen
Keyword(s):  
Relative Motion ◽  
Time Domain ◽  
Dry Friction ◽  
Nonlinear Response ◽  
Harmonic Component ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Response Analysis ◽  
Stick Slip ◽  
Moving Contact

In turbine jet engine, the rotating blades are subjected to cyclic loading, which makes the blades experience the so-called High Cycle Fatigue (HCF). Dry friction is often employed in turbine design to attenuate the blade vibration and increase aeroclastic stability of the turbine. The dry friction dampers are often classified into four types, i.e., blade-to-blade, blade-to-ground, shrouds, and wedge damper, respectively. Compared with the under-platform dampers, shrouds make fan behavior be significantly more complex. It is very difficult to model and predict the nonlinear response of shrouded blades. In the present study, an efficient approach to investigate the nonlinear response of the shrouded blades is suggested using an alternating frequency/time domain (AFT) method. On one hand, the friction force between shrouds is numerically solved in time-domain. The trajectory of relative motion of the moving contact point is traced, and the stick-slip-separation transition for 3-D relative motion of the shroud-contact interface is considered. On the other hand, the response of the shrouded blades is iteratively solved in frequency-domain using Harmonic Balance Method (HBM). In this approach, the influence of high frequency modes of blade, and the coupling of each harmonic component on damping behavior can be taken into account. As an application, the performance of shroud damper is systematically investigated using the AFT method. The influence of shroud-to-shroud preload and contact stiffness on the shroud damping potential is studied. Some valuable results are got to the design of the shroud contact.

Efficient Nonlinear Vibration Analysis of the Forced Response of Rotating Cracked Blades

2006 ◽  
Author(s):  
Akira Saito ◽  
Matthew P. Castanier ◽  
Christophe Pierre
Keyword(s):  
Finite Element ◽  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Piecewise Linear ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
New Method ◽  
Beam Model ◽  
Element Analysis

The efficient nonlinear vibration analysis of a rotating elastic structure with a crack is examined. In particular, the solution of the forced vibration response of a cracked turbine engine blade is investigated. Starting with a finite element model of the cracked system, the Craig-Bampton method of component mode synthesis is used to generate a reduced-order model that retains the nodes of the crack surfaces as physical DOF. The nonlinearity due to the intermittent contact of the crack surfaces, which is caused by the opening and closing of the crack during each vibration cycle, is modeled with a piecewise linear term in the equations of motion. Then, the efficient solution procedure for solving the resulting nonlinear equations of motion is presented. The approach employed in this study is a multi-harmonic, hybrid frequency/time-domain (HFT) technique, which is an extension of the traditional harmonic balance method. First, a simple beam model is used to perform a numerical validation by comparing the results of the new method to those from transient finite element analysis (FEA) with contact elements. It is found that the new method retains good accuracy relative to FEA while reducing the computational costs by several orders of magnitude. Second, a representative blade model is used to examine the effects of crack length and rotation speed on the resonant frequency response. Several issues related to the rotation are investigated, including geometry changes of the crack and the existence of multiple solutions.

scholarly journals Nonlinear Behavior of a Magnetic Bearing System

1995 ◽  
Vol 117 (3) ◽  
pp. 582-588 ◽  
Author(s):  
L. N. Virgin ◽  
T. F. Walsh ◽  
J. D. Knight
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Nonlinear Behavior ◽  
Analytical Techniques ◽  
Magnetic Bearing ◽  
Forced Response ◽  
The Mathematical Model ◽  
Two Degree Of Freedom ◽  
Sensitivity To Initial Conditions ◽  
Bearing System

This paper describes the results of a study into the dynamic behavior of a magnetic bearing system. The research focuses attention on the influence of nonlinearities on the forced response of a two-degree-of-freedom rotating mass suspended by magnetic bearings and subject to rotating unbalance and feedback control. Geometric coupling between the degrees of freedom leads to a pair of nonlinear ordinary differential equations, which are then solved using both numerical simulation and approximate analytical techniques. The system exhibits a variety of interesting and somewhat unexpected phenomena including various amplitude driven bifurcational events, sensitivity to initial conditions, and the complete loss of stability associated with the escape from the potential well in which the system can be thought to be oscillating. An approximate criterion to avoid this last possibility is developed based on concepts of limiting the response of the system. The present paper may be considered as an extension to an earlier study by the same authors, which described the practical context of the work, free vibration, control aspects, and derivation of the mathematical model.

Analysis of Beam-Like Structures With Displacement-Dependent Friction Forces: Part I — Single-Degree-of-Freedom Model

1995 ◽  
Author(s):  
Wayne E. Whiteman ◽  
Aldo A. Ferri
Keyword(s):  
Dry Friction ◽  
Damping Ratio ◽  
Strong Dependence ◽  
Time Integration ◽  
Single Mode ◽  
Stick Slip ◽  
Friction Forces ◽  
Equivalent Damping ◽  
Damping Characteristics ◽  
Parameter Values

Abstract The dynamic behavior of a beam-like structure undergoing transverse vibration and subjected to a displacement-dependent dry friction force is examined. In Part I, the beam is modeled by a single mode while Part II considers multi-mode representations. The displacement dependence in each case is caused by a ramp configuration that allows the normal force across the sliding interface to increase linearly with slip displacement. The system is studied first by using first-order harmonic balance and then by using a time integration method. The stick-slip behavior of the system is also studied. Even though the only source of damping is dry friction, the system is seen to exhibit “viscous-like” damping characteristics. A strong dependence of the equivalent natural frequency and damping ratio on the displacement amplitude is an interesting result. It is shown that for a given set of parameter values, an optimal ramp angle exists that maximizes the equivalent damping ratio. The appearance of two dynamic response solutions at certain system and forcing parameter values is also seen. Results suggest that the overall characteristics of mechanical systems may be improved by properly configuring frictional interfaces to allow normal forces to vary with displacement.

Impact Dynamic Analysis of Horizontally Vibrated Conveyor with Coulomb Friction Modeling

2012 ◽  
Vol 619 ◽  
pp. 26-29
Author(s):  
Chao Sheng Song ◽  
Qi Ming Huang ◽  
Zhan Gao ◽  
Jie Xu
Keyword(s):  
Coulomb Friction ◽  
Impact Analysis ◽  
Time Integration ◽  
Impact Excitation ◽  
Friction Modeling ◽  
Integration Algorithm ◽  
Conveyor System ◽  
Time Integration Algorithm ◽  
And Control ◽  
The Impact

This paper introduces dynamic impact analysis as an effective technique for studying the response of horizontal vibrated conveyor with time-varying impact excitation by the falling of the scrap. A two degree-of-freedoms impact dynamic model is formulated considering the static and dynamic coulomb friction between the scrap and chute. Then the time integration algorithm was applied in the program to solve the dynamic equations. Using the proposed method, the impact effects of ideal single scrap and multiple scraps on the dynamic response of the conveyor were analyzed. Computational results reveal numerous interesting dynamic characteristics which can be used to forecast and control the vibration of the scrap and conveyor system.

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