Nonlinear Response Research Articles

Piezoelectric polymer generators: The large bending regime

There is an important difference between piezoelectric polymer films and solid crystals for the application of piezoelectric generators. In the case of polymers, the optimal piezoelectric response imposes a large bending regime. Starting from the linear Curie’s constitutive equations, we develop an analytical model under the assumption of the large bending regime resulting from bulge testing configuration. This model shows a specific non-linear piezoelectric response, which follows a power of 2/3 of the mechanical excitation. The piezoelectric voltage and the corresponding power are then studied experimentally as a function of the angular frequency ω of the mechanical excitation, the load resistance R, and the thickness of the film ℓ. The experimental results carried out on piezoelectric polyvinylidene fluoride (PVDF) films validate the model.

Modelling reinforced masonry buildings by a mechanics‐based macroelement approach

AbstractThe seismic behaviour of unreinforced masonry (URM) buildings is frequently modelled using macroelements, in the framework of an equivalent‐frame schematisation of the walls. Although the advantages of this modelling technique, mainly related to the compromise between computational burden and accuracy of the results, appear to be valid also in the case of reinforced masonry (RM) buildings, few attempts have been made to extend its applicability to RM. This work proposes a mechanics‐based macroelement approach to simulate the in‐plane nonlinear response of RM piers, starting from a macroelement model widely adopted for URM and implemented in the TREMURI software. The strategy consists of discretising a masonry pier into sub‐macroelements, representative of masonry and horizontal reinforcement, with nonlinear beams representing vertical reinforcement. Experimental tests performed on clay blocks RM piers were simulated to test the efficiency of this model in capturing the strength and cyclic behaviour associated with different damage mechanisms. More complex structures were then studied, starting from assemblies of piers, up to entire buildings. Even in these cases, the modelling approach proved to be able to model the nonlinear cyclic behaviour. Finally, the model was used to compare the response of two buildings in their unreinforced and reinforced configurations, through nonlinear static and dynamic analyses.

Uneven global retreat of persistent mountain snow cover alongside mountain warming from ERA5-land

The warming of mountains has become evident in recent years, with a mean global warming rate of 1.19 °C from 1979 to 2022. However, unveiling the global divergent decline of persistent mountain snow cover in the face of climate shifts remains unexplored. However, the global decline of persistent mountain snow cover due to climate change is not well understood. This study uses reanalysis and satellite data to examine changes in snow cover lasting over six months across our global mountain regions. We reveal a significant global mean decline of 7.79% in persistent snow cover over the past 44 years. The regional snow cover trends exhibit a heterogeneous and non-linear response to its regional warming rate. Our findings highlight the interplay between global warming and snow cover, emphasizing the need for sustainable development strategies to address the potential impacts of diminishing mountain snow.

An efficient Volterra series approach for identifying nonlinear system vibration responses to an excitation

This paper focuses on the issue of nonlinear vibration responses identification of nonlinear systems. An efficient algorithm is presented, in which the nonlinear vibration system under studied is decomposed into a multiple-input/single-output (MISO) linear system with a series of power characterized inputs based on Volterra series, and the nonlinear output responses of different orders are identified by taking power spectra operation to the input and output data, revealing the contributions of each order nonlinearity to the output of the system. Compared to the existing method, the input signal of the system required in the presented approach need not remain unchanged in waveform and adjustable in magnitude. To verify the approach, a classic Duffing–Van der Pol oscillator was simulated, obtaining results very close to the fourth order Runge–Kutta method. Finally, an experiment analysis was carried out, in which the vibration transmission properties of a bolt connection were tested when the bolt was tight and loose, respectively. The results proved that the approach is effective in identifying nonlinear vibration frequency responses.

Nonlinear mechanical response of finite-length soft composites with random dislocations

The effects of random dislocations on the vibrational properties of finite-length RNA and DNA macro-structures have been investigated by means of a harmonic Hamiltonian and the Green’s function method. The RNA molecule has been modeled using a half ladder model, and three models (a fishbone model and two different strand models) have been employed to model the structure of DNA. The lengths of the finite and cyclic systems are gradually increased to more accurately approximate the structures of RNA and DNA. Springs whose behaviors are governed by Hooke’s constitutive law have been used to represent the bonds between the masses, with the stiffness of the vertical springs randomly changing along the length of each model. This results in a more realistic representation of the inherent randomness of the studied structures. To investigate the effect of random dislocations on the mechanical response of the studied systems, it has been assumed that a random mass-spring ensemble has been knocked out of place by an external force. It has been found that increasing the number of building blocks along the length of the models suppresses the influence of dislocations on the vibration spectra of RNA and DNA. It was also observed that at low frequencies, the influence of dislocations becomes more pronounced. Besides, taking into account the collective mass of the sugar-phosphate backbone results in the appearance of gaps in the vibration spectra. By introducing dislocations into the models, additional dislocation-induced vibrational states appear in the DOS curves. What stands out from the results is that the responses of the studied systems to these changes are strictly nonlinear. The employed methodology can be applied to investigate the mechanical response of damaged RNA and DNA.

Detection of Nonlinearity in Photonic Lattices

AbstractAlthough periodic photonic structures, especially associated with nonlinearity, play a prominent role in optics nowadays, effective detection of their nonlinearity still remains a critical challenge. Here, an approach is proposed to detect the nonlinearity of photonic lattices in a direct way. By properly launching structured beams, namely Airy beams, into the lattices, the nonlinear response function of the discrete system can be directly obtained in the nonlinearly‐shaped beam profiles. To be specific, a single Airy beam is utilized to map self‐defocusing nonlinearity, while self‐focusing nonlinearity, which is hard to visualize in the bulk case, is readily discerned by employing double Airy beams in photonic structures. The proposed method is validated numerically and experimentally by detecting different types of nonlinearities of photonic lattices fabricated in a nonlinear crystal. These findings introduce a promising route for characterizing the nonlinear response of optical structures, thereby broadening the scope of nonlinear measurement and is expected to be extended into other periodic photonic structures.

Nonlinear anomalous transverse responses induced by the Berry curvature quadrupole in systems with broken time-reversal symmetry

Nonlinear anomalous transverse responses induced by the Berry curvature quadrupole in systems with broken time-reversal symmetry

Inductive graph‐based long short‐term memory network for the prediction of nonlinear floor responses and member forces of steel buildings subjected to orthogonal horizontal ground motions

Inductive graph‐based long short‐term memory network for the prediction of nonlinear floor responses and member forces of steel buildings subjected to orthogonal horizontal ground motions

Research on the nonlinear resonance response of the high-speed spindle system supported by preloaded ball bearings

Research on the nonlinear resonance response of the high-speed spindle system supported by preloaded ball bearings

Microscopic examination of rf-cavity-quality niobium films through local nonlinear microwave response

The performance of superconducting radio-frequency (SRF) cavities is sometimes limited by local defects. To investigate the rf properties of these local defects, especially those that nucleate rf magnetic vortices, a near-field magnetic microwave microscope is employed. Local third-harmonic response (P3f) and its temperature dependence and rf power dependence are measured for one Nb/Cu film grown by direct current magnetron sputtering (DCMS) and six Nb/Cu films grown by high-power impulse magnetron sputtering (HiPIMS) with systematic variation of deposition conditions. Five out of the six HiPIMS Nb/Cu films show a strong third-harmonic response that is likely coming from rf vortex nucleation due to a low-Tc surface defect with a transition temperature between 6.3 and 6.8 K, suggesting that this defect is a generic feature of air-exposed HiPIMS Nb/Cu films. A phenomenological model of surface-defect grain boundaries hosting a low-Tc impurity phase is introduced and studied with time-dependent Ginzburg-Landau (TDGL) simulations of probe-sample interaction to better understand the measured third-harmonic response. The simulation results show that the third-harmonic response of rf vortex nucleation caused by surface defects exhibits the same general features as the data, including peaks in third-harmonic response with temperature, and their shift and broadening with higher microwave amplitude. We find that the parameters of the phenomenological model (the density of surface defects that nucleate rf vortices and the depth an rf vortex travels through these surface defects) vary systematically with film deposition conditions. From the point of view of these two properties, the Nb/Cu film that is most effective at reducing the nucleation of rf vortices associated with surface defects can be identified. Published by the American Physical Society 2024

Plasmon-Induced Nonlinear Optical Response of N,N′-Dioctyl-3,4,9,10-perylenedicarboximide Nanoribbons Doped with Gold Nanoparticles: Implications for Optical Limiting Applications

Plasmon-Induced Nonlinear Optical Response of <i>N</i>,<i>N</i>′-Dioctyl-3,4,9,10-perylenedicarboximide Nanoribbons Doped with Gold Nanoparticles: Implications for Optical Limiting Applications

Uncertainty quantification for seismic response using dimensionality reduction‐based stochastic simulator

AbstractThis paper introduces a stochastic simulator for seismic uncertainty quantification, which is crucial for performance‐based earthquake engineering. The proposed simulator extends the recently developed dimensionality reduction‐based surrogate modeling method (DR‐SM) to address high‐dimensional ground motion uncertainties and the high computational demands associated with nonlinear response history analyses. By integrating physics‐based dimensionality reduction with multivariate conditional distribution models, the proposed simulator efficiently propagates seismic input into multivariate response quantities of interest. The simulator can incorporate both aleatory and epistemic uncertainties and does not assume distribution models for the seismic responses. The method is demonstrated through three finite element building models subjected to synthetic and recorded ground motions. The proposed method effectively predicts multivariate seismic responses and quantifies uncertainties, including correlations among responses.

2D sheets of MoSe2 for waveguide based second harmonic generation

Two-dimensional transition metal dichalcogenides show a strong second-order nonlinear response, which can only be exploited if the interaction between light and 2D material is maximized as it happens in waveguiding structures. Such an approach also allows the addition of a second order nonlinear response to linear integrated optics components by just placing a sheet of transition metal dichalcogenides material on top. Here, we analyze the second harmonic generation in MoSe2 sheets combined with silicon nitride ridge and thin-film waveguides for both modal phase matching and quasi-phase-matching. The calculated second harmonic generation efficiency is comparable with that in lithium niobate waveguides and can further be enhanced by increasing the number of MoSe2 layers on top of the waveguides. This also holds true for flux correlated photons generated by spontaneous parametric down conversion as we show by quantitative analysis.

Investigation of linear and microscopic nonlinear optical responses of 1-indanone compounds in different environments based on polarity models

Molecular spectroscopic and nonlinear features can indicate positive changes by solvent molecules. In this work, DFT and spectroscopic techniques were used to study the polarity effects of different solvent environments. Polarity-based models were used for studying solvent induced interactions on the optical features of new groups of biomolecules. Despite the significant contribution of general effects on the molecular absorption spectra, there is considerable competition between general and specific environmental effects on the molecular emission properties. Under this condition, strong hydrogen bonds tend to increase molecular nonlinear responses. The same results were observed for the low order (first and second order) nonlinearity of biomolecules. Therefore, the studies on the environment effects on the biomolecules’ first order nonlinearity can give valuable information about higher-order optical responses. Moreover, 1-Indanone compounds with high nonlinearity can be considered as an effective element in designing optical devices.

A novel biaxial shaking table and its performance when investigating seismic actions

AbstractThe design of a new type of biaxial shaking table is presented. The shaking table is able to apply horizontal and vertical movements to models using two actuators. It is novel in that the two actuators are horizontally aligned, through its use of a scissor mechanism, and because of its compact design which permits simple anchorage to a laboratory strong floor. The scissor mechanism translates the movement of one of the actuators to a purely vertical movement at the table. The other actuator, which moves horizontally the scissor mechanism and its supports, causes the horizontal movement of the table. The horizontal and vertical movements are applied and controlled independently, individually or simultaneously. The capability of the shaking table to control and replicate a variety of uniaxial and biaxial movements is verified by conducting several shaking table experiments. This is done when the table is naked and when it supports a payload having a nonlinear dynamic response. Very good agreements between achieved and desired uniaxial and biaxial movements are attained. Rigidity of the scissor arm mechanism and connections, and preloaded roller bearings and rail blocks, are central to its success. Displacement errors, rolling, pitching and yawing of the table's top plate are negligible. The new table type is slightly more expensive than a uniaxial system, and substantially less expensive than a six degrees‐of freedom system, meaning biaxial vertical and horizontal shaking capability can now be achieved in a laboratory at reasonable cost.

Evaluation of overstrength-based interaction checks for columns in steel moment frames

Current design guidelines in the United States require a check for only column axial force under overstrength seismic loads for capacity-designed steel moment frames. A study is presented to examine the implications of this guidance, which disregards the column interaction check (including both axial force and moment) under overstrength seismic loads. A set of thirteen steel moment frames are designed using multiple rules that apply and disregard overstrength, drift, and cross-sectional compactness checks in various combinations. The frames are subjected to a suite of simulations including linear elastic, nonlinear static pushover, nonlinear response history, and continuum finite element simulations that are able to represent a range of physical behavior modes in the columns including interactive nonlinear geometric instabilities that could trigger loss of the load carrying capacity of the member. The simulations indicate no significant distinction between the seismic performance of steel moment resisting frames designed as per current code-based provisions (i.e., disregarding the column interaction check for overstrength seismic loads), and those designed with the use of the interaction check, with each providing acceptable response without failure. The simulations also indicate that design checks for drift and cross-sectional compactness play a significant role ensuring acceptable response, providing additional margin of safety beyond the member strength checks.

Non-destructive AC impedance spectroscopy (ACIS) analysis to characterize the evolution of impact damage in UHPC

Ultra-high performance concrete (UHPC) widely serves as protection material owing to superior impact resistance. Rapid and effective assessment of impact damage level is crucial for ensuring structural safety. The non-destructive AC impedance responds sensitively to impact-induced microstructural changes, providing important information for understanding the damage development mechanism. Therefore, this paper intends to investigate the feasibility of AC impedance spectroscopy (ACIS) for UHPC impact damage detection. UHPC specimens with different types and volume fractions of steel fibers were prepared, subjected to multiple repetitive low-velocity hammer impacts to induce cumulative damage, and the impedance responses were simultaneously tested in the frequency range of 10 Hz-5 MHz. Additionally, the effects of steel fiber distribution characteristics and pull-out mechanism on the conductive path and impact resistance were explained through microstructural analysis and 3D reconstructed model. The results show that ACIS exhibits a strong correlation with impact damage, where the increment of the imaginary part can be used as an effective and sensitive indicator to achieve whole-process damage assessment. Compared to straight steel fibers, hooked-end and corrugated fibers greatly enhance the impact resistance of UHPC but cause a nonlinear response in impedance due to extracted deformations and orifice complexities. These findings demonstrate the potential application of ACIS for detecting impact damage in UHPC and warrant further investigation.

Nonlinear vibration characteristics and damage detection method of blade with breathing fatigue crack

In aero-engine, blades operate under harsh conditions for extended periods, which makes them highly susceptible to fatigue cracks. The localized and nonlinear structural changes caused by blade crack lead to complex vibration characteristics that are not well understood, posing challenges to the identification of these cracks. This paper proposes an approach for identifying breathing fatigue crack in compressor blade, leveraging the nonlinear features induced by the cracks. Crucial sensitive characteristics are extracted and a crack indicator for accurate crack detection is defined. Initially addressing the typical morphology of fatigue breathing cracks, a dynamic model of blade with cracks is developed to analyze their impact on the natural frequencies. Nonlinear contact forces are introduced to characterize the "breathing" effect of the fatigue crack, allowing for the determination of the harmonic distribution patterns in the blade's vibration response under various excitation conditions. A finite element model is then established considering the crack morphology, by adopting the contact element. Based on that, the nonlinear response characteristics associated with the blade's primary, sub-harmonic, and super-harmonic resonances are explored. A crack-sensitive parameter is defined and extracted from the nonlinear responses, under different crack propagation stages. At last, effectiveness and reliability of the defined parameter for identifying cracks is validated through a vibration fatigue test.

Medium Amplitude Field Susceptometry (MAFS) for magnetic nanoparticles

The linear dynamic susceptibility is arguably the most important property to specify the magnetization dynamics of a given system. Therefore, this quantity has been studied in great detail and the corresponding measurements known as susceptometry are well-established. Notwithstanding its relevance, the linear susceptibility is inherently limited to describe the magnetization response to weak external fields only. Here, we suggest the framework of Medium Amplitude Field Susceptometry (MAFS) to study the non-linear response which complements the linear susceptibility and provides additional information on the magnetic properties of the system and is applicable to magnetic fields of medium amplitudes. In particular, we introduce the general third-order nonlinear susceptibility χˆ3 as a central quantity that completely specifies the lowest-order non-linear response to arbitrary time-dependent magnetic fields. We show that response functions in medium amplitude oscillatory magnetic fields and parallel superposition susceptometry are contained in χˆ3 as special cases. Also included in χˆ3 are interesting intermodulation effects when the system is probed by a superposition of oscillating magnetic fields with different frequencies. We work out the explicit form of χˆ3 for several model systems for the dynamics of magnetic nanoparticles (MNPs). We expect this unifying framework to be not only of theoretical interest, but also useful for a deeper characterization of MNP systems, giving additional information on their suitability for various applications.

Nonlinear Radiative Response to Patterned Global Warming due to Convection Aggregation and Nonlinear Tropical Dynamics

Abstract Climate responses to global warming exhibit large dependence on the spatial pattern of sea surface temperature (SST) changes. A Green’s function (GF) approach—predicting the global climate response to a complex SST pattern change as the linear superposition of the response to finite-area SST perturbations evaluated in isolation—has been used to systematically evaluate and understand the top of atmosphere (TOA) radiation response to patterned warming. However, in general, the linear GF approach fails for TOA radiation reconstruction under future global warming scenarios in coupled models. Here, we show that the linear superposition of global mean TOA radiation responses to large SST warming perturbations at multiple patches (the GF approach prediction) overestimates the actual response to simultaneous multipatch perturbation. This is because the linear superposition overestimates tropical large-scale convection aggregation strengthening upon localized heating that enhances longwave radiative cooling, which is further explained by the overestimation of circulation response and associated horizontal water vapor transport. The nonadditivity of TOA radiation response is caused by the nonadditivity of convection aggregation, ultimately rooted in nonlinear tropical dynamics. We also demonstrate that the prediction error of the GF approach grows with decreasing patch size (equivalently, increasing patch number). We conclude that using the GF approach to predict future climate change could overestimate longwave radiative cooling and underestimate (effective) climate sensitivity. Numerical experiments may be used to identify specific perturbation patterns where the errors are smaller than the signal. Our research also highlights that an increase in the degree of large-scale convection aggregation has a nonlinear and negative feedback for mean warming.