Nonlinear Behavior Research Articles

Exact solutions of the nonlinear space-time fractional Schamel equation

This study focuses on the nonlinear space-time behavior of a plasma system made up of electrons, positive ions, and negative ions using the fractional Schamel (FS) equation. The main goal is to find exact solutions to the nonlinear FS equation by applying the extended hyperbolic function (EHF) method. The study examines how the fractional order affects the phase velocity, amplitude, and wave width of solitary wave solutions. Different exact solutions were found based on various values of the fractional order. Graphical representations are included to show the physical properties of these solutions. Overall, the results demonstrate that the EHF method is effective and reliable for finding exact solutions to the nonlinear FS equation.

The stick-slip bending behavior of the multilevel helical structures: A 3D thin rod model with frictional contact

The multilevel helical structures in various engineering and natural fields offer excellent deformation flexibility and load bearing capabilities. Understanding the interplay between the local frictional contact and the geometric characteristics of the helical structure under complex external loads has attracted considerable interest. In this work, the effect of local frictional contact behaviors on the bending in multilevel helical structures is investigated by using a combination of theoretical modeling, finite element (FE) simulations, and experiments. In the case of pure bending, the kinematic parameters of the bent multi-stage helix are derived concisely by the idea of the kinematic analogy. The bending stiffness of the multi-stage helix is further obtained. In the case of the combined tension/torsion and bending, the 3D thin rod model incorporating Coulomb’s friction is established to describe the mechanical responses. It is found that the relationship between equivalent bending stiffness and the laying angle exhibits nonlinearity. A comparison with the classical Papailiou model reveals that, for helical structures at large laying angles, the influence of friction is primarily determined by the internal force in the tangential direction, which is the core assumption of the Papailiou model. However, in the case of small laying angles, the helical twisting characteristics and the contribution of the internal forces and moments in the other two directions (normal and binormal directions) to the friction cannot be ignored. Subsequently, a multilevel frictional contact transmission formulation is proposed according to the force action–reaction principle. Based on the above formulation, the non-simplified thin rod equations with Coulomb’s friction are extended to describe the multilevel stick-slip bending behaviors of the second stage cable (3*3). The dissipation capacity of helical structures is evaluated quantitatively under the hysteretic bending. Finally, the theoretical model is verified by FE simulations and experimental results. This work provides insights for unveiling the intrinsic relationship between the nonlinear bending and local frictional contact behaviors in the multilevel helical structures.

Nonlinear electromechanical behaviors of piezoelectric generators with hybrid stiffnesses

In this paper, we introduce a novel two-degree-of-freedom piezoelectric stack hybrid energy harvester including a piezoelectric stack and a set of piezoelectric layers. By incorporating a mechanical stopper and bending leaf springs to achieve frequency up-conversion, we significantly enhance the voltage response of the system. We compare the output performance of prototypes with different spring stiffness. The experimental results show that, at a frequency of 7.8 Hz and an acceleration of 0.8 g, the piezoelectric layers on the lower beam of bending leaf springs generate a peak voltage of 18.92 V, and its instantaneous output power is 32 mW. Meanwhile, the piezoelectric stack produces a peak voltage of 28.56 V, with an instantaneous output power of 3.83 W. Moreover, an increase in the stiffness of the bending leaf spring leads to a decrease in voltage response and power output. This research can facilitate the development of hybrid piezoelectric self-powered applications.

Investigation of changes in the modules and energy balance of polymer materials during mechanical experiments

Abstract In the paper, the evolution of mechanical characteristics of structural materials in the process of uniaxial loadings are experimentally investigated. The energy balance was studied in a series of tensile and creep experiments of caprolon specimens, taking into account the division of the work of external forces into the energy of volume change and the energy of shear deformations. Simultaneous registration of heat release and changes in the coefficient of transverse deformations by the optic-acoustic method allowed us to estimate the contribution of volume changes and shear deformations to the energy balance during quasi-static loading of caprolon specimens. The obtained results demonstrated the contribution of shear deformations to the change of latent energy at the stages of linear and nonlinear behavior of caprolon during deformation.

Numerical Analysis on Fatigue Behavior of Plain Concrete and Alkali-activated Concrete

Abstract Alkali-activated concrete (AAC) has recently gained a lot of potential to become one of the most recommended sustainable replacements for Ordinary Portland cement concrete (OPCC). In the present investigation, an attempt has been made to study the static and fatigue flexural behavior of AAC compared to that of OPCC by using numerical modeling FEA software, ABAQUS. The nonlinear behavior of the stress-strain curve of the concrete has been studied using the concrete damage plasticity (CDP) model. A 2D notched beam was modelled using plane stress condition and three-point bending tests were performed under monotonic loading to obtain the static behavior of concrete. The result obtained has been utilized to fix the loading range for cyclic loads in fatigue analysis and at different loading frequencies. The load-CMOD curves and load-deflection curves were obtained for both static and fatigue loading, and the number of cycles to failure during fatigue. From the results, it has been observed that the Ordinary Portland cement concrete specimens sustain more load than that of Alkali-activated concrete under monotonic loading. However, AAC has shown more resistance to fatigue than that of the OPCC and the frequency of loading significantly influences the fatigue performance.

Temperature-dependent acoustic emission characteristics and statistical constitutive model of granite under uniaxial compression

Understanding the temperature-dependent mechanical behavior and fracture characteristics of granite is crucial for many engineering projects. In this study, the real-time temperature curves of granite specimens were obtained during the heating and cooling process, and the thermal treatment tests were conducted. The physical properties of the specimen before and after thermal treatment, including mass, volume, and P-wave velocity, were measured. The acoustic emission (AE) signal in the uniaxial compression is monitored. The results indicate that the physical properties of granite deteriorate with temperature, while the mechanical properties show two effects of thermal strengthening and thermal weakening. This phenomenon is comprehensively analyzed by literature statistical data and optical microscopic observation. Furthermore, the AE characteristic is strongly dependent on temperature. High temperature induces more AE ring count to appear in the early stage of loading. As the temperature increases, the crack initiation stress decreases and the table crack propagation stage becomes longer. The attenuation of high-frequency signals and the enhancement of low-frequency signals are related to the development and interaction mechanism of thermally-induced crack and stress-induced crack. At 600 °C, the global b-value increases significantly. Meanwhile, the evolution of dynamic b-value helps explain the failure process of granite under axial load after thermal treatment. In addition, a new thermo-mechanical damage statistical constitutive model of granite considering temperature effects is proposed by introducing AE parameters. The main advantages of this model can well fit the nonlinear behavior of granite in the early loading stage after thermal treatment, and reflect the failure process of granite before the peak value.

Magnetosonic shock waves in degenerate electron–positron–ion plasma with separated spin densities

This study investigates magnetosonic shock waves in a spin-polarized three-component quantum plasma using the quantum magnetic hydrodynamic model. We explore the influence of spin effects, specifically spin magnetization current and spin pressure, on shock wave behavior. Numerical analysis of the linear dispersion relation under varying parameters such as positron imbalance, spin polarization ratio, plasma beta, quantum diffraction, and magnetic diffusivity reveals differential impacts, with diffusion exerting significant influence on the plasma frequency. Our findings highlight the sensitivity discrepancy between the real and imaginary parts of the dispersion relation. Furthermore, nonlinear behavior of magnetosonic shock waves is examined via the Korteweg–de Vries–Burgers equation, showcasing transitions between oscillatory and monotonic wave patterns based on changes in dimensionless parameters. Notably, we observe the combined effects of spin-up and spin-down positrons with spin-up and spin-down electrons on shock wave dynamics, contributing to a deeper understanding of spin-plasma interactions with implications across various fields.

Seismic Assessment of an Old Historical Unreinforced Masonry Power House Building

Abstract Design of unreinforced masonry buildings is a major concern in seismically active zones in Nepal. The ChandraJyoti Jalvidhyut Power House, a historical landmark in Nepal, represents the nation’s pioneering effort in hydropower generation and signifies its rich cultural heritage. This study comprehensively assesses the structural assessment and seismic performance deficiencies of the ChandraJyoti Jalvidhyut Power House. Material tests on bricks with the individual properties and behaviour of construction materials were done. Utilizing a finite element model in DIANA software V 10.5, the structure’s response under pushover loading conditions is simulated, providing insights into its structural behaviour. Additionally, fragility curves are developed to correlate earthquake intensity with the probability of damage, offering essential information for preservation strategies and seismic risk mitigation. The compressive strength test of bricks, with a value of 9.6 MPa, falls short of the 10 MPa minimum requirement specified by NBC 203:2015, indicating insufficient load-bearing capacity. The building’s pushover analysis shows that the longitudinal direction experiences higher lateral forces (base shear of 945.87 kN) and greater drift ratios exceeding 0.4%, which increases the likelihood of cracks compared to the transverse direction (base shear of 826.77 kN). The analysis also highlights significant nonlinear behavior in both directions, with maximum roof displacements of 35.18 mm (transverse) and 34.4 mm (longitudinal), reflecting the impact of structural irregularities.

Weakly nonlinear shape oscillations of viscoelastic drops

Axisymmetric shape oscillations of a viscoelastic drop in a vacuum are studied by a weakly nonlinear analysis. The two-lobed initial drop deformation mode is studied. The Oldroyd-B model is used for characterizing the drop liquid rheological behaviour. The equations of motion and the solutions up to second order are developed, where elastic effects appear. Solutions of the characteristic equation are validated against the decay rate and frequency of damped shape oscillations of polymer solution drops in an acoustic levitator. The theory shows enhancing or dampening of the nonlinear behaviour and enhanced mode coupling, as compared with the Newtonian case. The study reveals an excess time in the prolate shape and a frequency change, together with a quasi-periodicity of the oscillations. The Fourier power spectra of traces of the drop north pole position in time show mode coupling as a nonlinear effect. At moderate stress-relaxation Deborah number, the resultant drop motion for large Ohnesorge number, suggesting aperiodic drop behaviour, may nonetheless be oscillatory, where the drop elasticity is owing to the liquid bulk elasticity instead of surface tension. A method is developed to predict the oscillatory or aperiodic behaviour of a drop of a given size from a rheologically characterized viscoelastic Oldroyd-B liquid.

Rising total leukocyte counts correspond with rising platelet counts in thrombotic thrombocytopenic purpura

AbstractThrombotic thrombocytopenic purpura (TTP) is a rare disorder involving pathological platelet–von Willebrand factor interaction, resulting in microvascular thrombosis. The consumption of platelets in TTP microthrombi results in severe thrombocytopenia which resolves with resolution of the microvascular thrombosis. Over the course of treatment, patient platelet counts often rise and fall multiple times before stable remission is achieved. On casual inspection, we noted that total leukocyte counts follow a pattern that appears to correspond to platelet counts. To explore whether changing leukocyte counts track significantly with changing platelet counts, we examined paired daily platelet counts and total leukocyte counts in 27 episodes of TTP in 13 patients across 2 institutions comprising 423 days of data. We modeled the nonlinear behavior in the data using a threshold mixed-effects regression model, in which we found a significant temporal relationship between total leukocyte counts and platelet counts. The model proved that, on a day when platelet counts were rising in previous days, the total leukocyte count is predictive of the rise in platelet count. The higher the total leukocyte count, the greater the rise in platelet count. Our results support the hypothesis that leukocytes play a role in the resolution of TTP microvascular thrombosis.

Resonant Y-type soliton, interaction wave and other wave solutions to the (3+1)-dimensional shallow water wave equation

The current study aims to develop some novel wave solutions of the (3+1)-dimensional shallow water wave equation (SWWE). First, the Y-type soliton (YTS) solutions are developed via imposing the certain resonant condition to the N-solitons solutions (NSSs) that extracted by the Hirota bilinear approach. Then, the symbolic computation and ansatz function scheme are employed to explore the interaction wave solutions. Eventually, the sub-equation approach is utilized to find the diverse wave solutions which include the kink wave, singular wave and the singular periodic wave solutions. The dynamics of the obtained solutions are presented graphically for revealing the nonlinear physical characteristics. The investigative solutions in this article have not been probed elsewhere and can help us comprehend the nonlinear behaviors of the (3+1)-dimensional SWWE better.

Non-linear critical speed in high-speed ballasted railways with ground reinforcement

When constructing or upgrading high-speed railway lines on soft soils, reinforcing the soil foundation becomes crucial. This not only involves small track displacements but also increases the critical speed, thereby ensuring safe and efficient regular operations. Nevertheless, existing studies on the critical speed phenomenon in high-speed railway tracks with ground reinforcement are limited, and they all assume a linear elastic behavior for both the soils and reinforcement materials. The main novelty of this research is that it presents the first study on the effect of non-linear soil behavior on the critical speed of high-speed railway ballasted tracks with soil reinforcement and introduces a novel simplified approach based on an equivalent homogeneous soil layer by replacing the soil layer containing inclusions/columns. To accomplish this, a full 3D non-linear numerical model was developed and experimentally validated. The findings from a detailed and comprehensive parametric analysis demonstrate a significant influence of non-linear behavior on the critical speed, resulting in reductions of up to 30% compared to the linear elastic scenario. Furthermore, it is found that the soil-reinforcement stiffness contrast, the area replacement ratio, and the plasticity index of the soil foundation play a crucial role in the critical speed. Other aspects such as the installation pattern and the thickness of soft soil have a relatively lower impact on the critical speed.

Liver Tissue Surrogates: Development and Biomechanical Characterization

Human liver tissue often suffers extensive damage during impact-based trauma injuries, such as those that happen in vehicle accidents. However, it is challenging to study the biomechanics of human liver tissue under different loading situations through experiments in a clinical context due to ethical and biosafety concerns. In this work, biofidelic liver tissue surrogates, which exhibit realistic mechanical characteristics, have been developed for the first time. The tissue surrogates were made using a four-part elastomer material that could be cast to any size or form, mimicking the mechanical behavior of the liver tissue. The tissue's behavior was tested under six different strain rates, ranging from low to high, and its non-linear mechanical behavior was characterized using the Yeoh hyperelastic curve fit model. To the best of our knowledge, no liver tissue surrogates have been developed which possess the same biomechanical properties as real liver tissue. The use of precisely developed tissue simulants can be beneficial for surgical training, trauma research, and the development of medical models for different liver disorders such as liver cirrhosis, fatty liver, and liver fibrosis.

Design of chaotic circuit based on Knowm memristor

AbstractMost previous works in the field of nonlinear memristive chaotic systems mainly focus on non‐material memristor while seldom on material memristor. In this letter, the model and the corresponding parameter identification of the Knowm memristor is presented. The chaotic circuit based on the Knowm memristor is designed. Equilibrium points and stability of this Knowm‐memristor‐based chaotic system is analyzed. Nonlinear dynamic behavior is presented by the bifurcation diagram and Lyapunov exponents. Finally, the hardware circuit of this Knowm‐memristor‐based chaotic system is designed and the experimental results are presented for confirmation.

Intelligent diagnosis of magnetorheological clutch using image processing techniques

The clutch is one of the important components of a vehicle system. Therefore, it is crucial to keep an eye on them and spot any faults while they are operating so that the operators can be informed and possible issues can be solved before they arise. In general, a fault in the clutch causes it to get eccentricity in the disc and the contact between housing and disc during its operation which impacts the non-linear dynamic behaviour of the clutch mechanism and hence it affects the performance of the same. For condition monitoring, infrared imaging is essential since the thermographic patterns change based on the defect or machine condition. In this study, novel attempts have been made to present an intelligent tribological diagnosis of magnetorheological clutch under conditions such as eccentricity of the disc due to misalignment and the contact between housing and disc with the help of an image obtained from the thermal camera. The study for intelligent tribological diagnosis has been done by image processing algorithms in the MATLAB environment. The image segmentation for diagnosis is done by the thresholding technique followed by the feature extraction technique by the Circular Hough transform algorithm. The results successfully determine whether the eccentricity and the contact between the housing and disc due to misalignment are present or not, with the help of circular features in red and blue colour.

Dynamical analysis of hearing loss due to mumps virus with Caputo fractional derivative

Mumps is the most common disease for children, which causes hearing loss in all auditory systems. WHO initiated compulsory vaccination for children who are at age of 12 months to 12 years, since 1967. Children must take two doses of vaccination for mumps. The dynamics of the system describing the mumps transmission is studied in this work. The main aim is to elucidate the nonlinear behavior of the system which can provide insights into the long-term effects of Mumps infection on auditory function. As the fractional-order derivative preserves the impact of system memory, we employ the Caputo fractional derivative as the dynamical system describing modeling to simulate hearing loss in children brought on by the mumps virus. The boundedness existence of the solution and stability analysis of the dynamical system are derived in the framework. The result is derived using a well-known numerical method to capture the corresponding consequences and predict the future consequence of the dynamical system associated with parameters. To testify to the importance of the generalizing classical model with a fractional operator, we plot 2D graphs. This study helps to researcher beginners to understand the essential and fundamental tools while investigating real-world problems.

Applicability of linear models in modeling dynamic behavior of alkaline water electrolyzer stack

Linear equivalent circuit models are commonly used to estimate the effect of current ripple on the performance of water electrolyzers, thus it is important that the validity of this approach is examined. The effect of the amplitude and frequency of the sinusoidal current ripple on the performance of the alkaline water electrolyzer stack is studied experimentally. The increased current ripple amplitude produces additional losses in the electrolyzer stack, while the effect of ripple frequency appears to be insignificant. Linear models based on an equivalent circuit and polarization curve tangent are compared with waveform measurements with differing ripple amplitudes and frequencies to study their dynamic modeling capabilities. Under dynamic operation the experimental results show that operating voltage differs considerably from the static polarization curve, especially at low operating currents, due to nonlinear behavior. It is also shown that the dynamic equivalent circuit model using only linear components is not enough to accurately model electrolyzer behavior under dynamic operation.

Coupled vibration of low-medium-speed maglev vehicle-guideway system on isolated bridge with lead rubber bearings

This paper investigates the dynamic response of low-medium-speed (LMS) maglev vehicle moving on the isolated bridge with lead rubber bearings (LRBs). In the vehicle-guideway bridge model, the vehicle is simulated as a 50-degree-of-freedom model consisting of a car-body and ten bogie modules. The guideway bridge with LRB is established by the finite element method, and the guideway is interacted with the vehicle by the actively controlled electromagnetic forces. The LRB is simulated by the nonlinear spring element for reflecting the hysteretic performance, and a fast nonlinear analysis (FNA) method is proposed to achieve the potential nonlinear behavior of LRB under vehicle load. Then, the dynamic response of maglev vehicle running on the isolated bridge with LRB is investigated and compared to that on the non-isolated bridge. The effect of vehicle speed and LRB isolation degree on the coupled system responses is studied. Furthermore, the driving quality of vehicle on LRB bridge is discussed, and the applicability of LRB to maglev line bridge is thoroughly evaluated. The results show that the installation of LRB exhibits relatively insignificant influence on the vertical response of vehicle-guideway system, while could enlarge the lateral response. The lateral response of coupled system is much more vulnerable to the isolation degree, and it is recommended that the isolation degree of LRB should not exceed 2.50 to guarantee the driving comfort and running safety.

Nonlinear time-dependent behavior of rheodictic polymers: A theoretical and experimental investigation

The present study examined the nonlinear time-dependent behavior of rheodictic polymers, a class of noncrosslinked materials that exhibit flow. Such behavior was addressed with extended Schapery's nonlinear viscoelastic model by introducing new physical quantities, i.e., the flow term Φflow and corresponding nonlinear shift parameter g2,flow. While Φflow portrays irrecoverable deformation, g2,flow depicts a nonlinear contribution to flow acceleration. This theory was accompanied by analytical and experimental methodologies for identifying all the parameters in the linear and nonlinear viscoelastic domains. Predictions of long-term time-dependent behavior (in shear) at various stress states show excellent agreement with the experimental data, i.e., within 5% error, obtained for polycarbonate at 130°C. Surprisingly, the newly introduced g2,flow indicates that flow retardation occurs with increasing stress, implying that a highly deformed entangled system hinders molecular reptation/disentanglement. Nevertheless, the proposed extension of Schapery's nonlinear viscoelastic model not only allows accurate predictions of the nonlinear time-dependent behavior of rheodictic polymers but also enables a detailed outlook on the underlying molecular mechanisms under severe environmental and loading conditions.

Deformation theory and nonlinear dynamic behavior of PVC gel actuators

Polyvinyl chloride (PVC) gel generates complex nonlinear vibration behavior under an alternating current voltage excitation, which has potential application as a dynamic electromechanical actuator. However, there are few studies on the deformation theory of PVC gel actuators, especially the dynamic nonlinear response theory. In this paper, a complex dynamic model is established according to the electrodeformation mechanism of PVC film, and the nonlinear dynamic behavior of the actuator is numerically studied by a differential equation. The effects of applied voltage amplitude, voltage frequency, dibutyl adipate content, mechanical tension, and bias voltage on the dynamic properties of PVC film were analyzed under the condition of equal biaxial tension. The variation of amplitude and the generation and disappearance of the beat frequency during vibration are analyzed by using time-domain characteristics. The degree of PVC actuator nonlinearity as well as vibration stability and periodicity is also reflected based on the phase path and Poincare map. Finally, the law of influence of external condition parameters on the dynamic response of the PVC actuator is obtained.