Nonlinear Response Functions Research Articles

Geometrically non-linear forced vibrations of fully clamped functionally graded beams with multi-cracksresting on intermediate simple supports

The objective of this work is to investigate the non-linear forced dynamic response at large vibration amplitudes of fully clamped functionally graded beams containing a multiple open edge cracks and resting on intermediate simple supports. The theoretical model is based on the Euler-Bernoulli beam theory and the crack rotational spring model. The functionally graded beam properties are supposed to vary continuously through the beam thickness. A homogenization procedure based on the neutral surface approach taking into account the presence of the crack is developed to reduce the problem examined to that of an equivalent isotropic homogeneous multi-cracked beam. In the non-linear analysis, harmonic motion is assumed and the discretized expressions for the beam total strain and kinetic energies are derived by applying Hamilton’s Principle, so as to reduce the problem to a non-linear algebraic system solved using an approximate explicit method previously applied to various non-linear structural vibration problems. Considering the forced vibration case, the non-linear frequency response functions are obtained numerically in the neighbourhood of the predominant non-linear mode shape using a single mode approach. The effects of crack, the beam material gradient and the applied harmonic force are presented and discussed.

Geometrically nonlinear forced vibrations of fully clamped multi-span beams carrying multiple masses and resting on a finite number of simple supports

Geometrically nonlinear forced vibrations of fully clamped multi-span beams resting on multiple simple supports and carrying multiple masses may be encountered in many mechanical and civil engineering applications. The theoretical model developed here is based on the Euler-Bernoulli beam theory and the Von Karman geometrical non-linearity assumptions. Harmonic motion is assumed and the nonlinear beam transverse displacement function is expanded as a series of the linear modes, determined by solving first the linear problem. The discretised expressions for the beam total strain and kinetic energies are then derived, and by applying Hamilton’s principle, the problem is reduced to a nonlinear algebraic system solved using an approximate method (the so-called second formulation). The basic function contribution coefficients to the structure non-linear response function and the corresponding backbone curves giving the non-linear amplitude-frequency dependence is determined. Numerical results are given in the neighbourhood of the predominant nonlinear mode shape, based on the single mode approach, for a wide range of vibration amplitudes, showing the effect of the added masses and their locations, as well as the applied uniformly distributed harmonic force on its non-linear dynamic response.

A novel spatial optimization model for achieve the trad-offs placement of best management practices for agricultural non-point source pollution control at multi-spatial scales

The efforts to management agricultural non-point source pollution from the field to watershed scale is an ongoing challenge that needs to take into account trade-offs between environmental and economic objectives. Best management measures (BMPs) are considered as an effective means to achieve this balance in the management of agricultural non-point source pollution. Many studies have focused on a single spatial scale for placement of the BMPs, however, the effectiveness in improving water quality at different scale will affect by many factors such as the land use, soil type and the river network and so on. In order to demonstrating the relationship or impact of spatial scale changes on the allocation and effectiveness of BMPs. The present study attempts to development a novel multi-scale model framework and indices as a decision support platform for solve the impact of spatial scale change on the optimization of best management measures in the Chaohe River Watershed in Beijing and Hebei province. And used it in a drinking water source area which was affected by the agricultural nonpoint source pollution in recent decades in Beijing, China. A series of the utility functional between the utility of the water quality improvement and the number of watersheds, watershed size, the unit cost of BMPs and integrated these three functional relations by Generalized Reduced Gradient Algorithm. We found that the nonlinear threshold response function can play a key role in the configuration of BMPs from field to watershed scale. The results show that 1) the utility functions for pollution load reduction and the number of watersheds can be described by the log-sigmoid curve, and the optimal number of watershed for total nitrogen (TN) and total phosphorus (TP) control are 25 and 23 respectively, 2) the most utility function for the pollution load reduction and the mean sub-watershed area is exponential function curves, and the optimal mean sub-watershed areas are168 km2 and 214 km2 for TN and TP, respectively, 3) the relationship between pollution load reduction and cost of per unit after BMPs implemented can be drawing by the logistic curves, and the optimal average unit cost are 4622 and 7692 CNY·ha−1 for TN and TP, respectively, 4) the comprehensive optimal of these above functions shown that the total cost of BMP plans is 2.01 × 107 and 4.7 × 107 CNY for TN and TP, respectively at the trad-offs scenario. This study will provide a systematic approach to determine more reasonable and feasible management practices system on more reasonable spatial scale for the protection of water quality and safety in watershed.

Surrogate-based simulation optimization approach for day-to-day dynamics model calibration with real data

This paper investigates the day-to-day dynamics model from the perspective of travelers’ actual route choice behaviors, and calibrates and validates the route-based day-to-day dynamics model with the real-world license plate recognition (LPR) data. Due to the highly nonlinear and multi-modal response function in the calibration of the optimization problem, traditional gradient-based nonlinear regression algorithms or other analytical optimization approaches are inapplicable to deal with the calibration work. In this paper, a surrogate-based simulation optimization approach is proposed to deal with the expensive-to-evaluate response function in the day-to-day dynamics calibration work. More specifically, the kriging metamodel is adopted to surrogate the optimization function of the calibration process. With this meta-modeling approach, a sound solution can be achieved with only a few sampling points in a comfortably afforded computation burden, thus giving a valid estimation of the parameters in the day-to-day dynamics model. Finally, a case study based on the real-world LPR data is conducted to validate the proposed model and calibration method.

Breathing mode phenomena in the properties of the compact bright light pulse

The origin and characteristics of the breathing mode in the properties of the compact bright (CB) pulse described by the dispersionless nonlinear Schrödinger equation with nearly instantaneous nonlinear response function of the waveguide are investigated. We show that the breathing mode originates from the third order dispersion only and the conditions for its existence are derived. Its characteristics parameters namely the frequency of oscillations and the amplitude are also derived analytically and it appears that they are closely connected to the initial perturbations of the CB pulse parameters at the equilibrium state. In addition, these parameters as well as the condition of existence are modified by the presence of higher order (HO) terms namely the time derivative of the pulse envelope term on one hand and the Raman term on the other hand. This breathing mode consolidates the stability of the CB pulse during the propagation along the waveguide. However when the two HO terms act together on the system the breathing mode become unstable leading to the instability of the CB pulse after large distance of propagation.

Iterative approach to arbitrary nonlinear optical response functions of graphene

Two-dimensional materials constitute an exciting platform for nonlinear optics with large nonlinearities that are tunable by gating. Hence, gate-tunable harmonic generation and intensity-dependent refraction have been observed in e.g. graphene and transition-metal dichalcogenides, whose electronic structures are accurately modelled by the (massive) Dirac equation. We exploit on the simplicity of this model and demonstrate here that arbitrary nonlinear response functions follow from a simple iterative approach. The power of this approach is illustrated by analytical expressions for harmonic generation and intensity-dependent refraction, both computed up to ninth order in the pump field. Moreover, the results allow for arbitrary band gaps and gating potentials. As illustrative applications, we consider (i) gate-dependence of third- and fifth-harmonic generation in gapped and gapless graphene, (ii) intensity-dependent refractive index of graphene up to ninth order, and (iii) intensity-dependence of high-harmonic generation.

Dynamics analysis and numerical simulations of a delayed stochastic epidemic model subject to a general response function

This paper proposes a new delayed stochastic epidemic model with double epidemic hypothesis and a general nonlinear response function. The main purpose is to explore the effects of environmental noise and the general nonlinear response function on stochastic dynamics. By constructing appropriate Lyapunov functions and using some novel differential inequality techniques, we first investigate the long-time asymptotic properties of the stochastic delayed system. Moreover, the threshold conditions for the persistence in mean are established. At last, we carry out a series of numerical simulations to illustrate the performance of the theoretical results. The developed theoretical methods and stochastic inequalities techniques can be applied to explore stochastic differential systems with the general response function.

Combination algorithm for cracked rotor fault diagnosis based on NOFRFs and HHR

In this paper, a combination algorithm for diagnosing rotor crack fault is presented. Firstly, the nonlinear output frequency response functions (NOFRFs) are used to analyze the severity of crack damage in the rotor system qualitatively. The NOFRFs are obtained by processing the vibration signal through the nonlinear output frequency response functions. Further analysis of the NOFRFs can determine the crack depth qualitatively. Secondly, the position of the crack is then located using the crack position index (CPI) λ based on the higher harmonic response (HHR) and the dynamic compliance matrix. The simulation and experimental results show that the G2(j2wF) in NOFRFs is very sensitive to crack depth, and the crack position index (CPI) λ can determine the shaft segment effectively where the crack is located. The advantage of this combination algorithm is that it can detect the crack faults by measuring the vibration signal of the cracked rotor at two speeds, which makes the measurement process more simplified and reduces the measurement time for real-time monitoring. At each speed only the vibration response of the two nodes need to be measured, which greatly reduces the number of sensor used in the measurement process and reduces the cost of monitoring. The combination algorithm can diagnose cracked rotor faults effectively and has certain application value in the diagnosis of cracked rotor fault.

CAD based design of a high energy absorption metal oxide varistor

Metal Oxide Varistors are a very common power electronic device, applied for efficient overvoltage protection at any voltage level. This piece of equipment has a high non-linear current response function of the applied voltage, and, it provides a relatively high heat absorption capacity in case of accidental overvoltage shocks. The crossing response current is clearly activated by temperature of that device, and, by consequent, overheating could be disastrous. Actual researches must be carried out both for a new more performant material as well as for new technical solutions for the design of all equipment integrating them, by studying heat extraction and heat transfer inside a new complex varistor device. Our article proposes a totally new device, used basically for low voltage applications, having a supplementary metal mass added to the body of that varistor, shaped as small disk. It actions like a heat pump immediately after the voltage shock and as additional radiators at the end of the heating process caused by a transitory overvoltage. A CAD solution combined with a finite element model, followed by some experimental results are also presented, for confirming the performance of that newly design. By placing additional metal alloy masses inside a new varistor structure it will have a higher heat pumping and dissipation capability, in order to reduce temperature stress and all aging effects.

Theory of coherent two-dimensional vibrational spectroscopy.

Two-dimensional (2D) vibrational spectroscopy has emerged as one of the most important experimental techniques useful to study the molecular structure and dynamics in condensed phases. Theory and computation have also played essential and integral roles in its development through the nonlinear optical response theory and computational methods such as molecular dynamics (MD) simulations and electronic structure calculations. In this article, we present the fundamental theory of coherent 2D vibrational spectroscopy and describe computational approaches to simulate the 2D vibrational spectra. The classical approximation to the quantum mechanical nonlinear response function is invoked from the outset. It is shown that the third-order response function can be evaluated in that classical limit by using equilibrium or non-equilibrium MD simulation trajectories. Another simulation method is based on the assumptions that the molecular vibrations can still be described quantum mechanically and that the relevant molecular response functions are evaluated by the numerical integration of the Schrödinger equation. A few application examples are presented to help the researchers in this and related areas to understand the fundamental principles and to use these methods for their studies with 2D vibrational spectroscopic techniques. In summary, this exposition provides an overview of current theoretical efforts to understand the 2D vibrational spectra and an outlook for future developments.

PC-VINS-Mono: A Robust Mono Visual-Inertial Odometry with Photometric Calibration

<p>Feature detection and Tracking, which heavily rely on the gray value information of images, is a very importance procedure for Visual-Inertial Odometry (VIO) and the tracking results significantly affect the accuracy of the estimation results and the robustness of VIO. In high contrast lighting condition environment, images captured by auto exposure camera shows frequently change with its exposure time. As a result, the gray value of the same feature in the image show vary from frame to frame, which poses large challenge to the feature detection and tracking procedure. Moreover, this problem further been aggravated by the nonlinear camera response function and lens attenuation. However, very few VIO methods take full advantage of photometric camera calibration and discuss the influence of photometric calibration to the VIO. In this paper, we proposed a robust monocular visual-inertial odometry, PC-VINS-Mono, which can be understood as an extension of the opens-source VIO pipeline, VINS-Mono, with the capability of photometric calibration. We evaluate the proposed algorithm with the public dataset. Experimental results show that, with photometric calibration, our algorithm achieves better performance comparing to the VINS-Mono.�</p>

Research on Diagnosis Method of Rotor Misalignment-bumping Coupling Fault Based on Nonlinear Output Frequency Response Function

Research on Diagnosis Method of Rotor Misalignment-bumping Coupling Fault Based on Nonlinear Output Frequency Response Function

Research on Fault Feature Extraction Method Based on NOFRFs and Its Application in Rotor Faults

Rub‐impact between the rotating and static parts is a more common fault. The occurrence of faults is often accompanied by the generation of nonlinear phenomena. However, it is difficult to find out because the nonlinear characteristics are not obvious at the beginning of the fault. As a new frequency domain‐based method, nonlinear output frequency response functions (NOFRFs) use the vibration response to extract the nonlinear characteristics of the system. This method has a better recognition rate for fault detection. Also, it has been applied in structural damages detection, but the high‐order NOFRFs have the characteristics that the signals are weak and the features are difficult to extract. On this basis, the concept of the weighted contribution rate of the NOFRFs is proposed in this paper. The variable weighted coefficients with orders are used to amplify the influence of high‐order NOFRFs on the nonlinearity of the system so as to extract its fault characteristics. The new index RI is proposed based on Clenshaw–Curtis quadrature formula to eliminate the effect of artificially selected weighted coefficients on sensitivity. Especially in the early stage of the fault, the new index varies greatly with the deepening of the fault. Both simulation and experimental results verify the validity and practicability of the new index. The new index has certain guiding significance in the detection of mechanical system faults.

From Linear to Nonlinear Responses of Thermal Pure Quantum States

We propose a self-validating scheme to calculate the unbiased responses of quantum many-body systems to external fields of arbitrary strength at any temperature. By switching on a specified field to a thermal pure quantum state of an isolated system, and tracking its time evolution, one can observe an intrinsic thermalization process driven solely by many-body effects. The transient behavior before thermalization contains rich information on excited states, giving the linear and nonlinear response functions at all frequencies. We uncover the necessary conditions to clarify the applicability of this formalism, supported by a proper definition of the nonlinear response function. The accuracy of the protocol is guaranteed by a rigorous upper bound of error exponentially decreasing with system size, and is well implemented in the simple ferromagnetic Heisenberg chain, whose response at high fields exhibits a nonlinear band deformation. We further extract the characteristic features of excitation of the spin-1/2 kagome antiferromagnet; the wave-number-insensitive linear responses from the possible spin liquid ground state, and the significantly broad nonlinear peaks which should be generated from numerous collisions of quasiparticles, that are beyond the perturbative description.

Using Various Nonlinear Response Surfaces for Mathematical Description of the Type of Combined Toxicity.

The article considers the problem of characterizing the type of combined action produced by a mixture of toxic substances with the help of nonlinear response functions. Most attention is given to second-order models: the linear model with a cross-term and the quadratic model. General propositions are formulated based on the data on combined toxicity patterns previously obtained by the Ekaterinburg nanotoxicology team in animal experiments and analyzed with the help of the linear model with a cross-term. It is shown now that the quadratic model features these general characteristics in full measure, but interpretation of combined toxicity types based on isobolograms obtained by the quadratic model is more difficult. This suggests that where both models ensure a comparable quality of combined toxicity type identification, it would be enough to use the linear model with a cross-term.

DURAÇÃO DA FASE DE MUDAS EM EUCALIPTO SIMULADA EM CENÁRIOS DE AUMENTO DE TEMPERATURA

A mudança climática é um tema atual em debates científicos e de interesse na área florestal, porém, estudos da vulnerabilidade de espécies florestais cultivadas às mudanças climáticas são escassos. O objetivo deste trabalho foi simular a duração da fase de mudas de duas espécies de eucalipto (Eucalyptus saligna e Eucalyptus grandis) em cenários de aumento de temperatura do ar em Santa Maria-RS, considerando várias datas de emergência. A fase de mudas foi considerada da emergência das plântulas até o aparecimento da 25ª folha na haste principal. A taxa de aparecimento de folhas diária (TAF) foi estimada através de um modelo multiplicativo com uma função de resposta não linear da TAF à temperatura média do ar, com coeficientes para as espécies Eucalyptus saligna e Eucalyptus grandis. Foram considerados doze datas de emergência (dia 15 de cada mês do ano) e seis cenários climáticos (atual, +1°C, +2°C, +3°C, + 4°C, +5°C). Os cenários climáticos constituem-se séries sintéticas de cem anos de dados de temperatura mínima e máxima diária do ar. Em cada um dos anos dos cenários climáticos e em cada data de emergência, o modelo de TAF para cada espécie foi rodado e contabilizado o número de dias da emergência até o aparecimento da 25ª folha. A análise estatística constou de análise de variância para a variável duração da fase de mudas, considerando um experimento tri-fatorial 6 x 12 x 2 (cenários climáticos x datas de emergência x espécies), em delineamento inteiramente casualizado, sendo cada ano da simulação uma repetição (n=100). Os resultados indicaram uma diminuição na duração da fase de mudas em cenários climáticos mais quentes nas emergências ocorridas de março a setembro, e um aumento na duração nas emergências de outubro a fevereiro e, ao final de um ano, o aumento de temperatura tende a diminuir o tempo de mudas no viveiro e assim aumentar a produção anual de mudas de eucalipto. Benefícios e desvantagens destes resultados devem ser considerados em políticas de mitigação dos efeitos do aquecimento global na silvicultura.

Comparing Symbolic and Nonsymbolic Number Lines: Consistent Effects of Notation Across Output Measures.

The mental number line (MNL) is a popular metaphor for magnitude representation in numerical cognition. Its shape has frequently been reported as being nonlinear, based on nonlinear response functions in magnitude estimation. We investigated whether this shape reflects a phenomenon of the mapping from stimulus to internal magnitude representation or of the mapping from internal representation to response. In five experiments, participants (total N = 66) viewed stimuli that represented numerical magnitude either in a symbolic notation (i.e., Arabic digits) or in a nonsymbolic notation (i.e., clouds of dots). Participants estimated these magnitudes by either adjusting the position of a mark on a ruler-like response bar (nonsymbolic response) or by typing the corresponding number on a keyboard (symbolic response). Responses to symbolic stimuli were markedly different from responses to nonsymbolic stimuli, in that they were mostly powershaped. We investigated whether the nonlinearity could be explained by effects of previous trials, but such effects were (a) not strong enough to explain the nonlinear responses and (b) existed only between trials of the same input notation, suggesting that the nonlinearity is due to input mappings. Introducing veridical feedback improved the accuracy of responses, thereby showing a calibration based on the feedback. However, this calibration persisted only temporarily, and responses to nonsymbolic stimuli remained nonlinear. Overall, we conclude that the nonlinearity is a phenomenon of the mapping from nonsymbolic input format to internal magnitude representation and that the phenomenon is surprisingly robust to calibration.

Fault diagnosis of gearbox based on the nonlinear output frequency response functions and PNN

In this study, the fault diagnosis of nonlinear gearbox is investigated by using the frequency domain approach. The Nonlinear Output Frequency Response Functions (NOFRFs) of the nonlinear gearbox are evaluated and be used to diagnosis the abnormal conditions of the gears and the bearings. A case study is used to illustrate the NOFRFs based feature extraction method, then a probabilistic neural network (PNN) is mentioned to classify the failure modes. Finally, the results show that this method can complete the fault diagnosis of gearbox perfectly. The study provides a basis of the application of the NOFRFs and PNN in the fault diagnosis or condition monitoring of complex nonlinear systems.

Exploration on Explanations for Observed Long-Term Temporal Trend of the Short-Term Association between Fine Particulate Matter Concentration and Hospital Admissions in the U.S.

BackgroundIn earlier work, we examined whether the PM2.5-hospital admissions relative risk varies over time, using hospital admission data of U.S. Medicare beneficiaries and U.S. Environmental Protection Agency PM2.5 monitoring data. When assuming a linear temporal trend, the change in respiratory hospital admissions per 10 μg/m3 increase in same day PM2.5 decreased by 1.77% (95% CI: 0.92 to 2.63%) from the year 1999 to the year 2013, while no statistical significant temporal trend was observed for cardiovascular hospital admissions. To better understand drivers behind the observed temporal trends, this study provides details in our model specifications, as well as exploration on explanations to these observations.MethodsTo ensure internal validity of the modified Bayesian hierarchical model used, we conducted extensive sensitivity analyses with hypotheses tested stated a priori. Based on previous literatures and biological plausibility, we proposed and evaluated four possible explanations for the decreasing temporal trend for respiratory admissions as well as the lack of temporal trend for cardiovascular admissions: 1) the increase in relative measurement error at lower level of PM2.5 concentration; 2) flattening of concentration-response function at lower level of PM2.5 concentration; 3) change in chemical composition of PM2.5 total mass; 4) change in population susceptibility towards acute exposure to PM2.5 on respiratory adverse health outcomes.Results and conclusionsBased on qualitative evidence, changes in population susceptibility towards acute exposure to PM2.5 on respiratory adverse health outcomes, and combination of changes in multiple chemical components may partially explain the observed temporal trend. Future research should consider distributed lag model and non-linear concentration response functions, which will require additional exposure data.

Computation Offloading in Optical Access Cloudlet Networks: A Game-Theoretic Approach

Computation offloading to edge-computing technologies is highly desirable to enable the use of low-latency computation intensive mobile-applications. To meet the desired latency requirements, overloaded cloudlets can further offload the incoming job requests to their under-loaded neighbor cloudlets. A novel economic and non-cooperative continuous-kernel game theoretic model is proposed to analyze the computation offloading strategies between cloudlets of competing service providers, supported by optical access networks. This model achieves a fairness in resource utilization as well as provides incentives to the participants. We investigate the existence and uniqueness conditions of the pure strategy Nash equilibrium for the formulated game. By linearizing the non-linear best response functions, we derive an approximate Nash equilibrium for the formulated game. We explain the dependence of the Nash equilibrium on factors such as computational resources, total incoming job requests, cloudlet to cloudlet transmission latency and corresponding cost factors. Finally, we show improvements in overall latency performance while employing the proposed Nash equilibrium offload strategy.