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The present study is concerned with the application of a nonlinear frequency analysis approach to the detection and location of water tree degradation of power cable XLPE insulation without turning off electric power.

The use of power cable system responses to power line carrier signals are proposed to conduct the required signal analysis for damage location purpose. This technique is based on the fact that the water tree degradation in power cables can make the system behave nonlinearly. Consequently, the location of water tree degradation can be determined by detecting the position of nonlinear components in power cable systems.

A novel method has been proposed for locating water tree degradation in power cable systems; numerical simulation studies have demonstrated the effectiveness of the new technique.

The proposed technique has the potential to be applied in practice to more effectively resolve the power cable damage location problem.

The purpose of this paper is to present the application of Hilbert–Huang transform (HHT) for fatigue damage feature characterisation in the time–frequency domain based on strain signals obtained from the automotive coil springs.

HHT was employed to detect the temporary changes in frequency characteristics of the vibration response of the signals. The extraction successfully reduced the length of the original signal to 40 per cent, whereas the fatigue damage was retained. The analysis process for this work is divided into three stages: signal characterisation with the application of fatigue data editing (FDE) for fatigue life assessment, empirical mode decomposition with Hilbert transform, an energy–time–frequency distribution analysis of each intrinsic mode function (IMF).

The edited signal had a time length of 72.5 s, which was 40 per cent lower than the original signal. Both signals were retained statistically with close mean, root-mean-square and kurtosis value. FDE improved the fatigue life, and the extraction did not affect the content and behaviour of the original signal because the editing technique only removed the minimal fatigue damage potential. HHT helped to remove unnecessary noise in the recorded signals. EMD produced sets of IMFs that indicated the differences between the original signal and mean of the signal to produce new components. The low-frequency energy was expected to cause large damage, whereas the high-frequency energy will cause small damage.

HHT and EMD can be used in the strain data signal analysis of the automotive component of a suspension system. This is to improve the fatigue life, where the extraction did not affect the content and behaviour of the original signal because the editing technique only removed the minimal fatigue damage potential.

This paper aims to put forward a nonlinear vibration method for crack detection based on fiber Bragg grating (FBG), which is used to receive the waves in the plate.

First of all, measuring principle of nonlinear vibration technique and FBG sensing principle are introduced. Then nonlinear signal spectrum is analyzed to reveal various models of nonlinear vibration, and modal analysis of the plate structure is performed to lay the foundation for the later experiment. This approach is the cross-modulation effect from a persistent excitation to the receipt signal.

The experimental system is built and its results are in agreement with theoretical analysis, and show that this nonlinear vibration method based on FBG sensor is sensitive to crack damage.

Taking the board structure as the object, a new attempt by nonlinear vibration detection with FBG sensor has been investigated.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

The purpose of this paper is to investigate nonlinear vibrations of triple-walled carbon nanotubes buried within Pasternak foundation carrying viscous fluids.

Considering the geometry of nanotubes, the governing equations were initially derived using Timoshenko and modified couple stress theories and by taking into account Von-Karman expressions. Then, by determining boundary conditions, type of fluid motion, Knudsen number and, ultimately, fluid viscosity, the principal equation was solved using differential quadrature method, and linear and nonlinear nanotube frequencies were calculated.

The results indicated that natural frequency is decreased as the fluid velocity and aspect ratio increase. Moreover, as the aspect ratio is increased, the results converge for simple and fixed support boundary conditions, and the ratio of nonlinear to linear frequencies approaches. Natural frequency of vibrations and critical velocity increase as Pasternak coefficient and characteristic length increase. As indicated by the results, by assuming a non-uniform velocity for the fluid and a slip boundary condition at Kn = 0.05, reductions of 10.714 and 28.714% were observed in the critical velocity, respectively. Moreover, the ratio of nonlinear to linear base frequencies decreases as the Winkler and Pasternak coefficients, maximum deflection of the first wall and characteristic length are increased in couple stress theory.

This paper is a numerical investigation of nonlinear vibration analysis for triple-walled carbon nanotubes conveying viscous fluid.

Analytical determination of harmonic components of current in electric circuits containing semiconductor converters with the use of a small parameter method (SPM) in frequency domain. The paper aims to discuss these issues.

A SPM realized in frequency domain was used in the analytical analysis of electric circuits with semiconductor converters. An automated method of formation of orthogonal harmonic components of electrical values on the basis of discrete convolution algorithm was used to provide the possibility of realization of calculation in frequency domain. A nonlinear characteristic of a semiconductor converter was presented by the method of numerical approximation. A numerical structured simulation method was applied to determination of the reference values of current in the analyzed circuit. Laws of theoretical electrical engineering were used for formation of the equations of voltage balance in the circuit with a nonlinear element.

It is shown that application of a SPM with its realization in frequency domain enables significant simplification of the process of the analysis of electric circuits with semiconductor converters in an analytical form and facilitation of calculation automation. Analytical and numerical calculation of a circuit with a diode under active-inductive load demonstrated efficiency and sufficient accuracy of the proposed method. It is shown that increase of the order of approximating polynomial and of the number of the analyzed harmonics provides the improvement of the accuracy of numerical calculations.

The results of the work can be used in calculation of electrotechnical devices containing semiconductor appliances and electric devices with nonlinear characteristics. Moreover, the obtained results enable studying the processes of compensation of current higher harmonics in electric networks with a nonlinear load containing semiconductor converters.

For the first time it was proposed to apply a SPM with its realization in frequency domain to the analysis of nonlinear electric circuits. The significance of the paper consists in the fact that the offered method makes it possible to carry out both circuit analytical and numerical analysis with the possibility of its automation.

Charge pump phase locked loops (CPPLLs) are nonlinear systems as a result of the nonlinear behavior of voltage-controlled oscillators (VCO). This paper aims to specify jitter generation of voltage controlled oscillator phase noise in CPPLLs, by considering approximated practical model for VCO.

CPPLL, in practice, shows nonlinear behavior, and usually in LC-VCOs, it follows second-degree polynomial function behavior. Therefore, the nonlinear differential equation of the system is obtained which shows the CPPLLs are a nonlinear system with memory, and that Volterra series expansion is useful for such systems.

In this paper, by considering approximated practical model for VCO, jitter generation of voltage controlled oscillator phase noise in CPPLLs is specified. Behavioral simulation is used to validate the analytical results. The results show a suitable agreement between analytical equations and simulation results.

The proposed method in this paper has two advantages over the conventional design and analysis methods. First, in contrast to an ideal CPPLL, in which the characteristic of the VCO’s output frequency based on the control voltage is linear, in the present paper, a nonlinear behavior was considered for this characteristic in accordance with the real situations. Besides, regarding the simulations in this paper, a behavior similar to the second-degree polynomial was considered, which caused the dependence of the produced jitter’s characteristic corner frequency on the jitter’s amplitude. Second, some new nonlinear differential equations were proposed for the system, which ensured the calculation of the produced jitter of the VCO phase noise in CPPLLs. The presented method is general enough to be used for designing the CPPLL.

With the rapid-growing house market in the past decade, the purpose of this paper is to study the important issue of house price information flows among 12 major cities in China, including Shanghai, Beijing, Xiamen, Shenzhen, Guangzhou, Hangzhou, Ningbo, Nanjing, Zhuhai, Fuzhou, Suzhou and Dongguan, during the period of June 2010 to May 2019.

The authors approach this issue in both time and frequency domains, latter of which is facilitated through wavelet analysis and by exploring both linear and nonlinear causality under the vector autoregressive framework.

The main findings are threefold. First, in the long run of the time domain and for timescales beyond 16 months of the frequency domain, house prices of all cities significantly affect each other. For timescales up to 16 months, linear causality is weaker and is most often identified for the scale of four to eight months. Second, while nonlinear causality is seldom determined in the time domain and is never found for timescales up to four months, it is identified for scales beyond four months and particularly for those beyond 32 months. Third, nonlinear causality found in the frequency domain is partly explained by the volatility spillover effect.

Results here should be of use to policymakers in certain policy analysis.

The purpose of this study is to address the nonlinear oscillations of single-crystal silicon micro-electromechanical systems (MEMS) accelerometers subjected to mechanical excitation.

The nonlinear behavior was detected and analyzed by using experimental, analytical and numerical approaches. Piezoelectric shaker as a source of mechanical excitation and differential laser Doppler vibrometer in combination with a micro system analyzer were used in the experimental effort. Two types of devices considered included nonencapsulated samples and samples encapsulated in nitrogen gas compressed between two glasses. Numerical and analytical investigations were conducted to analyze the nonlinear response. A novel method has been suggested to calculate the nonlinear parameters. The obtained experimental, numerical and analytical results are in good agreement.

It has been found that the nonlinearity leads to a shift in frequencies and generates higher harmonics, but, most importantly, reveals new phenomena, such as the jump and instability of the vibration amplitudes and phases.

It has been shown that under the constant excitation force, the MEMS device can work in both linear and nonlinear regions. The role of the beat phenomenon has been also addressed and discussed. It has been found that the attributes of the nonlinear response are strongly dependent on the level and duration of the excitation. It is concluded that the nonlinear response of the systems is strongly dependent on the level of the excitation energy. It has been also concluded that larger quality factors are able to enhance dramatically the nonlinear effects and vice versa.

It has been verified that the WBZ‐α method of Wood, Bossak and Zienkiewicz can have unconditional stability and numerical dissipation for linear elastic systems. However, it is still unclear about its performance in the solution of nonlinear systems analytically. Hence, this study proposes to analytically investigate its numerical characteristics for solving nonlinear systems.

Two parameters are introduced to facilitate the basic analysis for nonlinear systems. One is the step degree of nonlinearity, which describes the stiffness change within a time step, and the other is the step degree of convergence, which describes the convergence error due to an iteration procedure.

It is theoretically proved that the sub‐family of WBZ‐α method of −1≤α<0, β=(1/4)(1−α)² and γ=(1/2)−α is unconditionally stable and has desired numerical dissipation for any nonlinear systems even with the presence of convergence error. These theoretical results are confirmed by numerical examples.

This analytical study reveals that the performance of the WBZ‐α method for nonlinear systems is in general the same as that for linear elastic systems.