Major Source Of Nonlinearity Research Articles

Effects of the Seal Wire on the Nonlinear Dynamics of the Aircraft Engine Turbine Blades

Abstract Complicated systems made of multiple components are known to be difficult to model, considering their solutions can change dramatically even with the slightest variations in conditions. Aircraft engines contain such complicated systems, and some components in aircraft engines' turbines can cause significant changes in the system's overall response. Hence, this study is focused on investigating the behavior of a turbine blade of an aircraft engine and the effects of the contact between the blade and the seal wire on the dynamics of the blade-disk system. The investigation is performed via various numerical simulations in time and frequency domains. One sector of the bladed disk is modeled using the finite element method with the lock plate and the seal wire imposing cyclic symmetry boundary conditions in the static, modal, and frequency domain forced response analyses. In time domain analyses, the cyclic symmetry is replaced with simplified displacement restricting boundary conditions. The time domain analysis contains steady-state forced responses of the system. The results show that contact with the seal wire is not a major source of nonlinearity and damping. The contacts with the lock plate contribute more to the vibration damping than the seal wire. However, compared to the contacts at the root of the blade, both components remain less significant with regard to frictional damping and nonlinearity.

Influence of PDC bit cutter layout on stick–slip vibrations of deep drilling systems

This paper extends the class of two degrees-of-freedom (2 DOF) models that simulate the self-excited vibrations of a rotary drilling system, by considering PDC bits equipped with round cutters and a realistic cutter layout. The extension requires an elaborate bit/rock interaction model that involves bit characterization, cutter projection and correlating the bit/rock engagement with the bit motion history. The governing equations are state-dependent delay differential inclusions with two major sources of nonlinearities: the regenerative effect in both cutting and frictional components of the drilling force and the unilateral nature of the frictional force. To solve for the state variables, the technical challenges involve a search of many delays and a fast and accurate geometric computation, which are respectively resolved with a modified inverse algorithm and the polygon clipping technique. The linear stability analysis is formulated based on the geometric variations of the bit/rock engagement surfaces, which result in critical rotation speeds that separate various stability regions of the decoupled axial dynamics. Determined by the bit design, the resulting stability boundaries are defined in terms of the rotation speed and the nominal bit penetration per revolution. With the time simulation, it is verified that the stability map, in conjunction with the exact location of unstable axial poles, can be used to predict the occurrence of axial stick–slip oscillations in the coupled dynamics, which eventually lead to sustained torsional stick–slip oscillations.

Iterative Nonlinearity Mitigation and Decoding for LED Communications

The light-emitting diode (LED) is the major source of nonlinearity in LED communication systems, which needs to be carefully handled to avoid significant performance degradation. Post-distortion is an effective and convenient way to compensate the nonlinear distortion at the receiver side. In this letter, we propose a soft-in-soft-out (SISO) post distorter, which works with an SISO decoder iteratively by exchanging log-likelihood ratios of the coded bits at the receiver. It is demonstrated that the proposed iterative technique can achieve a remarkable performance gain compared to the conventional post-distortion technique in the literature.

Reliability Analysis of Lead-Free Solders in Electronic Packaging Using a Novel Surrogate Model and Kriging Concept

A novel reliability evaluation procedure of lead-free solders used in electronic packaging (EP) subjected to thermomechanical loading is proposed. A solder ball is represented by finite elements (FEs). Major sources of nonlinearities are incorporated as realistically as practicable. Uncertainties in all design variables are quantified using available information. The thermomechanical loading is represented by five design parameters and uncertainties associated with them are incorporated. Since the performance or limit state function (LSF) of such complicated problem is implicit in nature, it is approximately generated explicitly in the failure region with the help of a completely improved response surface method (RSM)-based approach and the universal Kriging method (KM). The response surface (RS) is generated by conducting as few deterministic nonlinear finite element analyses as possible by integrating several advanced factorial mathematical concepts producing compounding beneficial effect. The accuracy, efficiency, and application potential of the procedure are established with the help of Monte Carlo simulation (MCS) and the results from laboratory investigation reported in the literature. The study conclusively verified the proposed method. Similar studies can be conducted to fill the knowledge gap for cases where the available analytical and experimental studies are limited or extend the information to cases where reliability information is unavailable. The study showcased how reliability information can be extracted with the help of multiple deterministic analyses. The authors believe that they proposed an alternative to the classical MCS technique.

Frequency Domain Equalization and Post Distortion for LED Communications With Orthogonal Polynomial Based Joint LED Nonlinearity and Channel Estimation

The light-emitting diode (LED) is the major source of nonlinearity in LED communications, and the nonlinearity needs to be effectively modeled and mitigated to avoid the degradation of communication performance. In indoor LED communications, multipath dispersion can lead to inter-symbol interference (ISI) at high data rates. In this paper, we jointly estimate the LED nonlinearity and ISI channel based on an orthogonal polynomial based technique. Then, frequency domain equalization and post-distortion are adopted to mitigate the ISI and nonlinearity. Simulation results are provided to demonstrate the effectiveness of the proposed technique.

Site-specific seismic design of damage tolerant structural systems using a novel concept

Designing more seismic load-tolerant structures is one of the major challenges of the world communities. It is due to the inability of the profession to predict future design earthquake time histories at a site compounded by the failure to appropriately incorporate uncertainties in other design variables and structural behavior just before failure. A site-specific method is proposed to generate a suite of ground excitation time histories and a novel risk estimation is developed considering major sources of nonlinearity and uncertainty. For wider application and acceptance, the risk evaluation procedure essentially consists of few deterministic time domain finite element analyses. The procedure is verified and showcased by estimating risks associated with three buildings designed by professional experts in the Los Angeles area satisfying the post-Northridge design criteria for the overall lateral deflection and inter-story drift. The accuracy of the estimated risk is verified using the Monte Carlo simulation technique. In all cases, the probabilities of collapse are found to satisfy the current code requirements. The spread in the reliability indexes for each building for both limit states cannot be overlooked, indicating the significance of the frequency contents of the time histories. The inter-story drift is found to be more critical than the overall lateral displacement. The reliability indexes for both limit states are similar only for few cases. The authors believe that they proposed an alternative to the classical random vibration and simulation approaches. The proposed site-specific seismic safety assessment procedure can be used by practicing engineers for routine applications.

Orthogonal Polynomial-Based Nonlinearity Modeling and Mitigation for LED Communications

The light-emitting diode (LED) is the major source of nonlinearity in LED communications, and the nonlinearity needs to be effectively modeled and thereby mitigated through predistortion or postdistortion to avoid degradation of communication performance. A memory polynomial is often used for LED nonlinearity modeling and mitigation in the literature. However, the estimation of memory polynomial coefficients suffers from numerical instability, resulting in inaccurate modeling and poor performance in nonlinearity mitigation. In this paper, we propose an orthogonal polynomial-based nonlinearity modeling and mitigation technique for LED communications with pulse amplitude modulation (PAM) signaling and show that the proposed technique significantly outperforms the conventional memory polynomial-based techniques.

Nonlinear distortion mitigation in visible light communications

Many physical devices used in VLC systems exhibit nonlinear effects, which can significantly degrade the overall system performance. For example, the LED is the major source of nonlinearity. The forward current is zero unless the forward voltage exceeds a turn-on value. The forward current is also limited with a maximum permissible value. In addition, the electrical-tooptical conversion is also nonlinear. In this article, we provide an overview of techniques related to modeling and distortion mitigation techniques of the nonlinearity in VLC systems. Appropriate models and robust nonlinearity mitigation techniques are crucial to support high-speed transmissions in practical VLC systems.

Adaptive Postdistortion for Nonlinear LEDs in Visible Light Communications

In a visible light communication (VLC) system, the light-emitting diode (LED) is the major source of nonlinearity. The nonlinear effects in the VLC system are different from the conventional wireless communications system. The channel separation in the VLC system is significantly larger than the signal bandwidth; thus, the adjacent channel interference is not an issue. Predistortion technique may not be a cost-efficient approach since it needs additional feedback physical circuits at the transmitter. In this paper, we propose a postdistortion technique to estimate and compensate for the LED's nonlinearity at the receiver. The postdistortion technique only needs some additional computational resources. In addition, the proposed approach significantly improves the error-vector-magnitude and bit-error-rate performance of the VLC system. Simulation results validate the theoretical analysis.

A Novel Risk Assessment for Complex Structural Systems

Risk management is an essential tool for safe, economical, and efficient design, operation, and maintenance of complex engineering systems. Seismic risk assessment of structures, particularly in nuclear power plants, needs special attention from the reliability community. Available risk assessment methods may not be sufficient to estimate the risk of complex systems made with different materials, numerous ways elements are connected to each other, and excited by dynamic loadings including seismic loading applied in the time domain. A hybrid risk assessment approach is proposed by intelligently integrating the stochastic finite element method, and the response surface method. It is capable of estimating the probability just before failure considering all major sources of nonlinearity and uncertainty, eliminating the deficiencies of the currently available reliability methods. With the help of the illustrative examples, it is shown that the method is robust, accurate, and efficient in estimating risk of complex systems excited by dynamic loadings applied in the time domain.

Nonlinear analysis of a steel frame

Nonlinear seismic analysis is used in structural engineering profession to design steel frames for moderate to strong earthquakes. Following the Northridge earthquake of 1994 in Southern California, widespread damage to many steel frames was discovered. As a result of multi-million dollar efforts by the professionals, many post-Northridge steel beam–column connection designs were proposed. They are essentially partially-restrained (PR) connections, and their presence adds yet another major source of nonlinearity that must be considered appropriately in nonlinear seismic response analysis. In this paper, a case study of analytical investigation of nonlinear seismic performance of a 9-story steel frame is presented. We consider major sources of nonlinearity in the system including the nonlinear behavior of the connections. Using the four-parameter Richard model, a mathematical model is proposed first to represent moment–relative rotation ( M – θ ) curves for a proprietary steel connection. The model can generate ( M – θ ) curves for other beam–column assemblies. Time-domain, nonlinear seismic response of a steel moment-resisting frame (SMRF) in the presence of this type of connection and pre-Northridge bolted-web, welded-flange (denoted here as BWWF) connections are evaluated. The results are then compared with fully-restrained (FR) steel connections typically used in the design. The results analytically confirmed the beneficial effects of connections observed in full-scale testing.

Nonlinear aspects of sea surface temperature in Monterey Bay

Nonlinear aspects of sea surface temperature (SST) in Monterey Bay are examined, based on an 85-year record of daily observations from Pacific Grove, California. Oceanic processes that affect the waters of Monterey Bay are described, processes that could contribute to nonlinearity in the record. Exploratory data analysis reveals that the record at Pacific Grove is non-Gaussian and, most likely, nonstationary. A more recent test for stationarity based on a power law approximation to the slope of the power spectrum indicates that the record is stationary for frequencies up to ∼8 cycles per year (∼45 days), but nonstationary at higher frequencies. To examine the record at Pacific Grove for nonlinear behavior, third-order statistics, including the skewness, statistical measures of asymmetry, the bicorrelation, and the bispectrum, were employed. The bicorrelation revealed maxima located approximately 365 days apart, reflecting a nonlinear contribution to the annual cycle. Based on a 365-day moving window, the running skewness is positive almost 80% of the time, reflecting the overall impact of warming influences. The asymmetry is positive approximately 75% of the time, consistent with the asymmetric shape of the mean annual cycle. Based on the skewness and asymmetry, nonlinearities in the record, when they occur, appear to be event-driven with time scales possibly as short as several days, to several years. In many cases, these events are related to warm water intrusions into the bay, and El Niño warming episodes. The power spectrum indicates that the annual cycle is a dominant source of variability in the record and that there is a relatively strong semiannual component as well. To determine whether or not the annual and semiannual cycles are harmonically related, the bispectrum and bicoherence were calculated. The bispectrum is nonzero, providing a strong indication of nonlinearity in the record. The bicoherence indicates that the annual cycle is a major source of nonlinearity and further implies that the annual and semiannual cycles are harmonically related. Based on the wavelet power spectrum (WPS), the appearance of the semiannual cycle is transitory; however, pathways between the annual and semiannual cycles appear at certain times when nonlinear interaction between them could occur. Comparisons between the WPS and the running skewness suggest that there is a tendency for periods when pathways exist, to coincide with increased positive skewness, and, often, with El Niño warming episodes. The Hilbert–Huang transform, a relatively new tool for nonstationary and nonlinear spectral analysis, was used to further examine the origin of the semiannual cycle. The time-dependent Hilbert spectrum reveals large and erratic variations in frequency associated with semiannual cycle but far greater stability associated with the annual cycle. As a result, the time-integrated Hilbert spectrum does not indicate the presence of a semiannual cycle. The method of surrogates from the field of nonlinear dynamics was also employed to test the Hopkins record for nonlinearity. Differences between the data and the surrogates were found that were statistically significant, implying the existence of nonlinearity in the record. Using the method of surrogates together with a one-year moving window, El Niño warming episodes appear to be a likely source of nonlinearity, consistent with the other analyses that were performed. Finally, the influence of stochastic variability due to serial correlation in the data was examined by comparing standardized statistics for the observations and for simulations based on an autoregressive model whose properties were obtained from the observations. The magnitude of the variability for the simulations was found to be far less than that associated with the original data, and thus stochastic variability does not appear to be a factor that significantly affects the interpretation of our results.

Orthogonal Polynomials for Complex Gaussian Processes

Power amplifiers are the major source of nonlinearity in communications systems. Such nonlinearity causes spectral regrowth as well as in-band distortion, which leads to adjacent channel interference and increased bit error rate. Polynomials are often used to model the nonlinear power amplifier or its predistortion linearizer. In this paper, we present a novel set of orthogonal polynomials for baseband Gaussian input to replace the conventional polynomials and show how they alleviate the numerical instability problem associated with the conventional polynomials. The orthogonal polynomials also provide an intuitive means of spectral regrowth analysis.

Triangular Configuration Tension Leg Platform behaviour under random sea wave loads

This study investigates the dynamic response of a Triangular Configuration Tension Leg Platform (TLP) under random sea wave loads. The random wave has been generated synthetically using the Monte-Carlo simulation with the Peirson–Moskowitz (P–M) spectrum. Diffraction effects and second-order wave forces have not been considered. The evaluation of hydrodynamic forces is carried out using the modified Morison equation with water particle kinematics evaluated using Airy's linear wave theory. Wave forces are taken to be acting in the surge degree-of-freedom. The effect of coupling of various structural degrees-of-freedom (surge, sway, heave, roll, pitch and yaw) on the dynamic response of the TLP under random wave loads is studied. Parametric studies for random waves with different H s and T z under the presence of current have also been carried out. For the orientation of the TLP, surge, heave and pitch degrees-of-freedom responses are influenced significantly. The surge power spectral density function (PSDF) indicates that the mean square response is affected by the amplification at the natural frequency of the surge degree-of-freedom and also at the peak frequency of the wave loading. The PSDF of the heave response shows higher peak values near the surge frequency and near the peak frequency of the wave loading. Surge response, therefore, influences heave response to the maximum. Variable submergence seems to be a major source of nonlinearity and significantly enhances the responses in surge, heave and pitch degrees-of-freedom. In the presence of current, the response behaviour of the TLP is altered significantly introducing a non-zero mean response in all degrees-of-freedom.

A micro-electro-mechanical model for polarization switching of ferroelectric materials

Ferroelectric and ferroelastic switching are the major source of nonlinearity and hysteresis in ferroelectric materials subjected to high electric field or mechanical stress. A computational micromechanics model for polycrystalline ferroelectric ceramics is developed based on consideration of the constitutive behavior of single crystals. This model simulates the tetragonal and the rhombohedral crystal structures. Saturation of the linear piezoelectric effect is included. Interaction between different grains in the polycrystalline ceramic is considered. A switching criterion is developed that accounts for different energy levels associated with 90° and 180° switching for the tetragonal structure (or 70.5°, 109.5°, and 180° for the rhombohedral structure). Experimental results on 8/65/35 PLZT are simulated and a parametric study of the effects of crystal structure, intergranular interaction, and phase transformation is performed.

Analysis of the spatial non-linear vibrations of a string

The problem of the free and forced quasilinear spatial vibrations of a string is investigated in the single-mode approximation of wave processes. A mathematical model is constructed in which geometric non-linearity, caused by the linear extensibility of a string, is the major source of non-linearity. As a result. the tension turns out to be variable both with respect to time and length. An asymptotic analysis of the free vibrations is carried out and the phenomenon of the instability of plane vibrations is investigated. The resonance curves corresponding to a plane harmonic excitation are constructed in terms of the system parameters and analysed. The stability of steady vibrations is completely investigated using Lyapunov's first method. Qualitative effects. associated with the stability and instability of plane and spatial forced vibrations. are detected and studied within the framework of the spatial model.

A digital filtration technique for scatter-glare correction based on thickness estimation

In order to quantitate anatomical and physiological parameters such as vessel dimensions and volumetric blood flow, it is necessary to make corrections for scatter and veiling glare, which are the major sources of nonlinearities in videodensitometric digital subtraction angiography (DSA). A convolution filtering technique has been investigated to estimate scatter-glare distribution in DSA images without the need to sample the scatter-glare intensity for each patient. This technique utilizes exposure parameters and image gray levels to assign equivalent Lucite thickness for every pixel in the image. The thickness information is then used to estimate scatter-glare intensity on a pixel-by-pixel basis. To test its ability to estimate scatter-glare intensity, the correction technique was applied to images of a Lucite step phantom, anthropomorphic chest phantom, head phantom, and animal models at different thicknesses, projections, and beam energies. The root-mean-square (rms) percentage error of these estimates was obtained by comparison with direct scatter-glare measurements made behind a lead strip. The average rms percentage errors in the scatter-glare estimate for the 25 phantom studies and the 17 animal studies were 6.44% and 7.96%, respectively. These results indicate that the scatter-glare intensity can be estimated with adequate accuracy for a wide range of thicknesses, projections, and beam energies using exposure parameters and gray level information.

Diskette test linearity

Test linearity occurs when results obtained using any test system agree with those obtained using the master test system used to prepare reference material. Linearity is necessary to obtain correlation within the diskette industry. Non-linearity can occur if other reference disks are substituted for PTB secondary reference material. Even when the test system is calibrated using proper reference material, that calibration is valid only for test results having values close to those of the reference disk. System non-linearities can affect results when test values can depart significantly from reference values. This causes poor correlation between test equipment which leads to confusion about conformance to specifications. Results of this investigation demonstrate non-linearity for the four most popular types of diskettes and suggest that the test drive is a major source of non-linearity. Since the average test facility may not have the proper technical resources for linearity measurements, the manufacturers of diskette test equipment must supply linear test drives to users of their equipment.

Scatter-glare corrections in quantitative dual-energy fluoroscopy.

Previous attempts to use time subtraction intravenous digital subtraction angiography for ventricular imaging have been hampered by artifacts due to cardiac and respiratory motion. We have previously reported a motion-immune dual-energy technique in which kVp is switched between 60 and 120, at 300-500 mA, 30 times/s. In order to quantitate parameters such as ejection fraction and left ventricular volume, it is necessary to correct for scatter and veiling glare (SVG), which are the major sources of nonlinearities in videodensitometric digital subtraction angiography (DSA). In this report, a convolution filtering method has been investigated to estimate SVG in DSA images. In the first step, a grey level transformation of the detected image is utilized to get an estimated SVG image. In the second step this image is convolved to produce an image with appropriate spatial frequency content. Estimates of SVG in several Humanoid chest phantom images were obtained using Gaussian convolution kernels with a full width at half-maximum (FWHM) of 51-125 pixels. The root-mean-square (rms) percentage error of these estimates was obtained by comparison with direct SVG measurement. A convolution kernel with a FWHM of 75 pixels in each dimension applied to 16 Humanoid phantom images with various projections, thicknesses, and beam energies resulted in an average rms percentage error of 9.7% in the SVG estimate, for the 16 cases studied. The SVG estimation consisting of grey scale-to-SVG fraction lookup table (LUT) is made based on previous measurements. The x-ray settings required for each patient are utilized to alter the LUT in order to account for patient thickness variations.(ABSTRACT TRUNCATED AT 250 WORDS)

Nonlinear analysis of reinforced concrete structures

For the prediction of yield and failure of concrete under combined stress, a generalization of the Mohr-Coulomb behavior is made in terms of the principal stress invariants. The generalized yield and failure criteria are developed to account for the two major sources of nonlinearity: the progressive cracking of concrete in tension, and the nonlinear response of concrete under multiaxial compression. Using these criteria, incremental stress-strain relationships are established in suitable form for the nonlinear finite element analysis. For the analysis of reinforced concrete members by finite elements, a method is introduced by which the effect of reinforcement is directly included. With this approach, the stress-strain laws for the constituent materials of reinforced concrete are uncoupled permitting efficient and convenient implementation of a finite element program. The applicability of the method is shown on sample reinforced concrete analysis problems.