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.

The Response of Nonlinear Systems to Modulated High-Frequency Input

1993 ◽  
Author(s):  
S. A. Nayfeh ◽  
A. H. Nayfeh
Keyword(s):  
Nonlinear Systems ◽  
Natural Frequency ◽  
Amplitude Modulation ◽  
Carrier Frequency ◽  
High Frequency ◽  
Degree Of Freedom ◽  
Resonant Excitation ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Different Types

Abstract We study the response of a single-degree-of-freedom system with cubic nonlinearities to an amplitude-modulated excitation whose carrier frequency is much higher than the natural frequency of the system. The only restriction on the amplitude modulation is that it contain frequencies much lower than the carrier frequency of the excitation. We apply the theory to different types of amplitude modulation and find that resonant excitation of the system may occur under some conditions.

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.

Effectiveness of neoprene pad vibration isolators at high frequencies

2021 ◽  
Vol 263 (4) ◽  
pp. 2172-2183
Author(s):  
Jerry Lilly
Keyword(s):  
Natural Frequency ◽  
Insertion Loss ◽  
Dynamic Stiffness ◽  
Degree Of Freedom ◽  
Frequency Wave ◽  
Single Degree Of Freedom ◽  
High Frequencies ◽  
Vibration Isolators ◽  
Single Degree ◽  
Wide Range

The natural frequency, dynamic stiffness, and insertion loss of commercially available neoprene pad vibration isolators have been measured in a simple, single degree of freedom system over a wide range of pad loadings out to a maximum frequency of 10 kHz. The results reveal that dynamic stiffness can vary significantly with pad loading as well as the durometer of the material. It will also be shown that insertion loss follows the theoretical single degree of freedom curve only out to a frequency that is about 5 to 10 times the natural frequency, depending upon the pad durometer rating. Above that frequency wave resonances in the material cause the insertion loss to deteriorate significantly out to a frequency near 1 kHz, above which the insertion loss maintains a relatively constant value, again depending upon the pad durometer rating. In some instances the insertion loss values can approach 0 dB or even become negative at specific frequencies in the frequency region that is 10 to 20 times the natural frequency of the system.

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