Nonlinear Behavior Research Articles

Online Identification of Nonlinear Systems With Separable Structure.

Separable nonlinear models (SNLMs) are of great importance in system modeling, signal processing, and machine learning because of their flexible structure and excellent description of nonlinear behaviors. The online identification of such models is quite challenging, and previous related work usually ignores the special structure where the estimated parameters can be partitioned into a linear and a nonlinear part. In this brief, we propose an efficient first-order recursive algorithm for SNLMs by introducing the variable projection (VP) step. The proposed algorithm utilizes the recursive least-squares method to eliminate the linear parameters, resulting in a reduced function. Then, the stochastic gradient descent (SGD) algorithm is employed to update the parameters of the reduced function. By considering the tight coupling relationship between linear parameters and nonlinear parameters, the proposed first-order VP algorithm is more efficient and robust than the traditional SGD algorithm and alternating optimization algorithm. More importantly, since the proposed algorithm just uses the first-order information, it is easier to apply it to large-scale models. Numerical results on examples of different sizes confirm the effectiveness and efficiency of the proposed algorithm.

GPU-accelerated approach for 2D fracture analysis of structures combining finite particle method and cohesive zone model

The fracture analysis of structures typically involves strong discontinuity and nonlinear behaviors, and it requires fine meshing and small time steps, making it time-consuming. This study proposes an approach accelerated by graphics processing units (GPU) for two-dimensional (2D) fracture analysis of structures combining finite particle method (FPM) and cohesive zone model (CZM). Specifically, the equations of motion of particles are presented, and the internal forces of planar triangular elements are derived based on FPM. Subsequently, the internal forces of four-particle cohesive element are derived to describe the CZM, and the linear elastic stage, softening stage, and failure stage are depicted according to the traction-separation criteria. An explicit GPU-based FPM analysis strategy for structural fracture analysis is then developed, and the parallel solvers for particles, triangular elements, and cohesive elements are implemented. A quasi-static fracture analysis of a concrete beam and a dynamic fracture analysis of the Kalthoff problem is conducted to verify the effectiveness of the proposed approach. The obtained crack propagation path, load vs. displacement curves, and crack propagation speed are in good agreement with the experimental results and the results in the literature. The efficiency of the proposed approach is also investigated. The achieved maximum speedup ratio of the GPU-accelerated approach to the central processing unit (CPU)-based approach reaches around 24, and the achieved speedup ratio relative to the commercial finite element software Abaqus/Explicit reaches around 11.5, demonstrating the computational efficiency of the proposed approach.

Evaluation of Pylon Shape and Cable Layout Interaction on the Seismic Behavior of Cable-stayed Bridges

Nowadays, cable-stayed bridges are among the most widely used bridges. In these bridges, the seismic behavior is critical due to the nonlinear behavior of the cables and the high seismic weight. In recent years, some research has been done on measuring the seismic behavior of cable-stayed bridges. Most of them have evaluated the seismic behavior of the pylon shape or cable layout separately. Nevertheless, it seems very unlikely that these two elements’ reactions do not affect each other. Therefore, this article has tried to consider the mutual effect of these variables in a wide range of span lengths using spectral nonlinear dynamic analysis. On the other hand, the connection angle of the cables to the bridge deck has also been investigated as another variable. The results show that the response of the bridge may change entirely according to the combination of pylon shape and cable layout. For example, in A and diamond-shaped pylons, using a Harp configuration of cables reduces the period of free vibration of the bridge and, as a result, provides the greatest stiffness. On the other hand, the Fan configuration creates more stiffness in the H-shaped and single pylons.

Nonlinear Elasticity of Blood Vessels and Vascular Grafts.

The transplantation of vascular grafts has emerged as a prevailing approach to address vascular disorders. However, the development of small-diameter vascular grafts is still in progress, as they serve in a more complicated mechanical environment than their counterparts with larger diameters. The biocompatibility and functional characteristics of small-diameter vascular grafts have been well developed; however, mismatch in mechanical properties between the vascular grafts and native arteries has not been accomplished, which might facilitate the long-term patency of small-diameter vascular grafts. From a point of view in mechanics, mimicking the nonlinear elastic mechanical behavior exhibited by natural blood vessels might be the state-of-the-art in designing vascular grafts. This review centers on elucidating the nonlinear elastic behavior of natural blood vessels and vascular grafts. The biological functionality and limitations associated with as-reported vascular grafts are meticulously reviewed and the future trajectory for fabricating biomimetic small-diameter grafts is discussed. This review might provide a different insight from the traditional design and fabrication of artificial vascular grafts.

Dynamic Wrinkling Instability of Elastic Films on Viscoelastic Substrates

Abstract The dynamic instability of stiff films on compliant substrates has received sustained attention due to the potential applications in flexible functional devices. Film/substrate system-based devices are increasingly utilized under dynamic conditions, including dynamic sensors, tunable optical components, anti-fouling surfaces, etc. To better design the dynamic characteristics of devices based on film/substrate systems, it is essential to establish a comprehensive dynamic model and find out the deterministic and non-deterministic instability domains of nonlinear dynamic wrinkling under time-varying biased loads. In this paper, a multi-level coupling time-varying parameter excitation dynamic model for films bonded on Kelvin viscoelastic substrates is developed. The damping effect on the nonlinear dynamic responses of wrinkled film/substrate systems under step, slope and biased sinusoidal axial time-varying excitations are analyzed. We revealed and analyze the nonlinear dynamic behavior of film/substrate systems, which are significantly influenced by the excitation frequency and viscous coefficients of substrates. Various response forms, such as excitation-following deterministic responses, chaotic responses, and double-period resonant responses, are observed. We analyzed the parametric excitation induced dynamic bifurcation of the time-varying energy barrier that causes the nonlinear dynamic phenomenon, and provided deterministic and non-deterministic dynamic response domains. Based on the theory and results, methods for generating responses of specific types are proposed, offering theoretical guidance for designing dynamic characteristics of devices based on film/substrate systems.

Nonlinear vibration behaviours of foam-filled honeycomb sandwich cylindrical shells: Theoretical and experimental investigations

In this study, the nonlinear vibration behaviours of foam-filled honeycomb sandwich cylindrical shells (FHSCSs) are investigated theoretically and experimentally. Initially, a time-domain minimum residual (TDMR) method is first adopted for the analysis of nonlinear free and forced vibrations of the FHSCSs, which is based on a dynamical model developed, with the effective material parameters of the foam-filled honeycomb core being obtained by employing the Gibson method and the Hamilton equivalence technique. Based on the high-order shear deformation shell principle and von Karman's theory, the nonlinear natural frequencies and resonant responses are solved using the Broyden iterative approach and TDMR method. Furthermore, several literature results are utilized for the rough verification of such a method. Meanwhile, the FHSCS specimens are made manually and comprehensive tests with various base excitation energies are undertaken to provide a thorough validation of the current method. It can be found that the largest calculation errors of natural frequencies and resonant responses are 4.9 and 12.3%, respectively. Finally, the influences of the core form and base excitation amplitudes on the nonlinear vibration behaviours of the FHSCSs are examined. It can be noticed that the foam-filled FHSCS structure exhibits a more excellent anti-vibration capability compared to the non-foam-filled structure. The solving method, fabrication technique, and valuable findings in the current study highlight the path for the design and implementation of such advanced shells.

Nonlinear inelastic behaviors of concrete-filled steel tubular beam-column structures

A new advanced method combining stability function and distributed plasticity model has been developed using Fortran programming language to predict the nonlinear inelastic behavior of concrete-filled steel tubalar (CFST) under static loading. The advantage of this method is the ability to accurately study the nonlinear behavior using only one or two beam-column elements per member instead of using solid and shell elements as traditional methods, thereby improving the model analysis time. The Generalized Displacement Control (GDC) algorithm, capable of analyzing beyond the limit point, will be used to solve the nonlinear equilibrium equations instead of the traditional Newton-Raphson algorithm. The element stiffness matrix is integrated through the Gauss-Lobatto numerical integration framework, while the nonlinear geometric effects P-Δ and P-δ are considered using stability functions and a corresponding geometric matrix. The reliability and accuracy of the proposed method are verified by comparing the analysis results with experimental data. The obtained results have demonstrated that using beam-column elements for simulation, the proposed method still provides accurate results while significantly reducing computational resources. Therefore, this new method holds promise as a useful tool for practical design and analysis of statically loaded CFST structures.

A force-restricted inerter damper for enhancing the resilience of seismically isolated structures

An inerter is a mechanical device that generates a resisting force proportional to the relative acceleration between its two terminals. Several inerter-based dampers have been developed and studied to protect critical structures from the damaging effects of strong earthquake events. However, under high-frequency excitations, conventional inerter-based dampers may generate high resisting forces, which can result in excessive stresses in the supporting members and degrade the performance of the isolation systems. To overcome this issue, a novel force-restricted inerter damper (FRID) is proposed in this study for use in base-isolated structures. A simplified mechanical model of the proposed FRID was developed, which consists of a parallel layout of a viscous damping element and a nonlinear inerter element with a friction force restriction mechanism. The nonlinear hysteretic behavior of the FRID is discussed with an emphasis on the frequency dependence. Time- and frequency-domain methods were developed to evaluate the nonlinear dynamic response of the FRID-controlled structure. The performance of the FRID was investigated and compared with that of commonly used fluid viscous dampers (FVDs) and viscous mass dampers, when incorporated into base-isolated structures under short- and long-period ground motions. Parametric studies were conducted to investigate the influence of the FRID’s characteristic parameters on the seismic performance of controlled structures. The analysis demonstrated that the viscous mass damper and FRID provided superior control than the FVD on the displacement of a base-isolated structure, and the FRID is more effective than the viscous mass damper in reducing the control force and structural acceleration. This confirms that the proposed FRID is a promising, high-performance, and cost-effective device for enhancing the resilience of seismically isolated structures.

Experimental Study on the Sloshing of a Rectangular Tank under Pitch Excitations

Fluid sloshing within containers subjected to external motion is a crucial yet intricate phenomenon with implications across various industries. This study investigates sloshing in a rectangular liquid tank through a series of experiments examining pitch excitations with diverse excitation frequencies and amplitudes across different liquid carrying rates. By analyzing pressure data and imagery of the free liquid surface, statistical trends in peak pressure at measurement points within the tank are identified, revealing the nonlinear behavior of the fluid. Spectral analysis generates power spectrum curves that delineate frequency components and energy distribution within the sloshing dynamics. Key findings include the identification of resonance-induced violent sloshing at a 20% liquid-carrying rate and a resonant frequency shift at a 70% liquid-carrying rate due to nonlinearity, displaying a “soft spring” characteristic in the frequency response. The free liquid surface exhibits four distinct waveforms depending on frequency. Notably, at a 70% liquid-carrying rate and resonant frequency excitation, three-dimensional vortex waves emerge, highlighting a complex three-dimensional effect within the tank. The power spectrum shows that the dominant response frequency aligns with the excitation frequency and its multiples. This investigation enhances our understanding of the intricate nature of sloshing in various liquid-carrying conditions, offering insights valuable for diverse industrial applications.

Nonlinear static and dynamic behaviors of partially and fully submerged rod pendulums in quiescent water

Nonlinear static and dynamic behaviors of partially and fully submerged rod pendulums in quiescent water

Application of machine learning for thermal exchange of dissipative ternary nanofluid over a stretchable wavy cylinder with thermal slip

This article explores the enhancement of thermal exchange in a dissipative Triple-nanoparticle (Al2O3+CuO+Cu) hybrid fluid over a stretchable wavy cylindrical surface with slip effect, incorporating Python bvp algorithm with artificial intelligence AI analysis of numerical results. The stochastic AI analysis gives the enhanced and optimized results with predictive modeling, incorporating randomness of influencing parameters and nonlinear turbulent behavior of model. The model has significant importance and application in noise reducing and drag reduction devices or structures. Moreover, the presented geometrical structure is useful in enhancing thermal conduction characteristic. The intricate interplay of constituent nanoparticles and their effect on complex heat transfer in drag optimization devices is the main focus of this study. Mathematical Model of PDEs of this flow problem is converted into system of ODEs by similarity transformations with introducing dimensionless parameters. Numerical solutions of the emerged system are obtained by Python bvp solver algorithm and graphical solutions by Python are presented. To expedite the solution process and enhance the accuracy of prediction, advanced AI algorithm, such as neural network and machine learning technique is adopted. Numerical dataset obtained from Python is embedded for further AI analysis by using Levenberg Marquardt Feed-forward Algorithm (LMFA) with 10 computing neurons and 4 output layers representing results for 4 parametric variations.A rise in the fluid flow speed is observed with higher of value yield stress or Newtonian-behavior i.e. of Casson parameter a1 and stretching parameter λ for the sheet, but shows a decline with enhancing turbulence s2. Temperature profile show a descending behavior with inclination of Eckert ratio Ec, and Prandtl ratio of momentum-thermal diffusivity.

Artificial neural network-based sequential approximate optimization of metal sheet architecture and forming process

Abstract This paper introduces a sequential approximate optimization method that combines the finite element method (FEM), dynamic differential evolution (DDE), and artificial neural network (ANN) surrogate models. The developed method is applied to address two optimization problems. The first involves metamaterial design optimization for metal sheet architecture with binary design variables. The second pertains to optimizing process parameters in multi-stage metal forming, where the discrete nature arises owing to changing tool geometries across stages. This process is highly nonlinear, accumulating contact, geometric, and material nonlinear effects discretely through forming stages. The efficacy of the proposed optimization method, utilizing ANN surrogate models, is compared with traditionally used polynomial response surface (PRS) surrogate models, primarily based on low-order polynomials. Efficient learning of ANN surrogate models is facilitated through the FEM and Python integration framework. Initial data for surrogate model training is collected via Latin hypercube sampling and FEM simulations. DDE is employed for sequential approximate optimization, optimizing ANN or PRS surrogate models to determine optimal design variables. PRS surrogate models encounter challenges in dealing with nonlinear changes in sequential approximate optimization concerning discrete characteristics such as binary design variables and discrete nonlinear behavior found in multi-stage metal forming processes. Owing to the discrete nature, PRS surrogate models require more data and iterations for optimal design variables. In contrast, ANN surrogate models adeptly predict nonlinear behavior through the activation function's characteristics. In the optimization problem of Metal Sheet Architecture for design target C, the ANN surrogate model required an average of 4.6 times fewer iterations to satisfy stopping criteria compared to the PRS surrogate model. Furthermore, in the optimization of multi-stage deep drawing processes, the ANN surrogate model required an average of 6.1 times fewer iterations to satisfy stopping criteria compared to the PRS surrogate model. As a result, the sequential global optimization method utilizing ANN surrogate models achieves optimal design variables with fewer iterations than PRS surrogate models. Further confirmation of the method's efficiency is provided by comparing Pearson correlation coefficients and locus plots.

Non-thermal emission in gap-mode plasmon photoluminescence

Photoluminescence from spatially inhomogeneous plasmonic nanostructures exhibits fascinating wavelength-dependent nonlinear behaviors due to the intraband recombination of hot electrons excited into the conduction band of the metal. The properties of the excited carrier distribution and the role of localized plasmonic modes are subjects of debate. In this work, we use plasmonic gap-mode resonators with precise nanometer-scale confinement to show that the nonlinear photoluminescence behavior can become dominated by non-thermal contributions produced by the excited carrier population that strongly deviates from the Fermi-Dirac distribution due to the confinement-induced large-momentum free carrier absorption beyond the dipole approximation. These findings open new pathways for controllable light conversion using nonequilibrium electron states at the nanoscale.

A subbands study on the resistivity of field-effect CNT-based piezoresistive nanocomposites

In this paper, an analytical model based on the percolation theory has been developed to predict the subbands effect on the effective electrical resistivity of carbon nanotubes (CNT)-based polymer nanocomposites. The CNTs are considered as randomly distributed or aligned channel material in the polymer transmitting electrons through tunneling. The tunneling effect takes into account the electron transmission between each connected pair of CNTs to evaluate electrical resistivity. The modeling approach contains two steps of primary prediction of resistivity and further calculation of CNTs’ displacements and subsequent change of the resistance. A good agreement is found between the analytical model predictions and experimental data when the tunneling behavior was considered in the percolation transition region. The effect of CNT diameter, orientation state, and subbands on the resistivity has been investigated. The results depict that subbands increment is a collateral benefit to the aspect ratio in decreasing the resistivity. The analytical results demonstrate that a random CNT dispersion leads to a decreased piezoresistivity, while an increased strain range depicts a more non-linear behavior.

Framework for evaluating photon-counting detectors under pile-up conditions.

While X-ray photon-counting detectors (PCDs) promise to revolutionize medical imaging, theoretical frameworks to evaluate them are commonly limited to incident fluence rates sufficiently low that the detector response can be considered linear. However, typical clinical operating conditions lead to a significant level of pile-up, invalidating this assumption of a linear response. Here, we present a framework that aims to evaluate PCDs, taking into account their non-linear behavior. We employ small-signal analysis to study the behavior of PCDs under pile-up conditions. The response is approximated as linear around a given operating point, determined by the incident spectrum and fluence rate. The detector response is subsequently described by the proposed perturbation point spread function (pPSF). We demonstrate this approach using Monte-Carlo simulations of idealized direct- and indirect-conversion PCDs. The pPSFs of two PCDs are calculated. It is then shown how the pPSF allows to determine the sensitivity of the detector signal to an arbitrary lesion. This example illustrates the detrimental influence of pile-up, which may cause non-intuitive effects such as contrast/contrast-to-noise ratio inversion or cancellation between/within energy bins. The proposed framework permits quantifying the spectral and spatial performance of PCDs under clinically realistic conditions at a given operating point. The presented example illustrates why PCDs should not be analyzed assuming that they are linear systems. The framework can, for example, be used to guide the development of PCDs and PCD-based systems. Furthermore, it can be applied to adapt commonly used measures, such as the modulation transfer function, to non-linear PCDs.

A simplified homogeneous approach for non-linear analysis of masonry infill panels under in-plane loads

This paper aims to create a unified model that effectively combines continuous 2-dimensional elements and discrete components to capture the nonlinear characteristics and failure mechanisms of solid and perforated masonry infill panels. Given that masonry infill behavior is primarily influenced by shear deformations, an equivalent model is developed by using multiple small square panels arranged diagonally and interconnected by two-component springs, encompassing axial and shear behavior at their intersections. For the sake of simplicity, the divided panels are assumed to behave elastically, with plasticity concentrated only in the axial component of the connector springs. Plastic behavior in the boundary elements was considered to involve both flexural and shear plastic hinges to provide an accurate estimation of the entire infill panel's behavior. To validate this approach, the simplified model is benchmarked against eight experimental masonry infill panels surrounded by steel or reinforced concrete frames and with or without openings. The results including global behavior and crack pattern were compared with available numerical predictions based on finite element method from the literature in addition to experimental outcomes. Ultimately, this comparison demonstrated that the homogeneous model could effectively predict the non-linear lateral behavior of the panels and accurately forecast crack patterns. Additionally, the use of unidirectional non-linear springs and the appropriate arrangement of elastic panels significantly reduced both pre-processing and analysis time.

Nonlinear Mechanical Behavior of Glass Fiber/ Epoxy Resin Composite Under Medium and Low Strain Rates Loading

Nonlinear Mechanical Behavior of Glass Fiber/ Epoxy Resin Composite Under Medium and Low Strain Rates Loading

Investigation of cerium as a surrogate for tetravalent actinides in monazite-type compounds

The incorporation of tetravalent cerium into the monazite structure via Ca(II)-coupled substitution was investigated using a solid state and a co-precipitation route for the synthesis of the La1-2xCaxCexPO4 solid solution. Based on powder XRD measurements and elemental mappings an optimised synthesis procedure was developed that averts the formation of secondary phases and allows the stabilisation of tetravalent cerium with a ratio of up to 0.21 Ce(IV)/Ce(III). In-situ HERFD-XANES measurements at the Ce L3 edge at up to 800°C were performed to study the cerium oxidation state during the phase transformation from rhabdophane to monazite, revealing an unexpected non-linear behaviour as well as a charge-directing effect of the lanthanum cation.

Periodic foundation piles for the seismic protection of structures

This study introduces a novel solution for seismic protection of structures based on resonant metamaterials, named Periodic Foundation Piles, which can be integrated with deformable soil deposits in order to filter shear waves in a specific frequency range. A Periodic Foundation Pile consists of an array of vertical periodic structural elements containing internal resonators suitably tuned to one or more natural frequencies of the soil deposit. The proposed system is equivalent to a discontinuous foundation pile and can be installed in the ground with approximately the same procedure for piles, thus making it suitable also for applications in existing structures. The performance of the Periodic Foundation Piles in reducing the amplitude of a seismic motion has been shown through non-linear site response analyses carried out using real acceleration records as input motion. A soil deposit with an increasing shear wave velocity profile has been considered; the nonlinear behaviour of the soil has been modelled through the Iwan model, calibrated using a normalized secant shear modulus curve accounting for the influence of the confining pressure on the stress-strain relationship. Numerical results, presented in terms of peak acceleration, horizontal displacement and shear deformation profiles, as well as in terms of Fourier amplitude and response spectra, indicate that Periodic Foundation Piles may noticeably reduce the amplitudes of seismic motion in a suitable frequency range, hence potentially representing an innovative strategy to mitigate the effects of earthquakes on structures.

A Data-Driven Approach for Cutting Force Prediction in FEM Machining Simulations Using Gradient Boosted Machines

Cutting simulations via the Finite Element Method (FEM) have recently gained more significance due to ever increasing computational performance and thus better resulting accuracy. However, these simulations are still time consuming and therefore cannot be deployed for an in situ evaluation of the machining processes in an industrial environment. This is due to the high non-linear nature of FEM simulations of machining processes, which require considerable computational resources. On the other hand, machine learning methods are known to capture complex non-linear behaviors. One of the most widely applied material models in cutting simulations is the Johnson–Cook material model, which has a great influence on the output of the cutting simulations and contributes to the non-linear behavior of the models, but its influence on cutting forces is sometimes difficult to assess beforehand. Therefore, this research aims to capture the highly non-linear behavior of the material model by using a dataset of multiple short-duration cutting simulations from Abaqus to learn the relationship of the Johnson–Cook material model parameters and the resulting cutting forces for a constant set of cutting conditions. The goal is to shorten the time to simulate cutting forces by encapsulating complex cutting conditions in dependence of material parameters in a single model. A total of five different models are trained and the performance is evaluated. The results show that Gradient Boosted Machines capture the influence of varying material model parameters the best and enable good predictions of cutting forces as well as deliver insights into the relevance of the material parameters for the cutting and thrust forces in orthogonal cutting.