A Comparison of the Effects of Nonlinear Damping on the Free Vibration of a Single-Degree-of-Freedom System

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Bin Tang ◽  
M. J. Brennan
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Nonlinear Damping ◽  
Degree Of Freedom ◽  
Damping Force ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree ◽  
Dependent Term ◽  
Quadratic Damping

This article concerns the free vibration of a single-degree-of-freedom (SDOF) system with three types of nonlinear damping. One system considered is where the spring and the damper are connected to the mass so that they are orthogonal, and the vibration is in the direction of the spring. It is shown that, provided the displacement is small, this system behaves in a similar way to the conventional SDOF system with cubic damping, in which the spring and the damper are connected so they act in the same direction. For completeness, these systems are compared with a conventional SDOF system with quadratic damping. By transforming all the equations of motion of the systems so that the damping force is proportional to the product of a displacement dependent term and velocity, then all the systems can be directly compared. It is seen that the system with cubic damping is worse than that with quadratic damping for the attenuation of free vibration.

scholarly journals Experimental investigation of a single-degree-of-freedom system with Coulomb friction

2020 ◽  
Vol 99 (3) ◽  
pp. 1781-1799
Author(s):  
Luca Marino ◽  
Alice Cicirello
Keyword(s):  
Experimental Investigation ◽  
Degree Of Freedom ◽  
Experimental Results ◽  
Systematic Observation ◽  
Stick Slip ◽  
Friction Forces ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree ◽  
Set Up

AbstractThis paper presents an experimental investigation of the dynamic behaviour of a single-degree-of-freedom (SDoF) system with a metal-to-metal contact under harmonic base or joined base-wall excitation. The experimental results are compared with those yielded by mathematical models based on a SDoF system with Coulomb damping. While previous experiments on friction-damped systems focused on the characterisation of the friction force, the proposed approach investigates the steady response of a SDoF system when different exciting frequencies and friction forces are applied. The experimental set-up consists of a single-storey building, where harmonic excitation is imposed on a base plate and a friction contact is achieved between a steel top plate and a brass disc. The experimental results are expressed in terms of displacement transmissibility, phase angle and top plate motion in the time and frequency domains. Both continuous and stick-slip motions are investigated. The main results achieved in this paper are: (1) the development of an experimental set-up capable of reproducing friction damping effects on a harmonically excited SDoF system; (2) the validation of the analytical model introduced by Marino et al. (Nonlinear Dyn, 2019. https://doi.org/10.1007/s11071-019-04983-x) and, particularly, the inversion of the transmissibility curves in the joined base-wall motion case; (3) the systematic observation of stick-slip phenomena and their validation with numerical results.

Single Degree-of-Freedom Modeling of the Nonlinear Vibration Response of a Machining Robot

2020 ◽  
Vol 143 (5) ◽  
Author(s):  
Yaser Mohammadi ◽  
Keivan Ahmadi
Keyword(s):  
Control Strategies ◽  
Vibration Response ◽  
Industrial Robots ◽  
Degree Of Freedom ◽  
Restoring Force ◽  
Single Degree Of Freedom ◽  
Machining Forces ◽  
Sdof System ◽  
Single Degree ◽  
Machining Robot

Abstract Highly dynamic machining forces can cause excessive and unstable vibrations when industrial robots are used to perform high-force operations such as milling and drilling. Implementing appropriate optimization and control strategies to suppress vibrations during robotic machining requires accurate models of the robot’s vibration response to the machining forces generated at its tool center point (TCP). The existing models of machining vibrations assume the linearity of the structural dynamics of the robotic arm. This assumption, considering the inherent nonlinearities in the robot’s revolute joints, may cause considerable inaccuracies in predicting the extent and stability of vibrations during the process. In this article, a single degree-of-freedom (SDOF) system with the nonlinear restoring force is used to model the vibration response of a KUKA machining robot at its TCP (i.e., machining tool-tip). The experimental identification of the restoring force shows that its damping and stiffness components can be approximated using cubic models. Subsequently, the higher-order frequency response functions (HFRFs) of the SDOF system are estimated experimentally, and the parameters of the SDOF system are identified by curve fitting the resulting HFRFs. The accuracy of the presented SDOF modeling approach in capturing the nonlinearity of the TCP vibration response is verified experimentally. It is shown that the identified models accurately predict the variation of the receptance of the nonlinear system in the vicinity of well-separated peaks, but nonlinear coupling around closely spaced peaks may cause inaccuracies in the prediction of system dynamics.

scholarly journals Dynamic Response of Breasting Dolphin Moored with 40,000 DWT Ship due to Parallel Passing Ship Phenomenon

2018 ◽  
Vol 147 ◽  
pp. 05003
Author(s):  
Heri Setiawan ◽  
Muslim Muin
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Dynamic Response ◽  
Computer Program ◽  
Lateral Force ◽  
Degree Of Freedom ◽  
Hydrodynamic Interactions ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree

When a ship is moving through another ship moored nearby, hydrodynamic interactions between these ships result in movements of the moored vessel. The movement may occur as surge, sway, and/or yaw. When a ship is passing a moored vessel parallelly, this effect will give a dominant lateral force on the moored ship and response from this phenomenon will appear in a certain time. Only dynamic response due to sway force is considered in this study, the sway force shall be absorb by the breasting dolphin. 40,000 DWT shall be moored to the breasting dolphin. Three passing ships size are considered, the breasting dolphin shall be modeled as a single degree of freedom model. This model will be subjected to a force caused by parallel passing ship. The model is assumed to be in a state of quiet water, this assumption is taken so that the fluid does not provide additional force on the model. The SDOF system shall be analyzed using a computer program designed to solve an ordinary differential equation.

Effect of Waveform on the Effectiveness of Tangential Dither Forces to Cancel Friction-Induced Oscillations

2005 ◽  
Author(s):  
Michael A. Michaux ◽  
Aldo A. Ferri ◽  
Kenneth A. Cunefare
Keyword(s):  
Numerical Integration ◽  
High Frequency ◽  
Frictional Contact ◽  
Degree Of Freedom ◽  
System Response ◽  
Periodic Signal ◽  
Method Of Averaging ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree

High-frequency dither forces are often used to reduce unwanted vibration in frictional systems. This paper examines how the effectiveness of these dither-cancellation techniques is influenced by the type of periodic signal employed. The paper uses the method of averaging as well as numerical integration to study a single-degree-of-freedom (SDOF) system consisting of a mass in frictional contact with a translating surface. Recently, it was found that sinusoidal dither forces had the ability to stabilize or destabilize such a system, depending on the system and frictional characteristics as well as the amplitude and frequency of the dither signal [1]. This paper extends this analysis to general, periodic dither forces. In particular, the system response for sinusoidal dither waveforms is compared to that of triangular dither waveforms and square dither waveforms. It is found that, for a given amplitude and frequency of the dither signal, square waveforms are much more effective in canceling friction-induced oscillations than sinusoidal dither; likewise, sinusoidal waveforms are more effective than triangular waveforms for a given amplitude and frequency. A criterion is developed that relates the effectiveness of the waveform to the properties of the integral of the dither signal.

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