By Liming Dai, Reza N. Jazar
Nonlinear ways in Engineering Applications makes a speciality of nonlinear phenomena which are universal within the engineering box. The nonlinear methods defined during this ebook supply a valid theoretical base and useful instruments to layout and research engineering structures with excessive potency and accuracy and with much less power and downtime. offered listed below are nonlinear methods in components resembling dynamic platforms, optimum keep an eye on and techniques in nonlinear dynamics and acoustics. insurance incorporates a wide selection of purposes and fields together with mathematical modeling and nonlinear habit as utilized to microresonators, nanotechnologies, nonlinear habit in soil erosion,nonlinear inhabitants dynamics, and optimization in decreasing vibration and noise in addition to vibration in triple-walled carbon nanotubes.
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Fig. 3 (a) A double-degree-of-freedom model of the HNC with its schematic draw. (b) The angular displacements, Â1 and Â2 , of the model . . . . . . . . . . . . . .. . . . . . . . . . Fig. 4 The mean values of the coherency functions for four subjects. Each graph belongs to one subject . . .. . . . . . . . . . Fig. ) results of the magnitudes of the transfer functions for four subjects. Note that the # sign indicates the subject number .
However, the variation of nonperiodic cases is relatively small, except when the overlapping boundary becomes extremely small. 5. Chaotic portion shifts up when the value of overlapping boundary decreases while quasiperiodic portion increases. However, shifting rate is gradually stabilized as the boundary becomes smaller than 10 5 . 6. Chaos and quasiperiodicity of the system cannot be detected if the overlapping boundary used is too large. 18 L. Dai and L. Han It should be noticed that there are cases that the maximum distances between some points in the Poincare map are smaller than the larger overlapping boundary but larger than the small boundary.
When the two values of B and k are specfied, the system is uniquely determined. Obtaining samples of the system means to determine the samples of the two parameters. Since the distributions of the two parameters can be independent, one may firstly select a value for B from its uniform distribution Œ0 W 0:1 W 15 and then a value for k from Œ0 W 0:01 W 1. For representativity of the samples to be selected, the samples need to be selected in a random manner. In other words, a proper pair of B and k values needs to be selected randomly.