Nonlinear Response Time Research Articles

Nonlinear vibration analysis of fractional viscoelastic Euler–Bernoulli nanobeams based on the surface stress theory

The nonlinear vibrations of viscoelastic Euler–Bernoulli nanobeams are studied using the fractional calculus and the Gurtin–Murdoch theory. Employing Hamilton's principle, the governing equation considering surface effects is derived. The fractional integro-partial differential governing equation is first converted into a fractional–ordinary differential equation in the time domain using the Galerkin scheme. Thereafter, the set of nonlinear fractional time-dependent equations expressed in a state-space form is solved using the predictor–corrector method. Finally, the effects of initial displacement, fractional derivative order, viscoelasticity coefficient, surface parameters and thickness-to-length ratio on the nonlinear time response of simply-supported and clamped-free silicon viscoelastic nanobeams are investigated.

Seismic vulnerability assessment of concrete shear wall buildings through fragility analysis

Seismic vulnerability assessment of shear wall buildings can be conducted through non-linear dynamic analysis, which requires detailed analytical modeling, the consideration of different earthquake intensity and structural performance measures. Reinforced concrete shear wall buildings were designed for Vancouver, representing a region of high seismicity in Canada, to assess seismic vulnerability of buildings constructed before and after the enactment of modern seismic design codes. The buildings either had a two-storey or a five-storey height, designed either using the 1965 or the 2010 National Building Code of Canada. Analytical models were generated for non-linear response time history analysis using computer software PRFORM-3D. Fiber-discretized sections were used for flexural response based on constitutive models for concrete and reinforcing steel. The nonlinear behavior in shear was modelled on the basis of sectional non-linear shear response. The shear wall models were validated against experimental data available in the literature before incremental dynamic analysis (IDA) was employed to generate fragility curves. Spectral acceleration at the fundamental period was used as seismic intensity parameter and inter-storey drift of the first floor was selected as the damage indicator. Performance limits considered include Immediate Occupancy, Life Safety and Collapse Prevention. The resulting fragility curves indicate that the life safety intent of the 2010 building designs has been met, while the same requirements could not be satisfied for the 1965 building designs.

“Total displacement of curved surface sliders under nonseismic and seismic actions: A parametric study”

Summary The re-centring capability is recognized as a fundamental function of any effective isolation system, not only because it is associated to small or negligible deformation at the end of the earthquake but rather because it prevents displacement build up that may limit the capability of the structure to withstand aftershocks and future earthquakes. The current Eurocode recommends to estimate the maximum total displacement of the isolated system as the superposition of the nonseismic offset displacement resulting from permanent actions, long-term deformations and thermal movements of the structure, and of the amplified seismic displacement induced by the design earthquake. For systems endowed with low re-centring capability, the estimation shall also account for the possible accrual of displacements during the lifetime of the structure. However, the aforementioned criteria have never been evaluated for curved surface sliders, which are characterized by an inherent nonlinear behaviour. The study aims at giving more insight into the matter by conducting a parametric study based on one-directional nonlinear response time history analyses and considering a variety of seismic scenarios. The first part of the study investigates the effect of a nonseismic displacement on the earthquake-induced displacement and formulates a criterion to evaluate the capability of curved surface sliders to provide a seismic response independent of the offset displacement. The response of the isolation system to natural sequences of earthquakes, where the offset displacement is the residual displacement from the previous shake, is addressed in the second part of the paper. The provisions of the Eurocode are eventually checked against the observed data.

Spectrum-based pushover analysis for estimating seismic demand of tall buildings

A quick and accurate estimate of the seismic demand of tall buildings is one of the important issues in the seismic evaluation of buildings. Nonlinear response time history analysis method (NLRHA) is considered as the most accurate and rigorous method, but the computation requirement of NLRHA for tall buildings can be complex and very time-consuming. Whereas the conventional pushover procedure is not capable of reasonably estimating seismic demand of mid and high rise-buildings, due to the oversimplification of conventional pushover approaches and the complexity of seismic performance of buildings. In this paper, a quick, yet effective, method of analysis, named as a spectrum-based pushover analysis (SPA) method, is proposed to estimate the seismic demand of tall buildings. In the SPA procedure, the very complex and complicated dynamic coupling effect of modes of the nonlinear seismic performance of a building is simplified, and the consecutive pushover technique is adopted to consider the simplified coupling effect. Comparison of the results obtained from NLRHA, the modal pushover analysis method, the consecutive modal pushover analysis method and the proposed SPA method is made. It is seen that the SPA method predicted the seismic demand of buildings well, including the inter-storey drift ratio and hinge plastic rotation, which are very close to those of NLRHA. Owing to its accuracy, effectiveness, and spectrum-based calculation procedure, the proposed SPA procedure is considered to be a very promising tool for predicting the seismic demand of tall buildings.

The impact of successive earthquakes on the seismic damage of multistorey 3D R/C buildings

Historical earthquakes have shown that successive seismic events may occur in regions of high seismicity. Such a sequence of earthquakes has the potential to increase the damage level of the structures, since any rehabilitation between the successive ground motions is practically impossible due to lack of time. Few studies about this issue can be found in literature, most of which focused their attention on the seismic response of SDOF systems or planar frame structures. The aim of the present study is to examine the impact of seismic sequences on the damage level of 3D multistorey R/C buildings with various structural systems. For the purposes of the above investigation a comprehensive assessment is conducted using three double-symmetric and three asymmetric in plan medium-rise R/C buildings, which are designed on the basis of the current seismic codes. The buildings are analyzed by nonlinear time response analysis using 80 bidirectional seismic sequences. In order to account for the variable orientation of the seismic motion, the two horizontal accelerograms of each earthquake record are applied along horizontal orthogonal axes forming 12 different angles with the structural axes. The assessment of the results revealed that successive ground motions can lead to significant increase of the structural damage compared to the damage caused by the corresponding single seismic events. Furthermore, the incident angle can radically alter the successive earthquake phenomenon depending on the special characteristics of the structure, the number of the sequential earthquakes, as well as the distance of the record from the fault.

Proportional-Resonant and Slide Mode Control for Single-Phase UPS Inverter

Slide mode control (SMC) is recognized as the most robust control with high stability, while the proportional-resonant (PR) control shapes the output waveform closely according to the reference sinusoidal signal. Keeping in view the characteristics of slide mode and PR control, a cascaded controller is proposed for bipolar single-phase uninterruptible power supply (UPS) inverter. The outer voltage loop uses the PR control while the inner loop uses the SMC. Chattering in the SMC has been removed using smoothed control law in narrow boundary layer condition. The stability of the controller has been analyzed using Lypunov stability criteria. The smoothed control law applied to the pulse width modulator results in fixed switching frequency of the inverter. The performance of the controller has been analyzed for single-phase inverter through simulations and experiments for both the linear and non-linear loads. The performance of controller has been compared with the other techniques of SMC and standard controllers. The proposed controller shows significant improvement in terms of reducing the total harmonics distortion to 0.5% for linear load and 1.25% for non-linear load, strong robustness, and fast response time of only 0.3 ms.

Homotopy analysis of a forced nonlinear beam model with quadratic and cubic nonlinearities

This study investigates forced nonlinear vibrations of a simply supported Euler-Bernoulli beam on a nonlinear elastic foundation with quadratic and cubic nonlinearities. Applying the homotopy analysis method (HAM) to the spatially discretized governing equation, we derive novel analytical solutions and discuss their convergence to present nonlinear frequency responses with varying contributions of the nonlinearity coefficients. A comparison with numerical solutions is conducted and nonlinear time responses and phase planes are compared to the results from linear beam theory. The study demonstrates that apart from nonlinear problems of free vibrations, HAM is equally capable of solving strongly nonlinear problems of forced vibrations.

Experimental realisation of parallel optical logic gates and combinational logic using multiple beam interference

In this paper, we report the experimental realisation of parallel optical logic gates and some combinational logic using multiple beam interference in three cascaded Michelson type interferometers. Considering light intensity at different points of 2-D interference pattern of four input laser beams as output, (i) two input AND, OR, NAND, NOR, XOR, XNOR optical logic gates in parallel, (ii) three input AND and NAND optical logic gates in parallel, and (iii) four input AND logic gate as well as some combinational logic in parallel were realised. By controlling the four input laser beams electro-optically or all-optically using nonlinear optical materials having large nonlinearity and fast response time, ultrafast photonic information processing can be performed utilizing present scheme due to parallel operation of large number of logic gates.

Studying linear and nonlinear vibrations of fractional viscoelastic Timoshenko micro-/nano-beams using the strain gradient theory

In this paper, the vibrational behavior of micro- and nano-scale viscoelastic beams under different types of end conditions in the linear and nonlinear regimes is investigated based on the fractional calculus. To capture the effects of small scale, the modified strain gradient theory is utilized. Also, the beams are modeled based on the Timoshenko beam theory, von Karman nonlinear relations and the fractional Kelvin–Voigt viscoelastic model. Derivation of governing equations is performed using Hamilton’s principle. For the linear solution, the generalized differential quadrature and finite difference methods are employed. Moreover, in the nonlinear solution procedure, the Galerkin method is first used to convert the fractional integro-partial differential governing equations into fractional ordinary differential equations which are then arranged in an effective state-space form. The predictor–corrector technique is finally used to solve the set of nonlinear fractional time-dependent equations. Selected numerical results are given on the linear and nonlinear time responses of the fractional viscoelastic small-scale beams to study the effects of fractional-order, viscoelasticity coefficient and length scale parameter.

Wavepacket delocalization, self-trapping and fragmentation in discrete chains with relaxing nonlinearity

The discrete nonlinear Schrodinger equation (DNSE) describes wave phenomena in several physical contexts, ranging from electronic transport in crystalline chains to light propagation in nonlinear media and Bose-Einstein condensates. Here, we study the influence of the nonlinear response time on the temporal evolution of a wavepacket initially localized in a single site of a finite closed chain. Distinct long-time wavepacket distributions are identified as a function of the nonlinear strength χ and the characteristic relaxation time τ. Besides the more standard delocalized and self-trapped regimes, we report the occurrence of intermediate phases. In one of them the wavepacket self-focus in the opposite chain site. A phase with asymptotically fragmented wavepackets also develops. A crossover regime on which the ultimate wavepacket distribution is strongly dependent on the precise set of model parameters is also identified. We provide the full phase diagram related to the long-time wavepacket distribution in the (χ, τ) space.

Zinc oxide (ZnO) nanoparticles as saturable absorber in passively Q-switched fiber laser

We demonstrate a passively Q-switched erbium-doped fiber laser using zinc oxide (ZnO) nanoparticles thin film as saturable absorber (SA). ZnO exhibits high nonlinear optical response and fast recovery time, fulfilling the requirements of an ideal SA. The nonlinear optical absorption is characterised by modulation depth of 3.5% with saturation intensity of 0.016MWcm−2. We insert the SA into the laser cavity and obtain stable Q-switched pulse whereby the repetition rate increases from 41.7kHz to 77.2kHz while the pulse width decreases from 9.6μs to 3.0μs as the pump power is increased from 60mW to 360mW. This result suggests that ZnO could be a promising SA for photonic applications.

Influence of Self-Diffraction Effect on Femtosecond Time-Resolved Single-Shot Optical Kerr Measurements**Supported by the National Natural Science Foundation of China under Grant Nos 11304242, 11474078 and 61427816, the Natural Science Basic Research Plan in Shaanxi Province under Grant No 2014JQ1024, the Financial Support from China Postdoctoral Science Foundation under Grant Nos 2013M542335 and 2014T70924, and the Collaborative Innovation Center of Suzhou

Femtosecond time-resolved single-shot optical Kerr gating (OKG) measurements are performed by focusing the probe pulse and using a cylindrical lens to introduce a spatially encoded time delay with respect to the pump pulse. By measuring the pump power and polarization dependence of the OKG signals in CS2, the contribution of self-diffraction effect which is independent of the nonlinear response time of the material is directly observed on the rising edge of the time-resolved OKG signals. The influence of the self-diffraction effect on the optical Kerr signal could be controlled effectively by varying the polarization angle between pump and probe pulses.

Modulation instability in noninstantaneous Kerr media with walk-off and cross-phase modulation for mixed group-velocity-dispersion regimes

Taking into account relaxing Kerr nonlinearity and walk-off effects, the conditions and gain spectra of cross-phase modulation-induced modulational instability (XPM-MI) of two incoherently copropagating optical waves of different frequencies and same polarization are investigated. We devote particular attention to the mixed case in which one pulse propagates under the normal group-velocity dispersion (GVD) regime, while the second one is under an anomalous GVD regime. We unveil that in the limit of an instantaneuous nonlinear response, the typical frequency with maximum gain converges to a finite value in the mixed GDV regime, while it continuously grows with the group-velocity mismatch in the normal GVD regime. As a result, the maximum gain typically decreases with the group-velocity mismatch in the mixed regime, contrasting with the opposite trend in the normal GVD regime. Further, we show that besides the mode having maximum gain at a frequency decaying with $1/{\ensuremath{\tau}}^{1/3}$ in the slow response limit, there is a second mode having maximum gain with a distinct scaling behavior ${\mathrm{\ensuremath{\Omega}}}_{\text{max}}\ensuremath{\propto}1/\ensuremath{\tau}$ in the absence of group-velocity mismatch. The associated maximum gains scale, respectively, as $1/{\ensuremath{\tau}}^{2/3}$ and $1/\ensuremath{\tau}$, thus signaling the corresponding quadratic and linear dispersion relation of these modes in the low-frequency limit. A detailed analysis of the influence of the nonlinear response time and group-velocity dispersion on the MI gain spectrum is also provided.

Optical attosecond pulses and tracking the nonlinear response of bound electrons.

The time it takes a bound electron to respond to the electromagnetic force of light sets a fundamental speed limit on the dynamic control of matter and electromagnetic signal processing. Time-integrated measurements of the nonlinear refractive index of matter indicate that the nonlinear response of bound electrons to optical fields is not instantaneous; however, a complete spectral characterization of the nonlinear susceptibility tensors--which is essential to deduce the temporal response of a medium to arbitrary driving forces using spectral measurements--has not yet been achieved. With the establishment of attosecond chronoscopy, the impulsive response of positive-energy electrons to electromagnetic fields has been explored through ionization of atoms and solids by an extreme-ultraviolet attosecond pulse or by strong near-infrared fields. However, none of the attosecond studies carried out so far have provided direct access to the nonlinear response of bound electrons. Here we demonstrate that intense optical attosecond pulses synthesized in the visible and nearby spectral ranges allow sub-femtosecond control and metrology of bound-electron dynamics. Vacuum ultraviolet spectra emanating from krypton atoms, exposed to intense waveform-controlled optical attosecond pulses, reveal a finite nonlinear response time of bound electrons of up to 115 attoseconds, which is sensitive to and controllable by the super-octave optical field. Our study could enable new spectroscopies of bound electrons in atomic, molecular or lattice potentials of solids, as well as light-based electronics operating on sub-femtosecond timescales and at petahertz rates.

A review on evapotranspiration data assimilation based on hydrological models

Accurate estimation of evapotranspiration (ET), especially at the regional scale, is an extensively investigated topic in the field of water science. The ability to obtain a continuous time series of highly precise ET values is necessary for improving our knowledge of fundamental hydrological processes and for addressing various problems regarding the use of water. This objective can be achieved by means of ET data assimilation based on hydrological modeling. In this paper, a comprehensive review of ET data assimilation based on hydrological modeling is provided. The difficulties and bottlenecks of using ET, being a non-state variable, to construct data assimilation relationships are elaborated upon, with a discussion and analysis of the feasibility of assimilating ET into various hydrological models. Based on this, a new easy-to-operate ET assimilation scheme that includes a water circulation physical mechanism is proposed. The scheme was developed with an improved data assimilation system that uses a distributed time-variant gain model (DTVGM), and the ET-soil humidity nonlinear time response relationship of this model. Moreover, the ET mechanism in the DTVGM was improved to perfect the ET data assimilation system. The new scheme may provide the best spatial and temporal characteristics for hydrological states, and may be referenced for accurate estimation of regional evapotranspiration.

Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory

In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler–Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler–Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor–corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.

An overview of the RFCS project V&V framework: optimization-based and linear tools for worst-case search

This article presents the application of nonlinear (simulation-based) and linear (structured singular value) worst-case tools to the VEGA launcher Verification and Validation process, during atmospheric ascent. The simulation-based worst-case evaluation is performed by minimizing a set of cost functions that capture the launcher’s performance objectives, using the Worst-Case Analysis Optimization Tool and a high-fidelity nonlinear simulator of VEGA. The linear worst-case search uses the structured singular value ( $$\mu $$ ) and a linear fractional transformation model representing the yaw rigid motion of the VEGA launcher but numerically evaluated using time simulation data from the VEGA simulator. To facilitate the analysis of the worst-case results as well as the comparison between the two analysis tools, a selection of the most critical uncertainties is performed using sensitivity analysis based on selected nonlinear simulator time responses. It is highlighted that the presented analysis tools are complementary to traditional Monte Carlo approaches in that they strive to identify worst-case uncertainty combinations as opposed to providing probabilistic guarantees on performance metric satisfaction. In addition, as it will be shown, these approaches require only a fraction of the time required to perform a Monte Carlo campaign.

The New Study Based on a Dual Ion Implantation PSD Structure

In the analysis of semiconductor position sensitive detector (PSD) based on the traditional structure, using dual ion implantation method to studying the new type of PSD structure. The new structure of the n-type silicon substrate by implanting a high dose, low energy boron ions and another high energy boron ion, Which subsequent annealing of 2h at 1050 °C in an ambient of dry O2to form a shallow and a low doped p-n junction. Experimental results show that the new structure of PSD can obtained high position resolution, smaller errors and nonlinear response time.

Damage response of multistorey r/c buildings with different structural systems subjected to seismic motion of arbitrary orientation

SummaryIn the present study the combined influence of seismic orientation and a number of parameters characterizing the structural system of Reinforced Concrete (R/C) buildings on the level of expected damages are examined. For the purposes of the above investigation eight medium‐rise buildings are designed on the basis of the current seismic codes. The structural characteristics examined are the ratio of the base shear received by the structural walls, the ratio of horizontal stiffness in two orthogonal directions and the structural eccentricity. Then, the buildings are analyzed by nonlinear time response analysis using 100 bidirectional earthquake ground motions. The two horizontal accelerograms of each ground motion are applied along horizontal orthogonal axes, forming 72 different angles with the structural axes. The structural damage is expressed in terms of the Park and Ang damage index. The results of the analyses revealed that the damage level of the buildings is strongly affected by the incident angle of the ground motion. The extent at which the orientation of the seismic records influences the damage response depends on the structural system and the distance of the record to the fault rupture. As a consequence, the common practice of applying the earthquake records along the structural axes can lead to significant underestimation of structural damage. Also, it was shown that the structural eccentricity can significantly differentiate the seismic damage level, as well as the impact of the earthquake orientation on the structural damage. Copyright © 2015 John Wiley & Sons, Ltd.

Ultrafast optical Kerr gate of bismuth–plumbum oxide glass for time-gated ballistic imaging

We demonstrated the time-gated ballistic imaging technique using a femtosecond optical Kerr gate (OKG) of bismuth–plumbum oxide glass, the nonlinear optical properties of which were also investigated. The third-order nonlinear refractive-index n2 of the bismuth–plumbum oxide glass was measured to be 2.19 × 10−15 cm2/W, and the nonlinear response time was estimated to be shorter than 180 fs. For the time-gated ballistic imaging, the maximum measurable optical density of turbid media using the OKG of bismuth–plumbum oxide glass was 9.3, while only 7.0 for the OKG of quartz glass. And the intensities of the images for the bismuth–plumbum oxide glass were approximately two orders of magnitude higher than that for the quartz glass. The experimental results indicated that the bismuth–plumbum oxide glass was an excellent optical material for nonlinear optical applications.