Dynamic Response Equation Research Articles

Dynamic response and stability analysis of vehicle systems with double time-delay feedback control

In this paper, the vehicle suspension dynamic response of time delay feedback control is analyzed considering the suspension of the seat. An active suspension vibration reduction control method based on double time-delay feedback control is proposed to further improve the ride comfort. Firstly, the double time-delay dynamic response equation of the system with three degrees of freedom is established. Then, the root mean square values of seat acceleration and body acceleration are used as the objective functions. Meanwhile, the RMS values of suspension dynamic deflection and tire dynamic displacement are used as constraints, and the optimal feedback parameters are obtained using particle swarm optimisation. The Routh-Hurwitz criterion and frequency domain scanning methods are used to verify the stability of the double time-delay system. Finally, simulation in the time domain and frequency domain is accomplished. It is verified that this feedback control method has strong robustness and anti-interference ability.

Experimental and numerical study on the blast performance of the corrugated double steel plate concrete composite wallboard under blast loads

The corrugated double steel plate concrete composite wallboard (CDSCW) exhibits superior axial compressive load-bearing capacity, lateral flexural stiffness, impact resistance, and seismic performance compared to the traditional reinforced concrete wallboard and plane double steel plate concrete composite wallboard (PDSCW). Therefore, it has great potential application in offshore engineering and military engineering. This study designs and fabricates two types of CDSCW specimens. Firstly, a comparative analysis is conducted to examine the damage patterns and dynamic responses of the two specimens under near-field explosion experiments. Secondly, the damage mechanisms and explosion response of CDSCW and PDSCW subjected to close-in explosions are numerically investigated by using ANSYS/LS-DYNA, and the results are then compared with experimental findings. Parameter analysis is performed to assess the influence of concrete thickness, steel plate thickness, and explosive charge on the blast resistance of CDSCWs. Furthermore, a nonlinear resistance equation and an equivalent single degree of freedom (ESDOF) theoretical model for simply supported beams is established to predict the dynamic response of CDSCWs under near-blast loads. This theoretical model considers the constitutive model of bilinear materials and the effect of plastic hinges. The reliability of the proposed theoretical model is verified by comparing the residual deflection of CDSCWs obtained from explosion tests with validated numerical simulation results. The results demonstrate that the CDSCWs, with the same concrete and component dimensions (length, width), exhibit greater flexural stiffness and superior energy dissipation capacity subjected to close-in explosion. Moreover, their blast resistance significantly surpasses that of PDSCWs. In particular, an increase in corrugation depth effectively improves the blast resistance of CDSCWs. The dynamic response equations, based on the established elastic-plastic model and primarily considering bending deformation of the components, precisely predict the dynamic response of simply supported CDSCWs under near-blast loads. consequently, these findings can provide a robust foundation for further research and the design of blast-resistant structures.

Wave-induced residual response and liquefaction of a nonhomogeneous layered seabed

Numerical studies were conducted on the wave-induced residual liquefaction of a silt–coarse sand layered seabed. Fully dynamic soil equations and residual seabed response equations were incorporated into the development of a numerical model. The numerical results were compared with theoretical solutions and experimental data from previous studies. Relatively good agreement was found in this comparison, validating the reliability of the proposed numerical model. The present model was applied to systematically investigate the wave-induced residual response with a silt–coarse sand layered seabed. The effects of coverage thickness, permeability, Young’s modulus in the upper silt layer on the residual response of the seabed were carefully examined. Numerical simulations indicate that the potential liquefaction is prone to occur with low permeability of the upper silt layer and shallower water depth, and the effect of coverage thickness of the silt layer on pore pressure and liquefaction potential is determined by shear stress ratio (χ) and effective normalized spreading parameter (Se) which represent the “generation power” and “dissipation potential” for residual pore pressure. The performance of the pore pressure and liquefaction in the layered seabed is the result of a trade-off between two non-dimensional parameters.

Bearing condition assessment of a simply elastic supported beam based on impact vibration testing

The mechanical properties of bridge bearings gradually deteriorate over time, resulting from daily traffic loading and harsh environmental conditions. However, efficient detection of in-service bridge bearings is still challenging, especially in quantifying support stiffness. This study presents a bridge bearing condition assessment framework of a simply elastic supported beam based on impact vibration testing and structural flexibility identification. Firstly, the dynamic response equation of a simply supported beam with elastic boundary constraints is established. The modal orthogonality of Euler-Bernoulli beams and the corresponding overall matrix of undetermined coefficients are derived using the separate variable method. Subsequently, the flexibility matrix of the simply elastic supported beam is derived and verified in the cases of forward and inverse analysis, respectively. Furthermore, the vertical and rotational stiffness of the bearings are established based on the structural flexibility matrix. Finally, experimental verification is performed to identify the flexibility and the vertical support stiffness of the simply elastic supported beam based on impact vibration tests. The results indicate that the proposed the bearing condition assessment framework can straightforwardly quantify support stiffness.

Intelligent ADRC‐based inertia control for offshore wind farm

AbstractThis paper proposes a virtual inertia control strategy for wind farms based on auto disturbance rejection controller with artificial bee colony (ABC) algorithm. First, based on the system frequency dynamic response equation, an active disturbance rejection controller is designed according to the non‐linear feedback control law and the extended state observer to improve the anti‐interference capability of the virtual inertia control system. Second, in order to solve the problem of difficulty in tuning the parameters of the active disturbance rejection control (ADRC), an ABC algorithm based on nectar collection behaviour was proposed to iteratively optimize the parameters of ADRC. Finally, the proposed control method is effectively verified based on Matlab/Simulink. The simulation results show that compared with traditional algorithms, the proposed ABC‐ADRC can effectively control the rotor speed to adjust the frequency of the power grid system, achieve power sharing and adaptive noise elimination, reduce the complexity of parameter settings, not only improve anti‐interference ability, but also enhance the robustness of the system.

Identifying Key In Silico Knockout for Enhancement of Limonene Yield Through Dynamic Metabolic Modelling.

Living cells display dynamic and complex behaviors. To understand their response and to infer novel insights not possible with traditional reductionist approaches, over the last few decades various computational modelling methodologies have been developed. In this chapter, we focus on modelling the dynamic metabolic response, using linear and nonlinear ordinary differential equations, of an engineered Escherichia coli MG1655 strain with plasmid pJBEI-6409 that produces limonene. We show the systems biology steps involved from collecting time-series data of living cells, to dynamic model creation and fitting the model with experimental responses using COPASI software.

Dynamic Behavior and Parameter Characteristics of Buried Pipeline in Airports

Buried pipeline, as one of the crucial facilities of airport ground engineering, has been extensively utilized for the transportation of petroleum, natural gas, industrial wastewater, and more. However, there are significant gaps in the research on the dynamic response of buried pipelines in airports under the action of dynamic traffic loads, which severely hampers the design and engineering quality of oil transmission pipelines. This study builds a three-dimensional finite element model to simulate the action of vehicles on the pipe–soil structure with actual loads. Moreover, the current research establishes a dynamic analysis model of pipe–soil interaction to analyze the material damping and load parameters. Using the structural dynamic response equation and Rayleigh damping calculation theory, this study investigates the change law of pipe dynamic stress and influencing factors and presents the recommended values of the parameters related to the pipe–soil interaction. Results are as follows. A damping ratio of 0.05 can enhance the time lag of the dynamic response of the structure and weaken the response peak. For the Rayleigh damping parameters, the viscous damping coefficient [Formula: see text] has almost no effect on the dynamic response of the pipe–soil structure, so it can be disregarded in the calculation. With the increase of the axial weight of the traffic load above the pavement structure, the peak value of each dynamic response quantity of the pipe–soil structure and load magnitude. The suggested value of the dynamic load coefficient of the pipe–soil structure is 1.5. Lastly, the earth pressure and dynamic load coefficients are suggested to take values for different load and axle type cases.

Lateral response of a pile group embedded in the transversely isotropic saturated soil due to surcharge loads

This paper investigates the behavior of pile groups in the transversely isotropic saturated soil under an adjacent surcharge load using a coupling method. The analytical layer-element theory is utilized to the transversely isotropic saturated soil model, and the fundamental solutions of the soil are applied to derive the soil flexibility matrices. And the FEM is used for the piles modeled as Bernoulli–Euler beams considering pile–pile interaction. Then, the dynamic response equations of pile groups are derived by using the FEM–BEM coupled method and considering pile-soil boundary coordination condition. The results of the present model compared well with those in existing solutions. Numerical examples are presented to examine the influences of the soils’ transverse isotropy, the magnitude of the surcharge load, the pile's physical properties and the distance between the load and the pile on the behavior of pile groups. It is observed that as the surcharge load grows, the position of the pile maximum displacement response changes from the middle of the soft soil layer to the top of the pile. The impact of the surcharge load is not significant when the loading action distance is greater than twice the thickness of soft soil layer. Furthermore, relatively large bending moments appear in the middle of the soft soil layer and at the interface of the soil layers.

A two-dimensional semi-analytic solution on two-layered liquid sloshing in a rectangular tank with a horizontal elastic baffle

A semi-analytic study on two-layered liquid sloshing in a horizontal excited two-dimensional rectangular tank with a horizontal elastic baffle was performed. The present work is a further development of the semi-analytical technique for solving the single-layer liquid sloshing problem. The horizontal elastic baffle was located in the lower liquid or upper liquid. First, the complex liquid domain in a baffled tank was divided into several simple sub-domains to solve the analytic solution. The wet mode of a horizontal baffle was presented according to the Eulerian Bernoulli beam. The continuity boundary condition on the interfaces between two liquids and the virtual interfaces was given. Then, the formal solution was derived for each sub-domain and a horizontal baffle using the superposition principle and the method of separation of variables. Then, the total velocity potential subject to lateral excitation was summed over the container potential function and the liquid disturbance potential. The dynamic response equation for two-layered liquid sloshing was established. Multiple methods verified the semi-analytic solution's correctness and agreed well with other methods. Finally, the numerical analysis mainly shows that the density ratio becomes more significant for the coupled frequency when the baffle is in the upper liquid. A large baffle's width suppresses the liquid flow in the baffled tank effectively. Furthermore, adjusting the baffle and the layered liquid parameters can significantly suppress layered liquid sloshing. For the seismic response, the elevation energy is mainly located after 2.5 s.

Semi-analytical method for liquid sloshing in the rigid super-elliptical tank with the ring baffle

Tanks with super-elliptical cross-sections can improve space utilization. The effect of the submerged ring baffle on liquid sloshing in the tank is studied. The semi-analytical method is developed to solve the three-dimensional (3D) sloshing problem in the baffled non-axisymmetric tank, using linear potential theory by dividing the liquid domain into sub-domains. The formal solutions are obtained analytically for the 3D non-axisymmetric sub-domains with arbitrary cross-sections, allowing for the determination of natural frequencies and modes by substituting the formal solutions into the linearized free surface condition, the boundary conditions on the baffle and tank wall and the continuity conditions at the interfaces of the interconnecting sub-domains. The dynamic response equation is derived using the mode superposition method with the damping term for swaying excitation. The obtained solution is validated by comparing it with a numerical model, demonstrating excellent accuracy and efficiency. Parametric studies are performed to determine the effect of the baffle on liquid sloshing, indicating that the baffle can considerably reduce the liquid sloshing when considering an optimal baffle position and width. This technique can be extended to investigate the sloshing reduction in vertical containers with arbitrary cross-sections.

Vibration isolation of row of piles due to moving harmonic loads embedded in the layered isotropic saturated medium

AbstractThis paper develops an analytical layer element‐boundary element coupling method to study the vibration isolation effect of pile rows in multi‐layered isotropic saturated soils subjected to a moving harmonic load. The isotropic saturated soil is represented using an analytical layer‐element solution as a kernel function, and the pile‐soil boundary integral equation is applied to obtain the soil flexibility matrices. The finite difference method is used for the piles modeled as a Bernoulli–Euler beam. The dynamic response equations of the pile rows under a harmonic moving load are achieved by considering pile‐soil displacement coordination condition. Then, the displacements of the observation point with and without the pile effect are calculated, respectively. Several numerical examples are presented to examine the influences of the soils’ stratification characteristics, the pile length, pile spacing, pile‐soil Young's modulus ratio, and the load moving speed on the isolation effect of the pile rows.

Modal analysis and harmonic response analysis of energy-absorbing and anti-scouring columns

Many field observations have found that damage to the support did not increase with the magnitude of the impact ground pressure. To enhance the impact protection performance of “support and surrounding rock” system. From the perspective of preventing the resonance of the “support and surrounding rock” system, the dynamic response of energy-absorbing and anti-scouring column is studied. Using the block theory, a dynamic model of the roadway enclosure-absorbing anti-scouring column under impact loading was established, and the dynamic response equation of the rock block at the support end was obtained. Based on the structural dynamics and Love shell theory, the characteristic equations of the energy-absorbing and anti-scouring column were derived, and the theoretical equations for the natural frequency and vibration mode function of the energy-absorbing and anti-scouring column were obtained. The ABAQUS numerical simulation method was used to carry out pre-stress modal analysis and harmonious response analysis of energy-absorbing and anti-scouring columns and conventional columns. We obtained the natural frequencies and vibration modes of the two columns and analyzed the effect of the setting load on the modalities of the columns. The column dynamic response law was determined by monitoring the displacement and velocity response curves at different positions. The results show that the natural frequency and vibration mode of the energy-absorbing and anti-scouring column are related to the density, elastic modulus, and length. The vibration of the energy-absorbing and anti-scouring column has two forms: beam vibration mode and cylindrical shell vibration mode, and the first four orders of vibration mode are transverse bend. The setting load has a small effect on the natural frequency and vibration mode of both types of columns, where the natural frequency decreases as the setting load increases. When the excitation frequency is close to the vibration frequency of the surrounding rock, the radial, axial, and circumferential response amplitudes of the primary and secondary columns of the energy-absorbing and anti-scouring column are the largest. Reinforcement and strengthening measures should be implemented to reduce the column deformation amplitude.

A fast semi-analytic solution of liquid sloshing in a 2-D tank with dual elastic vertical baffles and walls

Liquid sloshing characteristics in a lateral excited two-dimensional (2-D) rectangular tank with dual elastic vertical baffles and walls have been investigated analytically. The elastic baffle or wall is regarded as an Eulerian Bernoulli beam. The complex liquid domain divides into six simple sub-domains according to the superposition principle. The formal solution of the potential function in each sub-domain is obtained using the separation of variables method. Then the formal baffle or wall deflection solution can be derived from the transverse vibration equation. The Eigen equation can be established according to the free surface, interface, and coupled vibration conditions. The coupled frequency can be obtained by solving the Eigen equation. The velocity potential under lateral excitation consists of the rigid container velocity potential and the disturbance potential. Then the coupled dynamic response equation is established using the free liquid surface equation and the coupled vibration equation. The correctness of the semi-analytic solution is verified against available data. Therefore, the numerical model of the present work can be computed quickly with semi-analytic solution and obtain the mechanism of liquid-structure interaction. Finally, the effect of baffle parameters and excitation frequency on liquid sloshing is discussed in detail.

Virtual inertia control based on fast frequency response

In order to improve the inertia support of wind power system in case of load disturbance events, a control frequency response method based on Hammerstein-Neural Network (HNNFC) is proposed in this paper. First, the sliding mode control (SMC) law is designed according to the system frequency dynamic response equation. Then, the system is identified based -Hammerstein-Neural Network (HNN). Moreover, the system disturbance is designed of the ESO which is used as the compensator of the Hammerstein model to improve the fast and stable recovery performance of the system. Finally, the simulation results show that this method can not only release the active power through the rotor kinetic energy, but also improve the system stability recovery ability. The simulation can be seen that the proposed method can well reproduce the original control method. Compared with traditional control methods, the proposed method can improve the robustness ability of the wind power system.

Failure Patterns of Transmission Tower-Line System Caused by Landslide Events

A transmission tower-line system consists of many towers and cables, which is a long-span structure. Due to topographical restrictions, the structure inevitably passes through wide areas prone to landslide hazards. The landslide causes the failure of the tower foundation and threatens the safety of the power transmission system. Therefore, the aim of this study was to investigate the collapse patterns of a transmission tower-line structure under landslides. The explicit analysis method was used to deal with the nonlinear dynamic response equations of the structure. To prove the effect of the landslides on the collapse patterns of the transmission tower-line structure, two foundation failure cases (Case 1 and Case 2) under landslides were considered. For each case, the displacement responses at tower tops and the progressive collapse behavior were analyzed, which illustrate that the failure patterns of the tower-line structure under landslides are dominated by two factors, i.e., the failure mode of the tower foundation and the pulling effect of cables. The overall tilting and hinge formation in the middle of the tower body are the main collapse patterns of the structure under Case 1 and Case 2, respectively. In addition, because of the pulling of cables, the collapse of one tower induced by the landslides always triggers the local failure of neighboring tower heads.

Analysis of random wind-induced response of isolation structure with viscoelastic damper and TMD

The analysis method of wind vibration response of the seismically isolated structure with viscoelastic damper and tuned mass damper(TMD) under Davenport wind load was studied systematically. Firstly, using the general integral models of viscoelastic dampers to establish the exact dynamic integral-differential response equations in original structural space for isolated structure with general linear viscoelastic damper and TMD. Then, adopting the transfer function method to obtain the exact non-orthogonal modal superposition solution in original structural space for the displacement response standard deviation and the equivalent wind force transient response in the time domain of the isolated structure with viscoelastic damper and TMD under wind loading. These exact solutions can accurately discover the vibration properties of viscoelastic dissipative structures. That is, the dissipative structural modes are not orthogonal, the dynamic equations cannot be decoupled with the structural modes, while transient structural response can be accurately represented as an individual superposition of modal responses. The analysis of the calculation example showed that the isolated structure with viscoelastic damper and TMD can more effectively reduce the actual values of wind-induced displacement response standard deviation, equivalent wind vibration force and design value of equivalent wind. Since the results obtained in this paper are exact solutions, it can provide a theoretical basis for the design of the structures with viscoelastic damper and TMD, the optimization of damper and TMD parameters.

A Semi-Analytical Solution of Liquid Response in a Two-Dimensional Rectangular Tank with a Vertical Rigid Baffle Under Pitching Excitation

The present work uses a semi-analytic mathematical model to study the dynamic response of the partially liquid-filled rectangular tank equipped with a vertical rigid baffle at the bottom subjected to pitching excitation. The velocity potential consists of the rigid container velocity potential and the disturbance potential, which contains a Stokes–Joukowski potential. The liquid domain is divided into four simple sub-domains. The formal solution of the Stokes–Joukowski potential in each sub-domain is solved using the superposition principle and the separation of variables method. The dynamic response equation is established by using the free liquid surface equation. The ADINA solution is compared with the present method solution, which verifies the correctness of the proposed method. Finally, the effect of baffle parameters on liquid sloshing for a baffled tank subjected to harmonic and seismic pitching excitations is discussed in detail.

Analysis of Energy Accumulation and Dispersion Evolution of a Thick Hard Roof and Dynamic Load Response of the Hydraulic Support in a Large Space Stope

Aiming at the mining disaster of a thick hard roof, based on the analysis of the mining instability influence of the thick hard roof, this study constructs the mining bearing mechanical model of the thick hard roof by using mechanical theory and obtains the mechanical distribution equation of mining bearing and energy accumulation, the mining instability energy release equation, and the dynamic load response equation of a hydraulic support in the working face, as well as the dynamic load response characteristics of the hydraulic support in the working face, putting forward the technical countermeasures for the strong dynamic pressure control of the thick hard roof in the working face. This research shows that 1) the larger the overburden load and suspension span of the thick hard roof, the more serious the mining bearing state and energy accumulation evolution; the greater the rock thickness and elastic modulus of the thick hard roof, the greater the flexural stiffness of the roof, resulting in the increase of the roof mining limit breaking span, which indirectly aggravates the mining bearing state and self-energy accumulation evolution; 2) the dynamic support resistance of the hydraulic support is composed of the dynamic support resistance caused by the release of elastic energy accumulated by mining of the thick hard roof, the work done by the overlying load, and the static support resistance caused by the direct roof gravity; 3) the dynamic support resistance caused by the work of the overlying load accounts for the highest proportion, followed by the dynamic support resistance caused by the release of mining elastic energy by the thick hard roof; the cause of mining instability and the strong dynamic pressure of the thick hard roof lie in the large span of the mining suspended roof, and the large-scale mining suspension structure of the thick hard roof leads to a high overlying load and large accumulated energy; and 4) the mining instability of the thick hard roof leads to a strong dynamic load response of the hydraulic support; adopting pre-splitting and roof cutting technology to reduce the breaking span of the thick hard roof and reducing the impact dynamic load caused by mining instability of the thick hard roof can effectively eliminate the potential safety hazard of overlimit bearing of the hydraulic support.

Dynamic analysis of soil-structure interaction shear model for beams on transversely isotropic viscoelastic soil

Dynamic response problem of the Timoshenko shear beam resting on the transversely isotropic viscoelastic foundation and subjected to a moving load is investigated. The extended Hamilton's principle is used to obtain the dynamic response equations of the beam-soil system. The corresponding partial differential equations are derived using variational principle. Using the analytical solutions, finite-element method, and central difference method, these differential equations are solved and mutually verified. The Newmark-β iterative algorithm is employed to decouple the dynamic equations of the beam-soil system. A modified two-parameter spring foundation model is used to simulate the dynamic characteristics of soil medium. Finite-element analysis demonstrates that the developed shear model of beam-soil is effective and accurate. Other numerical examples are carried out to analyze the effect of the shear beam, the load speed, and transverse isotropy of the dynamic medium model.

A mathematical model of the room temperature dynamic response in multi-zone buildings

There are many factors that affect the change of room temperature, especially outdoor environmental factors, which makes it difficult to establish a model to describe the dynamic changes of the real time room temperature. In response to this problem, this study proposes a RC network two-node wall structure method to describe and analyze the heat conduction process of the building envelope. With this method, we first divide building envelope such as walls and floors into two-story structures, and then use energy balance theory to establish the energy balance equation of each node. Finally, we obtained the dynamic response equations of room temperature and humidity in each room of the whole building. This method simplifies the complex heat transfer process of the building envelope to a simple mathematical problem. The experimental validation indicated the accuracy of the proposed model.