Dynamic Response Of System Research Articles

Trajectory optimization method based on ellipse model for dynamic motion control of piezoelectric transducer in an optical resonance cavity

External-cavity diode laser (ECDL) can continuously change the output wavelength by scanning its optical resonance cavity (ORC), which is a piezoelectric transducer (PZT) actuated mechanical system. However, because of the inherent hysteresis characteristic of PZT and limited system bandwidth, the dynamic response of the ORC system exhibits both the nonlinearity and vibration while high-frequency triangular wave scanning, thereby resulting in the degradation of the output wavelength performance of the ECDL. As a result, a trajectory optimization method is presented to improve the scanning characteristics of the ORC system. Firstly, the hysteresis behavior of PZT is described by the elliptic model to generate a compensation voltage for the PZT. Secondly, the cusp region of the compensation voltage is optimized by a frequency domain objective function to greatly reduce the high-order harmonic components of the compensation voltage. Finally, an optimal voltage trajectory for driving the ORC system is obtained. The experimental results demonstrate the validity of our proposed trajectory optimization method for simultaneously suppressing the nonlinearity and vibration of the ORC system within the scanning frequency of 100 Hz.

Influence of clearance between cradle and barrel on nonlinear dynamic response of the artillery system

The artillery weapon system,characterized as a complex nonlinear mechanical system, is influenced by various factors affecting its muzzle vibration response.In the article, the model of the artillery system with variable cross-section and multistep barrel is established on the basis of the bending deformation equation, and the fundamental frequency equation is obtained, and the auxiliary verification is completed through modal testing and finite element methods. Then, considering the clearance between the barrel and the cradle, the equivalent nonlinear dynamic model of the vertical vibration of the muzzle is established is established. Furthermore, the multi-scale analysis method obtains the amplitude-frequency curve of the equivalent model under sinusoidal excitation, and analyzes the influence of parameters on the response characteristics. Finally, the vibration research system of the model of the artillery system is constructed to study the vibration characteristics of the muzzle. The results show that the equivalent nonlinear dynamic model established in the paper has certain accuracy, which can provide a certain reference for the related research of the artillery system

Modeling the dynamic response of a light-powered self-rotating liquid crystal elastomer-based system

Self-oscillating systems possess the capability to convert ambient energy directly into mechanical work. Consequently, the development of novel self-oscillating systems holds significant potential for applications in energy harvesting, engines, and actuators, making them highly worthwhile to be designed and implemented. Inspired by the rotation of a skipping rope, we creatively developed a self-rotating liquid crystal elastomer (LCE)-based system composed of a LCE fiber and a mass, which triggers self-rotation under steady illumination. In this work, a nonlinear dynamic model is proposed to study the dynamic behaviors of optically-responsive LCE-based systems. Numerical calculations show that the self-rotating LCE-based system can undergo a supercritical Hopf bifurcation between the static state and the self-rotation state, which is maintained by the energy input of ambient illumination to compensate the damping dissipation. In addition, the Hopf bifurcation conditions, as well as the important system parameters affecting the frequency of self-rotation, are studied in detail. Especially for the cases of unilateral asymmetrical lighting, the system parameters have different effects on the clockwise and counterclockwise rotation. Different from the existing abundant self-oscillating system, the self-rotating LCE-based system has the advantages of simple structure, customizable size and multimode rotation, and is expected to provide more diversified design ideas for soft robotics, energy harvesters, micro-machines, etc.

Absolute nodal coordinate formulation – Multilevel finite element framework for the nonlinear multi-scale multibody dynamic analysis of composite structures

In this paper, a multi-scale modeling approach for the dynamic response of flexible multibody system made of composite material is suggested using the absolute nodal coordinate formulation (ANCF) – multilevel finite element (FE2) method. On many occasions, the analysis of composite structures requires a multi-scale modeling approach. FE2 method is one of the famous multi-scale modeling methods. And it is a versatile computational homogenization approach that is commonly applicable to many different materials. Because the present FE2 is capable of computing the mechanical response at two different scales simultaneously, ANCF element will be used at the macroscopic scale. And the microscopic RVE at each macroscopic integration point will be obtained by the finite element method. Since ANCF element uses only the absolute nodes and gradients, the mass matrix will be constant. Due to such characteristics, when combined with FE2, the linearization process will become easier compared against the existing formulation. And Coriolis or centrifugal force will not need to be considered in the dynamic formulation. Therefore, computational cost will be reduced, and the relevant algebraic manipulation will become simplified. Several numerical examples are presented to demonstrate the improved accuracy and diminished computational cost of the present suggestion.

Dynamic Responses of Train-Symmetry-Bridge System Considering Concrete Creep and the Creep-Induced Track Irregularity

This work considers the influence of concrete creep on track irregularities and establishes the dynamic motion equation of the train-track-bridge coupling system. The track irregularity is obtained by superposition of the initial geometric irregularity and additional geometric irregularity of the steel rail caused by creep. When high-speed railway trains pass through bridges; the vertical acceleration and vertical displacement of continuous beam bridges are related to the train’s operating speed, and the influence of creep camber is relatively small. At the same time, considering the randomness of track irregularities, the dynamic responses of the train track bridge coupling system under the action of random track irregularities are analyzed, and the dynamic responses of trains at different operating speeds are obtained. The deterministic and uncertain dynamic responses of the train track bridge system were compared and analyzed to verify the accuracy of the Karhunen Loéve expansion (KLE)-Point estimate method (PEM) calculation results. The results indicate that the random characteristics of track irregularities have a significant impact on train dynamic response. Based on the random system vibration analysis and considering the safety and comfort indicators of high-speed railway trains, the creep deformation limit of a continuous beam bridge with a length of 48 m + 80 m + 48 m is obtained to be 19 mm. This is the first time that the dynamic responses of train-symmetry-bridge system are calculated by considering concrete creep and the creep-induced track irregularity, which has certain significance for understanding the dynamics of train -bridge system. In addition, the proposed creep threshold is also of great significance to ensure the safety of traveling.

Prediction of stochastic responses of vehicle running through the multi-spans bridge based on an optimized method

The dynamic response of a vehicle-bridge system (VBS) has been a key problem in assessments of train-running safety on bridges, ultimately requiring reliability analyses owing to uncertain parameters and random rail irregularities. To improve the computational efficiency and promote the development of a reliability analysis for VBS, this paper proposes a novel approach incorporating a stochastic pseudo-excitation method (SPEM) to optimize a deep learning approach. This approach can more efficiently calculate the dynamic responses of a VBS than the traditional methods. In this study, the dynamic responses of the uncertain system produced by the SPEM were utilized as the training datasets for the deep learning approach. Based on the training datasets, a neural network was established to construct a numerical model consisting of two functional modules: a full convolutional network (FCN) training for the input rail irregularities and gated recurrent unit (GRU) layer for the VBS response prediction, i.e., a SPEM–FCN–GRU (SFG). The GRU cell was simulated by introducing the randomness of the excitation and uncertain parameters of the system into a portion of the cell, thereby enabling the numerical model to convey the randomness of the VBS and to obtain its stochastic response. Addition, long-time-domain samples of the VBS responses were predicted based on the short-time-domain samples. To verify the accuracy and applicability of the proposed method, a train running through a multi-span simply supported railway bridge was investigated. The dynamic responses of the train were analyzed using the training set data and Monte Carlo method (MCM) and the results showed good agreement with each other. Next, by introducing an algorithm combining a convolutional neural network (CNN) with the MCM and GRU (an MCM–CNN–GRU) and comparing it with the method proposed herein, it was verified that the proposed method has better predictions and higher efficiency than those of a traditional neural network. The prediction efficiency of the SFG was analyzed. Based on the shortcomings of the SFG, we proposed an optimized SFG algorithm. The short-time-domain results predicted by the proposed method were input into the training datasets for the deep learning architecture to enhance the number of training data for the prediction of long-time-domain responses. The efficiency and accuracy of the proposed method were verified by comparing them with those of traditional neural networks. As an example, the dynamic responses of a train running through a three-span bridge were computed by the SPEM; these could be adopted to predict those of a train running through a 10-span bridge. Finally, based on the simulated and predicted results, the reliability of the VBS was studied using a first-order reliability method.

Dynamic response analysis of a train braking system with time-varying coefficient of friction excitations

Coefficient of friction (COF) is a key parameter that reflects the interface tribological behavior and influences the system dynamic response. In this research, the tribological properties of the train braking system friction blocks with different perforation diameters are experimentally explored using a block-on-disc apparatus. And the distribution law of the interface COF is revealed by statistical analysis. It is found that the histogram of the COF approximately follows a normal distribution. Considering the time-varying of the COF, a time-varying COF model is then established based on the normal distribution parameters. Further, the time-varying COF model is integrated into a proposed train braking system numerical model to construct the association between the disc–block friction properties and the braking system dynamic response. Based on this, the dynamic behavior of the braking system subject to interface time-varying COF excitations and block perforation structure is analyzed. The results show the time-varying COF excitations should be considered to accurately reveal the dynamic response of the braking system. Moreover, the friction block processed a perforation diameter of 2 mm obviously reduces disc–block friction vibration and improves the stability of the train braking system.

On the coupled dynamics of vertical cladding panels and industrial frame structures subject to out-of-plane seismic loading

Industrial facilities typically consist in large-span single-storey prefabricated buildings having a rectangular floor space. Frame structures made with either steel, timber or precast concrete members are mostly employed to support the roof, while cladding panels create the building enclosure. Their interaction with the frame typically plays a relevant role in the overall building dynamics, potentially leading under seismic excitation to both local and global collapses. Experience shows that a critical component failure is that of the panel-frame connection. Current design approaches classify the panels as “non-structural members” and the forces at the connections induced by the out-of-plane seismic loading are evaluated with approximate expressions. Neglecting the dynamic interaction between the panel and the frame, however, may lead to an oversimplified description of the mechanical problem and inaccurate estimates of the forces at the connections. To overcome these drawbacks, in this work a different approach is pursued in which the interaction between the fundamental sway mode of the frame and the out-of-plane motion of the cladding panel is studied within a rigorous mechanical setting. The focus is on the very frequent case of vertical cladding panels, supported at the ground and retained out-of-plane by the frame. Starting from the development of the equations of motion for the coupled frame-panel structure, a minimal set of parameters controlling the dynamics of the system is identified. The spectral properties of the structure are analytically investigated to gain a clear insight on the coupled frame-panel structure. This is characterized by frequency veering and hybridization between the mode deforming the frame and the local modes of the panel. The system response for seismic excitation, then, is studied with a stochastic approach. Parametric analyses focusing on the values of the forces at the top and bottom connections of the panel and on the lateral displacement of the frame show that while the frame drift is controlled mainly by the first mode of the coupled frame-panel system, the top and bottom connection forces of the panel require at least consideration of the first two modes of the coupled system. This information is of great importance in deriving a reduced model of the coupled system. The proposed procedure allows for a thorough understanding of the coupled system dynamic response, and represents a viable alternative to derive the design response quantities of interest.

A time variant uncertainty propagation method for high-dimensional dynamic structural system via K-L expansion and Bayesian deep neural network.

In this paper, a time variant uncertainty propagation (TUP) method for dynamic structural system with high-dimensional input variables is proposed. Firstly, an arbitrary stochastic process simulation (ASPS) method based on Karhunen-Loève (K-L) expansion and numerical integration is developed, expressing the stochastic process as the combination of its marginal distributions and eigen functions at several discrete time points. Secondly, the iterative sorting method is implemented to the statistic samples of marginal distributions for matching the constraints of covariance function. Since marginal distributions are directly used to express the stochastic process, the proposed ASPS is suitable for stationary or non-stationary stochastic processes with arbitrary marginal distributions. Thirdly, the high-dimensional TUP problem is converted into several high-dimensional static uncertainty propagation (UP) problems after implementing ASPS. Then, the Bayesian deep neural network based UP method is used to compute the marginal distributions as well as the eigen functions of dynamic system response, the high-dimensional TUP problem can thus be solved. Finally, several numerical examples are used to validate the effectiveness of the proposed method. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 1)'.

A universal phase condition in solving quasi-periodic responses with multiple self-excited fundamental frequencies

Solving quasi-periodic (QP) responses of nonlinear dynamical systems, particularly when multiple self-excited fundamental frequencies have to be determining, has been a challenging task. The presence of unknown frequencies usually leads to an under-determined problem, where the number of unknowns exceeds that of equations, as obtained through harmonic balancing or difference techniques, for instance. Therefore, it is necessary to introduce supplementary equations to ensure the well-posedness of the solving process. To the best of our knowledge, some existing methods are only applicable to cases with a single unknown frequency or they require prior numerical results attained, for example, by time-marching integration techniques. In this paper, we propose a new phase condition that is unconditionally valid for QP solutions with multiple unknown frequencies. This condition reveals an inherent feature of QP motion in a multi-dimensional hyper-time domain and provides a theoretical basis for solving QP responses in such a domain. To demonstrate its effectiveness, we apply the phase condition to both the finite difference and the harmonic balance methods. Numerical examples illustrate that, by employing the phase condition, both methods can solve stable as well as unstable QP solutions accurately. As the phase condition holds universally, it is suitable to be incorporated into other solution techniques based on either frequency or time-domain analysis.

Assessment of train running safety on railway bridges based on velocity-related indices under random near-fault ground motions

Random analysis has emerged as the dominant approach for analyzing train-bridge coupled (TBC) systems, replacing deterministic analysis. This shift is driven by considerations of system economy and randomness. However, the seismic train running safety assessment with multiple non-Gaussian distribution parameters faces the double dilemma of low computational efficiency and inaccuracy for TBC systems. In this study, an approach is applied by the combination of the new point estimate method and moment expansion approximation (NPEM-MEA) to address this problem. Furthermore, the application of this approach is illustrated by the random dynamic responses of a three-dimensional TBC system subjected to random near-fault ground motions. Validation of the NPEM-MEA’s feasibility is conducted using the Monte Carlo method, and comparative analysis confirms the accuracy and efficiency of the method. Additionally, the influences of random near-fault ground motions are discussed based on the random dynamic responses and train running safety indices in the TBC system. The simulation results underscore the necessity of simultaneously considering the randomness of multiple parameters in seismic train running safety assessment. This methodology holds potential for safety assessments involving non-Gaussian random processes in complex systems of a similar nature.

Hydrodynamic Characteristics of Floating Photovoltaic Systems under Ocean Loads

The floating photovoltaic (FPV) array, which consists of tens or hundreds of rows of floating photovoltaic systems, exhibits great economic and environmental benefits. An FPV array arranged in the ocean will be subjected to the combined action of wind, waves, and currents during the installation, service, and maintenance processes; however, systematic research in this field is still lacking. As a representative of the FPV array, this study on the hydrodynamic characteristics of a single-row FPV system is a fundamental prerequisite for the safe design of large-scale FPV arrays in the near future. In this paper, based on the potential theory, a numerical model of a single-row FPV system with ten floating platforms is established with ANSYS-AQWA software. Following this, the hydrodynamic coefficients of a single floating platform are calculated and evaluated. After that, the dynamic responses of the FPV system under different load combinations are explored. Finally, the influence mechanism of wave parameters on the hydrodynamic characteristics of the FPV system is discussed in detail, including the wavelength and wave height. The results indicate that, within the scope of this study, the floating platforms have good seakeeping and stability. The wave load dominates for all conditions, and the presence of the current will affect the parameters of the wave. In addition, the relative relationship between the wavelength and the length of FPV system will affect their resonance effect, and the increase in wave height will significantly enhance the dynamic response of the FPV system. This study can help to provide references for the safety design of FPV arrays.

Analysis of Dynamic Characteristics of Tristable Exponential Section of Piezoelectric Energy Harvester

Variable-cross-section beams have better mass and strength distribution compared with constant cross-section beams, which can optimize the harvesting power of piezoelectric vibration energy harvesters, which are widely used in self-supplied and low-power electronic devices, providing more convenience and innovation for the development of micromechanical intelligence and portable mobile devices. This paper proposes a piezoelectric energy harvester with a tristable-exponential-decay cross section, which optimizes the strain distribution of the cantilever beam through exponential decay changes to improve the harvesting efficiency of the harvester in low-frequency environments. First, the nonlinear magnetic force is obtained based on the magnetic dipole, and the dynamic model is established by using the Euler–Bernoulli beam theory and Lagrangian equation. The influence of the structural parameters of the harvester on the system dynamics and output characteristics is analyzed in the two dimensions of time and frequency, and the influence of the exponential decay coefficient on the system dynamic response and output power is deeply studied. The research shows that the exponential decay section can reduce the first natural frequency of the cantilever beam; by changing the amplitude, frequency, d and dg of the excitation acceleration, the switching of the monostable, tristable and bistable states of the system can be realized. With a decrease in the exponential decay coefficient, under a low-frequency excitation of 0–7 Hz, the output power of the cantilever beam per unit volume is significantly improved, and under a 4 Hz low-frequency excitation, the acquisition output power per unit volume of the cantilever beam is increased by 7 times, thus realizing low-frequency, high-efficiency energy harvesting.

Three-Dimensional Prestressed Tuned Mass Damper for Passive Vibration Control of Coupled Multiple DOFs Offshore Wind Turbine

Large megawatts offshore wind turbine (OWT) with low natural frequency and low damping is subjected to significant vibration from wind and wave actions in its service environment. The one-dimensional prestressed tuned mass damper (PSTMD) is further extended to a 3D-PSTMD for the control of vibrations of the OWT in this paper. A multiple DOFs coupled system of turbine, blades, tower, and foundation under aerodynamic and hydrodynamic forces is considered in this study of vibration mitigation at fore-aft and side-side directions. The dynamic model is derived with the Lagrangian equation, and the superiorities of the PSTMD are proved from the perspective of theoretical analysis. Aerodynamic and hydrodynamic loads are generated with the blade element momentum (BEM) theory and Morrison equation, and the dynamic responses of different systems are computed by using the Wilson-θ method. The analysis results indicate that a damping coefficient of the 3D-PSTMD corresponding to the first vibration mode can be tuned to take up values larger than that in traditional three-dimensional pendulum (TMD) (3D-PTMD). The bidirectional vibration suppression competences of the 3D-PSTMD in the dynamic responses when under aerodynamic and hydrodynamic loads are better than those of the traditional 3D-PTMD.

Influence of interlayer types and thicknesses on the blast performance of laminated glass panels

Several new laminated glass (LG) polymer interlayer materials are now available in the market such as Ethylene-Vinyl Acetate (EVA), and SentryGlas (SG). In this paper, quasi-static testing was conducted using a full-scale static water chamber to investigate the influence of interlayer type and thickness on the extreme static response of the LG panels. However, due to the high danger and cost of explosion tests, numerical modeling was used to study the effect of these parameters on the dynamic response of the LG systems. The dynamic numerical model was verified using previously published experimental data. Results demonstrate varying pressure resistance capabilities with changes in interlayer type. EVA interlayer panels exhibit the highest deformation in dynamic behavior, while SG interlayer panels demonstrate the least deformation. Consequently, LG panels with SG interlayers exhibit the highest strength among the three types. Furthermore, the resistance of LG panels improves in the pre-cracked stage by increasing interlayer thickness.

Influence of Variable Height of Piers on the Dynamic Characteristics of High-Speed Train–Track–Bridge Coupled Systems in Mountainous Areas

With the increase in the occupancy ratio of bridges and the speed of trains, the probability of trains being located on bridges during earthquakes increases, and the risk of derailment increases. To investigate the influence of unequal-height piers on the dynamic response of high-speed railway train bridge systems, a seismic action model of high-speed train–track–bridge dynamic systems was established based on the in-house code using the finite element method and multi-body dynamics method. It is found that (1) compared to equal-height piers, the peak lateral dynamic response of unequal-height piers (with gradually increasing pier heights) decreases, while the peak vertical dynamic response increases; (2) the peak lateral dynamic response of unequal-height piers (with a steep increase in pier height) increases sharply, while the peak vertical dynamic response decreases; and (3) the safety indicators of equal-height piers are significantly superior to the two unequal-height pier operating conditions.

Study on seismic response difference of horizontal and inclined liquefied site-pile-structure

In recent years, many earthquake disasters have shown that the liquefaction side expansion of the soil in the inclined liquefaction site will increase the damage degree of pile, which will cause the failure of the superstructure. In this study, an efficient-finite element model is built for the shaking table test of the interaction of inclined liquefied site-pile group-superstructure. By comparing with the experimental results, the rationality of the model building method is proved. Based on the verified method, finite element models of typical horizontal and inclined liquefied site-pile group-superstructure interactions are built. Then, the dynamic response of the soil-pile group-superstructure system under different non-liquefiable crust thicknesses in horizontal and inclined liquefaction sites are analyzed, and the differences between the systems under the two sites are discussed. The calculation result indicate that the pore pressure ratio, pile displacement, soil displacement and pile curvature in horizontal and inclined sites decrease obviously with the thickness of the non-liquefiable crust increases. Compared with the horizontal site, the attenuation amplitude of the inclined site is more obvious. There is little difference in pore pressure and acceleration of soil in horizontal and inclined liquefaction sites under different non-liquefiable crust thicknesses. Compared with the horizontal site, the lateral expansion flow in the inclined site produces permanent lateral displacement, which increases the damage degree of the pile.

Simultaneous Optimization of SWMM Parameters by the Dynamic System Response Curve with Multi-Objective Function

Simultaneous Optimization of SWMM Parameters by the Dynamic System Response Curve with Multi-Objective Function

Application of Modal Analysis of Earthquake Force and Natural Frequency Tanjung Baru Bridge

The dynamic response of a structural system can be described by modal analysis. In the present study, the modal analysis that adopts an Undamped Degree of Freedom (Undamped-DOF) System is implemented to describe the modal descriptors such as the natural frequency and mode shape of a bridge. Furthermore, the earthquake load acting on the bridge is also evaluated and hence the possibility of a resonance associated with this load is investigated. For this objective, the earthquake data collected during the past ten years in Indonesia is explored. This study considers the Tanjung Baru Bridge, a prestressed concrete bridge situated on the Medan-Kualanamu-Tebing Tinggi highway, as the case study. The modal analysis and the evaluation of the earthquake load confirm that the possibility of resonance for the Tanjung Baru Bridge is extremely low. The study also proves that this bridge has a sufficient capacity to withstand earthquake loads.

Enhancing transient stability and dynamic response of wind-penetrated power systems through PSS and STATCOM cooperation

The large-scale integration of doubly-fed induction generator (DFIG) based wind power plants poses stability challenges for power system operation. This study investigates the transient stability and dynamic performance of a modified 3-machine, 9-bus Western System Coordinating Council (WSCC) system. The investigation was conducted by connecting the DFIG wind farm to the sixth bus via a low-impedance transmission line and installing power system stabilizers (PSSs) on all automatic voltage regulators (AVRs). A three-phase fault simulation was carried out to test the system, with and without power system stabilizers and a static synchronous compensator (STATCOM) device. Time-domain simulations demonstrate improved transient response with PSS-STATCOM control. A 50% reduction in settling time and 70% decrease in power angle undershoots at the slack bus are achieved following disturbances, even at minimum wind penetration levels. Load flow analysis shows the coordinated controllers maintain voltages within 0.5% of nominal at 60% wind penetration, while voltages at load buses can deviate up to 15% without control. Eigenvalue analysis indicates the PSS-STATCOM boosts damping ratios of critical oscillatory modes from nearly 0% to over 30% under high wind injection. Together, the present findings provide significant evidence that PSS and STATCOM cooperation enhances dynamic voltage regulation, angle stability, and damping across operating ranges, thereby maintaining secure operation in systems with high renewable integration.