Vibrations (Waves - volume one)

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.

Vibration 01 'Apparent Serenity Surreptitiously Seeding' (03:42)

a revisitation of a Latin choir joined by a chorus of dead people singing.

Vibration 02 'Comforting Sullenness' (05:52)

a statement of tolerance within a artificial place of worship somewhere in Russia.

Vibration 03 'Air Leaving No Residue' (02:25)

an Eastern European choir joined by the same culprits in (1) for a while, later being reanimated with a choir comprising a popular singer from the 21st Century.

Vibration 04 'Nobody Feels The Torment Of Embers' (07:50)

features necessary angels and strings, together with an internal fantasia that reeks of the infernal.

Vibration 05 'The Sunshine Outside The Counter' (03:15)

a detection of the airwaves within a summer resort with a definite air of despondence about it.

Vibration 06 'The Other Dimensional Washing Flow' (03:34)

a study in the transformative power of happiness into melancholy with a later foray in to the morose.

Vibration 07 'Forced Sadness' (05:44)

a ten count view of what a choir may sound like if suitably mutated over a period of twelve centuries.

Vibration 08 'You Are Fucked Up' (05:05)

a modern take on a French poem from the 19th century

Vibration 09 'Fineness After The Onslaught' (04:36)

a sort of jazz interprtation of what a sort of string and choir outfit might sort of make of a drum machine if they found it in 1845.

Vibration 10 'Malignant Judgment From An Unrecognised Judge' (05:13)

what warriors sing to when they are alone, probably

Vibration 11 'Endless Affinity' (03:27)

a view of southern Italy

Vibration 12 'Machinery of Prosecution' (04:48)

a rhythmic take without words which needs them and which likely you will find in your head without them being told to you.

Vibration 13 'Seeded into Blossom' (01:33)

a non-vocal return to the initial state, which is where we leave it.

All titles composed, arranged and performed by Mike Dickson aside from extract within Vibration 05, music by Max Steiner.

Additional titles supplied by Danielle Ashley from a reading of Movements.

Full CD download available here with support file here. Burned using IMGBURN available here.

© 2017, Black Cat Music Factory