Narrow Results

This paper aims to employ the Darboux transformation (DT) to discover the interaction solutions of the Zakharov equation (Eq. (1.2) for $\delta =1$). Through partial degradation of eigenvalues, interaction solutions of the model are constructed on the basis of high-order breather solutions. The study derives interaction solutions involving breather and b-positon solutions through partial degradation of eigenvalues (${\lambda }_j\to {\lambda }_1$). Further, interaction solutions comprising breather and lump solutions are obtained through partial double degradation of eigenvalues (${\lambda }_j\to {\lambda }_0$). Then, several interaction solutions containing b-positon and lump solutions are extracted through mixed degradation of eigenvalues (${\lambda }_j\to {\lambda }_1$ and ${\lambda }_k\to {\lambda }_0$). In particular, the dynamic evolution characteristics of these solutions are studied. It is believed that these studies make a significant contribution to the understanding of the Zakharov equation and its possible applications in physics.

Human–Structure Interaction (HSI) can significantly influence the dynamic characteristics of pedestrian footbridges, particularly those distinguished by their lightness and slenderness. This study examines the performance of Tuned Mass Dampers (TMD) and Semi-Active Tuned Mass Dampers (STMD) on pedestrian footbridges when their modal parameters change due to the influence of HSI. For this purpose, a 30 m long simply-supported footbridge with linear mass values ranging from 200kg/m to 2000kg/m and a fundamental frequency varying from 1Hz to 5Hz has been considered. In addition, several pedestrian streams with different pedestrian densities have been used to assess the structural dynamic response. The analysis highlights that structural lightness and slenderness are critical factors in determining whether the incorporation of an HSI model is relevant to accurately predict the dynamic performance of the structure. The findings indicate that while TMDs can become ineffective due to shifts in natural frequencies caused by HSI, resulting in a degradation of vibration reduction from 70–75% to 40–45%, STMDs demonstrate a robust capability to adjust and cope with these frequency changes, maintaining a higher average vibration reduction of around 55–60%. Consequently, STMDs emerge as a necessary solution for very slender structures where HSI significantly alters the global frequency response. This study highlights the importance of considering HSI in the design and implementation of damping solutions to ensure optimal functionality and user comfort on lightweight pedestrian bridges.

The hangers represent the crucial load-bearing component of arch bridges and are susceptible to dynamic vehicle load. However, little effort has been made to carry out dynamic analysis of arch bridge hangers under high-speed train loads. This paper presents an investigation of the dynamic behavior of the arch bridge subjected to high-speed train with emphasis on the flexible hangers, using train–bridge interaction simulation and field measurement data. Coupled train–bridge system model composed of three-dimensional train model, bridge model, and wheel–rail interaction model is established to account for hanger transverse vibration, spatial train loading, and track irregularity excitation, among others. Vibration data of bridge components including the hanger are measured through field test on a typical high-speed railway tied-arch bridge. A total stress-based dynamic amplification factor is subsequently proposed to describe the effect of hanger transverse vibration. The influence of significant parameters such as train speed and track irregularity on the dynamic effects of hangers is examined by the experimentally validated train–bridge interaction model. It is found that the dynamic responses of the hangers are considerably different from bridge global responses. In-plane and out-of-plane transverse vibrations of the hanger result in a large increase in the hanger dynamic effects which prove to be sensitive to train speed, track irregularity, train loading position, etc. Moreover, the dynamic amplification factor formula in the current high-speed railway code may not be sufficient to characterize the dynamic amplification of hangers under operating conditions.

In this paper, a bolted joint of two prismatic parts subjected to a shear impact force applied in the structure’s longitudinal direction is studied. The base part is made from steel and the connected one is from aluminum alloy. An elastomeric layer is inserted between the assembled parts in order to reduce vibration resulting from external excitation. An equivalent dynamic model is developed to analyze the behavior of bolted structure. The formulation of the problem gives a system of nonlinear equations. Solving differential equations is based on Euler’s method. Dynamic responses which correspond to the two degrees of freedom of the model are shown. The joint nonlinear behavior strongly depends on the interface properties. A cubic stiffness and damping factor are considered for the layer in the model, which gives it more realistic responses. Experimental tests are done for a case study of bolted joint under transient hummer impact. Model results are agreed with those issued from experiments. The damping layer (DL) effect is experimentally observed as well as in the model results.

Functionally Graded Triply Periodic Minimal Surface (FG-TPMS) structures are an advanced variation of TPMS with spatially varying mechanical properties. Known for their high strength-to-volume ratio, these structures offer lightweight yet robust structural solutions. This study investigates the dynamic characteristics of FG-TPMS structures under the influence of moving loads and supported by a viscoelastic foundation. To manage the challenges related to moving loads and the sensitivity of FG-TPMS plates to boundary conditions, the Moving Element Method (MEM) is employed. The influence of several parameters on the dynamic performance of FG-TPMS plates is studied, including porosity distribution, relative density, plate thickness, and load velocity. The findings highlight the superior strength-to-volume ratio of FG-TPMS plates compared to their isotropic counterparts, emphasizing their potential for practical applications in engineering and materials science. Detailed numerical analyses demonstrate how different porosity distributions and other factors influence the mechanical behavior of FG-TPMS plates, offering insights into optimizing their design for enhanced performance. This comprehensive investigation underscores the advantages of FG-TPMS structures, particularly in applications requiring high strength and lightweight materials, showcasing the efficacy of MEM in solving complex dynamic problems involving moving loads.

This research investigates the dynamic behavior of functionally graded graphene platelet honeycomb sandwich (FG-GPLHS) plates coupled with stiffeners under moving loads, a critical area lacking in current research. Utilizing sandwich equivalence theory, a model of the FG-GPLHS plate is constructed, and the coupling of stiffeners is achieved through displacement continuity conditions combined with displacement coordinate transformation. Artificial virtual spring methods are employed to simulate boundary conditions and establish the force matrix for moving loads. The spectral geometry method (SGM)-Chebyshev method is employed to solve for the model, yielding insights into its dynamic behavior. This research takes into account a number of factors such as honeycomb parameters, boundary conditions, loading velocities, stiffeners cross-section properties, graphene platelet (GPL) distribution pattern and mass fraction to evaluate their effects on the vibration damping effectiveness of the structure. In particular, the effect of honeycomb dimensions and GPL parameters on the vibration resistance and stability of the model under moving loads, which can realize a wider range of application values for this structure in engineering.

In this study, the center of a concave surface was analytically studied using the volume of fluid approach to simulate hollow and dense droplets on a variety of solid obstacles. OpenFoam software was used to carry out the numerical simulations. The hollow droplet’s fluid phase, Glycerine, has an outer diameter of 5.25 mm and its gas phase, air, has a diameter of 4 mm. We looked at the laminar flow of an incompressible Newtonian fluid phase. Jet characteristics and droplet collision hydrodynamic behavior were investigated. Due to the interaction between droplets and shells on the obstacle’s surface and the concave surface, which causes a pressure difference and improves fluid movement, the largest jet size is consequently produced in rectangular obstacles. The sharp obstacle, on the other hand, molds the jet’s shortest length and height.

In this research, we will introduce and study the localized interaction solutions and their dynamics of the extended Hirota–Satsuma–Ito equation (HSIe), which plays a key role in studying certain complex physical phenomena. By using the Hirota bilinear method, the lump-type solutions will be firstly constructed, which are almost rationally localized in all spatial directions. Then, three kinds of localized interaction solutions will be obtained, respectively. In order to study the dynamic behaviors, numerical simulations are performed. Two interesting physical phenomena are found: one is the fission and fusion phenomena happening during the procedure of their collisions; the other is the rogue wave phenomena triggered by the interaction between a lump-type wave and a soliton wave.

This paper presents a method of automatically constructing a model or a set of constraints from domain principles for solving the dynamic behavior of a mechanical system through qualitative simulation. It emphasizes the following issues: the extraction of a set of necessary and sufficient constraints which provides the minimum uncertainty associated with qualitative simulation, from the fundamental principles and laws of physics based solely on the physical description of a given mechanical system; and the modification of constraints through time by detecting and identifying “system discontinuities” due to collisions, separations, and other critical states associated with each of the object primitives.

The first is accomplished by describing a mechanical system by a collection of object and inter-connection primitives, which allows direct instantiating of all the relevant physics laws from the knowledge base. Then, the final set of constraints having the minimum complexity and uncertainty is extracted from the relevant physics laws, based on an A* algorithm with heuristics providing the problem solving expertise. The second is accomplished by monitoring whether the states of any individual sub-systems evolve to system discontinuities represented by intra/inter subsystem critical states.

Recently, a series of typical three-dimensional dissipative chaotic flows where all but one of the nonlinearities are quadratic are studied. Based on this research, a novel chaotic model with only one single linearity is proposed by introducing cubic terms and four new chaotic systems with various characteristics are found. Besides, a chaotic family with a single linearity is constructed with those four chaotic systems and 12 existing systems SL₁–SL${}_{12}$ of the chaotic flows. Exploiting the new systems, basic dynamic behaviors are analyzed, including the strange attractors, equilibrium points, Lyapunov exponents as well as the property of multistability. In addition, the corresponding simulation results are illustrated to show those properties expressly. In realizing the chaotic circuit, we utilize the field programmable gate array (FPGA), which is of considerable flexibility, good programmability and stability, instead of analog devices that are easily affected by surroundings. More importantly, the circuit of the proposed chaotic family is realized on a single FPGA over register transfer level (RTL) using 32-bit fixed-point operation. Finally, an experimental FPGA-based circuit is constructed, and the output results are shown on oscilloscope, which agree well with the numerical simulations.

In this paper, a physical SBT memristor-based chaotic circuit is presented. The circuit dynamic behavior of dependence on the initial state of the SBT memristor and a key circuit parameter are investigated by theoretical analyses and numerical simulations. The results indicate that different initial states of the SBT memristor and the key circuit parameter can significantly impact the dynamic behavior of the chaotic circuit, such as stable sink, periodic cycle, chaos, and even some complex transient dynamics. It can guide future research on the realization of chaotic circuit based on physical SBT memristor.

In this paper, we focus on a class of optimal eighth-order iterative methods, initially proposed by Sharma et al., whose second step can choose any fourth-order iterative method. By selecting the first two steps as an optimal fourth-order iterative method, we derive an optimal eighth-order one-parameter iterative method, which can solve nonlinear systems. Employing fractal theory, we investigate the dynamic behavior of rational operators associated with the iterative method through the Scaling theorem and Möbius transformation. Subsequently, we conduct a comprehensive study of the chaotic dynamics and stability of the iterative method. Our analysis involves the examination of strange fixed points and their stability, critical points, and the parameter spaces generated on the complex plane with critical points as initial points. We utilize these findings to intuitively select parameter values from the figures. Furthermore, we generate dynamical planes for the selected parameter values and ultimately determine the range of unstable parameter values, thus obtaining the range of stable parameter values. The bifurcation diagram shows the influence of parameter selection on the iteration sequence. In addition, by drawing attractive basins, it can be seen that this iterative method is superior to the same-order iterative method in terms of convergence speed and average iterations. Finally, the matrix sign function, nonlinear equation and nonlinear system are solved by this iterative method, which shows the applicability of this iterative method.

Aiming to explore the influence of ultrasonic burnishing technology on the wear behaviors of Al7075 alloy friction pairs, the recurrence analysis method is employed to study the evolutions of recurrence plot (RP) and recurrence quantification analysis (RQA) parameters of friction coefficient signals. The results show that the RPs of burnishing Al7075 alloy specimens evolve from an abrupt structure to a homogeneous structure in the wear process. The average value of determinism $(\overline{\mathrm{\text{DET}}})$ and the average value of entropy $(\overline{\mathrm{\text{ENTR}}})$ of burnishing specimens as a whole are larger than those of nonburnishing specimens. For the burnishing specimens, the $\overline{\mathrm{\text{DET}}}$ and $\overline{\mathrm{\text{ENTR}}}$ are the highest under the load of 25N, with the values of 34.2008 and 4.3129, respectively. It demonstrates that the friction system of burnishing Al7075 alloy under the load of 25N has superior determinism and stability.

In this study, the influence of several fractal identifiers of granular materials on dynamic behavior of a flexible pavement structure as a particulate stratum is considered. Using experimental results and numerical methods as well, 15 different grain-shaped sands obtained from 5 different sources were analyzed as pavement base course materials. Image analyses were carried out by use of a stereomicroscope on 15 different samples to obtain quantitative particle shape information. Furthermore, triaxial compression tests were conducted to determine stress–strain and shear strength parameters of sands. Additionally, the dynamic response of the particulate media to standard traffic loads was computed using finite element modeling (FEM) technique. Using area-perimeter, line divider and box counting methods, over a hundred grains for each sand type were subjected to fractal analysis. Relationships among fractal dimension descriptors and dynamic strain levels were established for assessment of importance of shape descriptors of sands at various scales on the dynamic behavior. In this context, the advantage of fractal geometry concept to describe irregular and fractured shapes was used to characterize the sands used as base course materials. Results indicated that fractal identifiers can be preferred to analyze the effect of shape properties of sands on dynamic behavior of pavement base layers.

The performance-based design of coupled core wall systems offers a number of advantages over conventional strength-based methods in terms of constructability and structural performance. Under large seismic loads, the expected degradation of the coupling beams in coupled wall structures results in an evolution of the lateral force resisting system from a coupled wall system to a system of linked cantilever wall piers. The present study focuses on the performance of the eventually obtained linked wall pier systems and defines their performance in a novel way: as the minimization of transmissibility of horizontal ground motion. In this paper, fixed point theory (FPT) is used to establish initial design values for the coupling beams required to optimize the dynamic response of the linked wall pier system. An initial parametric study of the application of FPT to optimizing the behavior of linked wall piers is presented. The resulting optimized wall systems are compared with practically obtainable, rigid and uncoupled systems subject to a linear time history analysis to assess the extent and practicality of optimization obtained.

Telescopic cranes are usually steel beam systems carrying a load at the tip while comprising at least one constant and one moving part. In this work, an analytical model suitable for the dynamic analysis of telescopic cranes boom is presented. The system considered herein is composed — without losing generality — of two beams. The first one is a jut-out beam on which a variable in time force is moving with constant velocity and the second one is a cantilever with length varying in time that is subjected to its self-weight and a force at the tip also changing with time. As a result, the eigenfrequencies and modal shapes of the second beam are also varying in time. The theoretical formulation is based on a continuum approach employing the modal superposition technique. Various cases of telescopic cranes boom are studied and the analytical results obtained in this work are tabulated in the form of dynamic response diagrams.

The present work focuses on the evaluation of the dynamic behavior of a centenary steel arch bridge, located in Portugal, under light railway traffic loads. This works aims to assess the dynamic behavior of the bridge subjected to an alternative type of railway vehicle, more specifically, a typical underground vehicle that is currently in service in the Lisbon Metro. The dynamic response of the system has been evaluated using two distinct methodologies, namely a moving loads model and a vehicle–bridge interaction model. To achieve this goal, finite element (FE) models from both the bridge and the vehicle have been developed and a comprehensive study has been carried to evaluate the influence of distinct factors in the dynamic response of the bridge–train system, namely the methodology used to assess the dynamic response, the location of the response reference point in the deck, the train speed and the vehicle configuration (single or double vehicle). Moreover, both the traffic safety, passenger comfort and pedestrian comfort have also been evaluated using normative criteria based on acceleration responses. The results shown that the normative limits related to traffic safety and passenger comfort were never exceeded in any condition analyzed in the study. However, the pedestrian comfort was jeopardized when the train speed exceeded 20km/h.

The road–rail dual-use bridge can simultaneously meet the requirements of both the highway and railway transportation owing to its unique bridge type, which makes it environmentally friendly and cost-effective when compared to independent railway and road bridges. This study establishes a dynamic model of a wind-road vehicle–bridge system considering the aerodynamic sheltering effect of trains based on the coupling vibration method of wind-road vehicle–bridge systems. A container truck and a CRH2 high-speed train are considered as the research objectives, and a series of wind tunnel tests are conducted for the train and truck running simultaneously on a road–rail dual-use bridge to determine the effect of the aerodynamic interference of trains on the aerodynamic characteristics and dynamic behavior of vehicles under crosswinds. The entire process of driving the truck through the cable-stayed bridge under crosswinds and the interference of stationary trains is subsequently simulated to generate the time histories of the dynamic displacements of the truck. Consequently, the effect of the stationary trains is separately compared at different locations, such as on the track of the bridge deck and on the truck placed upwind and downwind. Furthermore, the interference effect of stationary trains on the truck placed upwind and downwind is analyzed corresponding to different wind yaw angles. The results demonstrate that the presence of trains on the bridge significantly affects the aerodynamic coefficients and dynamic responses of the truck placed downwind when compared to the truck placed upwind. Additionally, the presence of the trains on the bridge deck has a different effect on the aerodynamic coefficients and dynamic responses of the truck placed downwind. The effect of the trains on the truck at different wind yaw angles presents different patterns of change for different locations of the trains on the bridge deck.

Cracking frequently encountered in railway bridges can lead to significant changes in bridge dynamic characteristics and further dynamic performance of train–bridge interaction (TBI) system. It is desirable to develop an effective method to understand the dynamic behavior of coupled train and cracked bridge systems. This paper proposes a framework for coupled vibration analysis of train and cracked bridge systems using multiscale finite element modeling. A multiscale bridge model adopting frictional surface–surface contact to characterize nonlinear breathing phenomenon of the crack is incorporated into the three-dimensional coupled TBI model. Subsequently, a multiloop numerical solution strategy is formulated to solve the established dynamic equation of coupled train and cracked bridge systems. The proposed framework is used to analyze the cracked beams presented in the literature, and the obtained and literature data are compared. Moreover, an actual heavy-haul railway bridge is taken as an illustrative example, in which vehicle dynamic response, bridge vibration, and train running safety index are calculated considering various crack types, train speeds, and track conditions. The results show that apart from the bridge displacement and acceleration, the presence of crack can have a large influence on the vehicle acceleration response, derailment factor, and offload factor. Differences larger than ±10% in the maximum dynamic indices associated with the intact and cracked bridges are observed, indicating the necessity of considering the crack damage in train–bridge coupled dynamic analysis.

In this paper, a finite element model was built using ANSYS/LS-DYNA to study the effect of strain rate on the dynamic out-of-plane plateau stress of aluminum honeycombs under constant velocity impact. The strain rates vary from 10² to 10⁴ s^-1. It has been found that the t/l ratio (wall thickness to edge length ratio) and strain rate have great influence on deformation pattern and plateau stress. The effect of strain rate on the plateau stress under high velocity impact was found to be different from that under low strain rate compression. The threshold impact velocity is approximately 100 m/s for the aluminum honeycomb studied.