Vibrations by Mike Dickson

Thirteen adventures in choral sounds. Some are fake. Some are real. Some are real fakes.

2.3. Chaotic response
Under harmonic excitation, a nonlinear isolator may exhibit chaotic behavior over a certain range of system and excitation parameters. A simple method for describing the arbitrary multi-axial loading process of vibration isolation with large nonlinear stiffness and damping was proposed by Ulanov and Lazutkin. Qing et al. studied the vibration isolation behavior of a nonlinear vibration-isolation system in a desired chaotic state. The transmitted force was characterized by a broad frequency band, although the excitation was sinusoidal. In order to control the system in a desired chaotic state, the isolator has to possess variable stiffness and damping.

Other types of nonlinear dynamic stiffness modeling were introduced by Kari ; Jiang and Zhu analytically and numerically studied the vibration isolation of a nonlinear system. They estimated the vibration isolation performance under different operating conditions and showed that the vibration isolation performance at the primary harmonic frequency is better than that of the linear system. Furthermore, the vibration isolation performance of the nonlinear vibration isolator in the chaotic states was found to be much better than that in the non-chaotic vibration states.

Liu et al. took advantage of chaotic vibration isolation to eliminate the periodic component in water-borne noise and to improve the concealment capability of warships. The influence of hard stiffness nonlinearity on the performance of nonlinear isolators was numerically studied by Yu et al. . Yu et al. conducted numerical and experimental investigations to evaluate the performance of nonlinear vibration isolation system under chaotic state. They found that the nonlinear isolator exhibits excellent performance and can reduce the line spectrum when the system operates under chaotic state. The spectra of the radiated waterborne-noises of marine vessels constituted of a broad-band noise having a continuous spectrum superimposed on a line spectrum. At high-speed, the signature was found to be dominated by a broad-band noise, while at low-speed the signature was dominated by a line spectrum. For soft spring nonlinearity both amplitude and transmissibility of displacement were found to outperform those observed in hard spring nonlinearity.

Ravindra and Mallik extended their previous work and considered both symmetric and asymmetric nonlinear restoring forces. Two typical routes to chaos, namely through period-doubling and intermittency, were found to be present with damping exponent values of p=2 and 3. It was concluded that the bifurcation structure is unaffected by the damping exponent. However, the values of the damping coefficient required for complete elimination of the subharmonic and chaotic responses were found to depend on the value of p. It was shown that nonlinear damping can be used as a passive mechanism to suppress chaos.

Tracklist

1.	Vibrations 01	3:42

2.	Vibrations 02	5:52

3.	Vibrations 03	2:25

4.	Vibrations 04	7:50

5.	Vibrations 05	3:15

6.	Vibrations 06	3:34

7.	Vibrations 07	5:44

8.	Vibrations 08	5:06

9.	Vibrations 09	4:37

10.	Vibrations 10	5:14

11.	Vibrations 11	3:27

12.	Vibrations 12	4:48

13.	Vibrations 13	1:34

Credits

released May 20, 2017

All music is (c) 2017, Black Cat Music Factory
All titles performed, orchestrated and arranged by Mike Dickson
All titles composed, arranged and performed by Mike Dickson aside from extract within Vibration 05, music by Max Steiner.

Recorded in Edinburgh and East Lothian
Artwork (c) Black Cat Art House

Numerous samples stolen and mutated beyond belief from many different sources, without credit or any possibility of recognition, mostly because that amount of paperwork is not something that anyone really deserves.

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