By Thor I. Fossen
Parametric Resonance in Dynamical platforms discusses the phenomenon of parametric resonance and its prevalence in mechanical platforms, cars, bikes, plane and marine craft, alongside micro-electro-mechanical platforms. The members presents an advent to the basis factors of this phenomenon and its mathematical similar, the Mathieu-Hill equation. additionally incorporated is a dialogue of the way parametric resonance happens on ships and offshore structures, and its frequency in mechanical and electric structures. This quantity is perfect for researchers and mechanical engineers operating in software fields comparable to MEMS, maritime, airplane and floor automobile engineering.
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Extra resources for Parametric Resonance in Dynamical Systems
Since the running STDs tend to converge to the ensemble averages of the standard deviations, it is suggested that the wave elevation and pitch motion in irregular waves can be regarded as ergodic process within practical accuracy, that is, 3% or less. This assumption is well established in conventional seakeeping studies. In contrast, the running STDs of the roll motions in irregular waves as shown in Figs. 6, do not converge to the ensemble averages of the standard deviations. In Case A the dispersion is approximately 20% and in Case B more than 40%.
Consequently robustification of the spectral correlation is needed. This is obtained by bandpass filters that narrow in the roll and pitch signals frequency ranges of interest. The pass-bands regions are centered about ωφ and ωe = 2ωφ , to focus on frequency ranges where parametric roll resonance can develop. 52) where the superscript f addresses that the computation involves the filtered signals. 52) is still calculated from the raw roll and pitch signals. 24) to adapt to weather conditions. Furthermore, the H0 parameters are estimated on-line.
The driving signal d(t) is heavily correlated due to the narrowband process that creates this signal. 3. If whitening of z(k) should subsequently be needed, a simple discrete filter could be employed for this purpose. The autocorrelation behavior makes z(k) a natural choice for subsequent statistical analysis in the time-domain. As to the distribution of z(k), a scrutiny showed that a Weibull distribution characterizes z(k) quite well. 26) and probability density function, PDF: p(z) = z β (z)β −1 exp − β υ 2υ β , where υ and β are scale and shape parameters, respectively.
Parametric Resonance in Dynamical Systems by Thor I. Fossen