Free vibration response: Single-degree-of-freedom system

2012 ◽  
pp. 203-238
Keyword(s):  
Free Vibration ◽  
Vibration Response ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Free Vibration Response

Free Vibration Response Characteristics of a Simple Elasto-Hereditary System

1998 ◽  
Vol 120 (2) ◽  
pp. 628-632 ◽  
Author(s):  
A. Muravyov ◽  
S. G. Hutton
Keyword(s):  
Free Vibration ◽  
Vibration Response ◽  
Degree Of Freedom ◽  
Relaxation Kernel ◽  
Viscoelastic System ◽  
Single Degree Of Freedom ◽  
Response Characteristics ◽  
Single Degree ◽  
Hereditary System ◽  
Free Vibration Response

An analysis is conducted of the free vibration response characteristics of a single-degree-of-freedom (SDOF) elasto-hereditary (viscoelastic) system. The viscoelasticity is characterized by a relaxation kernel consisting of one exponential term. For this problem analytical results are presented that define the regions of oscillatory and nonoscillatory response. A possible application of the described technique to multi-degree-of-freedom diagonalizable viscoelastic systems is shown.

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.

Demonstrator to show the effects of negative stiffness on the natural frequency of a simple oscillator

2008 ◽  
Vol 222 (7) ◽  
pp. 1189-1192 ◽  
Author(s):  
A Carrella ◽  
M J Brennan ◽  
T P Waters
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Degree Of Freedom ◽  
Negative Stiffness ◽  
Test Rig ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Horizontal Beam ◽  
Additional Correction

This article describes a demonstrator to show the effects of negative stiffness on the free vibration of a simple oscillator. The test rig consists of a horizontal beam that is hinged at one end and is supported by two coil springs to form a single-degree-of-freedom system. Additional correction springs, which provide negative stiffness, can be attached to lower the natural frequency of the system. The effect of the change in natural frequency can be easily seen visually, and it is shown that for one of the configurations of correction springs, the natural frequency can be reduced by a factor of about 4.

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.

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