A new method for the accurate measurement of higher-order frequency response functions of nonlinear structural systems

Methodologies for modeling and identification of breathing crack: A review

Swift development of technology for monitoring complex structures demands major attention on the precision of damage detection methods. The early detection of any type of deterioration or degradation of structures is of paramount importance to avoid sudden catastrophic failure. It warns users about the impending state of the system. At the initiation of a crack or some other system faults, the system may generate a time-varying state of crack under ambient vibration. It represents the nonlinear breathing phenomena of crack. An assessment of this degree of nonlinearity can be utilized for the detection, localization, and quantification of breathing cracks. Appropriate modeling of such cracks is thus necessary to capture distinctive nonlinear features. Recognizing this importance, various methods of modeling and nonlinear system identification which have been employed in the past for the detection of breathing crack are reviewed. The present study also explores some of the available vibration as well as acoustic-based damage identification techniques, chronologically connecting their evolutions. It summarizes the advantages and limitations of the methods to inspect potential future applications. The future scopes drawn from this review are highlighted to pave the path of wide-spread applications of nonlinear features of crack.

Determination of the characteristic curves of a nonlinear first order system from Fourier analysis

Based on Fourier analysis, we develop an expression for modeling and simulating nonlinear first order systems. This expression is associated to a nonlinear first order differential equation [Formula: see text], where [Formula: see text] is the dynamical variable, [Formula: see text] is the driving force, and the f and g functions are the characteristic curves which are associated to dissipative and memory elements, respectively. The model is obtained from the sinusoidal response, specifically by calculating the Fourier analysis of y(t) for [Formula: see text], where the model parameters are the Fourier coefficients of the response, and the values of [Formula: see text], [Formula: see text] and [Formula: see text]. The same expression is used for two kinds of time-domain simulations: to calculate other driving force [Formula: see text] based on a dynamical variable [Formula: see text]; and, to calculate the dynamical variable [Formula: see text] based on a driving force [Formula: see text]. In both cases, the dynamical variable must remain in the range [Formula: see text]. By analyzing this expression, we found an equivalence between the Fourier coefficients and the polynomial regressions of the characteristic curves of f and g. This result allows us to obtain the system modeling and simulation based on the amplitude and phase Fourier spectrum obtained from the Fast Fourier Transform (FFT) of the sampled [Formula: see text] version of y(t). It is shown that this technique has a low computational complexity, and it is expected to be suitable for real-time applications for system modeling, simulation and control, in particular when the explicit expressions of the characteristic curves are unknown. Fourier analysis is a fundamental tool in electronics, mathematics and physics, but to the best of the author's knowledge, no work has found this clear evidence of the connection between the Fourier analysis and a first order differential equation. The aim of this work is to initiate a systematic study on this topic.

New Type of Spectral Nonlinear Resonance Enhances Identification of Weak Signals

Some nonlinear systems possess innate capabilities of enhancing weak signal transmissions through a unique process called Stochastic Resonance (SR). However, existing SR mechanism suffers limited signal enhancement from inappropriate entraining signals. Here we propose a new and effective implementation, resulting in a new type of spectral resonance similar to SR but capable of achieving orders of magnitude higher signal enhancement than previously reported. By employing entraining frequency in the range of the weak signal, strong spectral resonances can be induced to facilitate nonlinear modulations and intermodulations, thereby strengthening the weak signal. The underlying physical mechanism governing the behavior of spectral resonances is examined, revealing the inherent advantages of the proposed spectral resonances over the existing implementation of SR. Wide range of parameters have been found for the optimal enhancement of any given weak signal and an analytical method is established to estimate these required parameters. A reliable algorithm is also developed for the identifications of weak signals using signal processing techniques. The present work can significantly improve existing SR performances and can have profound practical applications where SR is currently employed for its inherent technological advantages.