Dynamic Response In Time Domain Research Articles

Research on dynamic responses of mooring line system of semi-submersible platforms in Vietnam sea conditions using random model

Recently, due to the nearshore oil fields in Vietnam were nearly exhausted, oil and gas extraction proceeds to deeper water areas using the mooring floating offshore structures. Therefore, the durability of the mooring system in deep water should be studied through determining the dynamic tension of the mooring line system using random wave models. However, full stochastic dynamics analysis for mooring line system takes up a lot of time and requires large computing resources. This paper is going to study the hydrodynamic interaction of random waves onto a semi-submersible platform, thereby analysing the dynamic responses in time domain of the mooring system using the “time window” method to optimize computational time and computing resources. This method performs the dynamic simulations around the maximum quasi-dynamic tension values to determine the dynamic tension and the dynamic amplification factor (DAF) of a maximum load-bearing mooring line, thereby evaluating the dynamic responses for the whole mooring system. The method is applied to calculate for a semi-submersible platform in Dai Hung field in Vietnam Sea.

Simulation of transient dynamic response of a locomotive considering its flexibility and rigidity

Time-domain or transient dynamic response method is the most traditional method used to evaluate the dynamic response of a vibratory system subjected to deterministic inputs. The inertia or damping effects are very crucial in the time scale of loading. The present work determines the time domain analysis of railway locomotive using finite element analysis for Indian tracks. The track inputs are modelled as an ellipsoidal bump, and variations in displacement at different key locations of the truck and carbody models are plotted subjected to standard loading conditions. The response plot of the front and rear locations of the locomotive truck and carbody indicate that these regions are more responsive to wheel inputs in comparison to the mid portion due to unbalanced mass distribution. In the further study vertical-lateral random inputs are measured through track recording car and modelled to express in the form of PSD. These random inputs are provided to finite element modelled flexible bogie frame, and acceleration response is determined. The results obtained are compared with the same obtained from rigid bogie frame formulated using an analytical model. The results obtained from the flexible and rigid body models are found to be in good agreement.

Dynamic Characterization of Optical Coherence-Based Displacement-Type Weight Sensor

Dynamic characteristics play a crucial role in evaluating the performance of weight sensors and are essential for achieving fast and accurate weight measurements. This study focuses on a weight sensor based on optical coherence displacement. Using finite element analysis, the sensor was numerically simulated. Frequency domain and time domain dynamic response characteristics were explored through harmonic response analysis and transient dynamic analysis. The superior dynamic performance and reduced conditioning time of the non-contact optical coherence-based displacement weight sensor were confirmed via a negative step response experiment that compared the proposed sensing method to strain sensing. Moreover, dynamic performance metrics for the optical coherence displacement-type weight sensor were determined. Ultimately, the sensor’s dynamic performance was enhanced using the pole-zero placement method, decreasing the overshoot to 4.72% and reducing the response time to 0.0132 s. These enhancements broaden the sensor’s operational bandwidth and amplify its dynamic response capabilities.

Complex mode superposition method of non-classically damped systems based on hysteretic damping model with frequency-dependent loss factors

For non-classically damped systems, it is easy to construct a damping matrix based on a hysteretic damping model. However, the damped natural frequency is non-physical, and the frequency response function is non-causal. These two drawbacks can be overcome by the hysteretic damping model with frequency-dependent loss factors. In this paper, a complex mode superposition method for non-classically damped systems based on the hysteretic damping model with frequency-dependent loss factors is proposed. Frequency-dependent loss factors of the natural frequencies are considered in the transient vibration response, while frequency-dependent loss factors of the external excitation frequencies are considered in the steady state vibration response. By decoupling complex modes in state space and physical space, non-proportional damping characteristics of hybrid structures can be effectively considered. Therefore, the proposed method can be used to calculate the time-domain dynamic responses of hybrid structures, whose loss factors are sensitive to frequency variation and have strong non-proportional damping characteristics. The time-domain dynamic responses of numerical examples are compared based on different mode superposition methods. Shaking table tests are performed on cantilever plates with different damping characteristics. The numerical and test results validate the proposed method. Moreover, the proposed method has a wide range of applications.

Reduced Order Modeling of Dynamic Mechanical Metamaterials for Analysis of Infinite and Finite Systems

Abstract Dynamic mechanical metamaterials (MMs) are artificial media composed of periodic micro-structures, designed to manipulate wave propagation. Modeling and designing MMs can be computationally demanding due to the broad design space spanned by the geometric and material parameters. This work aims to develop a generalized reduced order modeling approach for determining MM dynamics in low frequency ranges with accuracy and speed, using a limited number of parameters and small matrices. The MM unit cells are treated as assemblies of structural elements with discrete degrees-of-freedom, whose effective stiffness and inertia are determined by optimizing energy criteria based on continuum results derived from a small number of eigen-study simulations. This proposed approach offers a parameterized and discretized representation of MM systems, which leads to fast and accurate computation of eigen-study results for periodic arrays, as well as dynamic responses in time domain for finite-sized arrays. The high computational efficiency and physical accuracy of this method will help streamline the modeling process and aid in design discovery and optimization, especially in combination with machine learning and data-driven techniques.

Efficient Power Management and Control Strategy of Hybrid Renewable Energy System in Microgrid

Currently, the use of renewable energy has gradually increased due to the environmental problems present nowadays. The intermittency of distributed renewable generation poses significant challenges for the operation and integration of microgrids. Unlike the main power grid, where load balancing resources, in general, are abundant, the balancing of generation and load in a microgrid must be done by small gas turbines, diesel generators, or energy storage devices with very limited capacity and at much higher costs. Consequently, the proposed methodology seeks a model for minimizing the Energy Cost (EC) and enhancing the power supply for rural areas by designing and analyzing four different hybrid system configurations based on integrating a biomass system with a photovoltaic (PV), wind turbine (WT) and battery system. To ensure the desired power demand with minimum production cost, the research proposed an energy-efficient Hybrid DC/AC microgrid using four renewable energy sources. Lithium-ion batteries were chosen for this study due to their high energy density, long life cycle, and high efficiency. The existence of both AC and DC microgrids has led to a new concept of hybrid AC/DC microgrids which consists of both AC and DC grids tied by an Interlinking Converter (ILC). It comprises a DC grid and AC grid interlinked by a bidirectional DC/AC converter. Such a hybrid AC/DC microgrid has the advantages of both AC and DC with increased efficiency and less cost. To provide higher voltages, the Multi-Input Booster (MIB) DC-DC converters are used as a power converter in between load and source to enforce and increase the PV depending on the voltage output signal. Further extract maximum power from the solar PV system, perturb and observe algorithm-based power point tracking control mechanism is proposed DC link voltage of ILC is regulated usually by DC side control in load sharing among sources in the DC microgrid. In addition, to overcome the load fluctuation problem in a microgrid, the research introduced a Mamdani type 2 PID-fuzzy controller. Performance index parameters of the transient response characteristics are also improved by using the proposed control approach. The time-domain dynamic responses reveal that the proposed type-II fuzzy PID controller can balance the power generation and demand properly and control both system frequency and tie-line power effectively.

Vibration Suppression on the Composite Laminated Plates Subjected to Aerodynamic and Harmonic Excitations Based on the Nonlinear Piezoelectric Shunt Damping

This paper proposes a nonlinear piezoelectric shunt damping circuit to mitigate the vibration of the plate structures subjected to the aerodynamic and harmonic excitations. The nonlinear piezoelectric shunt damping circuit consisting of the piezoelectric patch, inductor, resistor, negative capacitor and nonlinear capacitor is considered. Firstly, the governing equations of the electro-mechanical coupling nonlinear system are formulated based on the energy method and modified Ritz method. Furthermore, the complexification-averaging method combined with pseudo arc-length continuation method is adopted to analyze the steady-state response of the coupled system with aerodynamic and harmonic forces. A considerable number of numerical cases are performed to validate the proposed model and the time domain and frequency domain dynamic responses of the plate structures with and without control are further compared to validate the effectiveness of the proposed control strategy. Meanwhile, the energy transfer analysis between the plate structure and external piezoelectric shunt damping circuit is investigated. Finally, the effects of key parameters of the nonlinear piezoelectric shunt damping circuit including the negative capacitance and nonlinear capacitance on the vibration suppression performance of the piezoelectric shunt damping are discussed.

Improved pseudo-force approach for Monte Carlo Simulation of non-linear fractional oscillators under stochastic excitation

This paper presents a step-by-step procedure for the numerical integration of the fractional differential equation governing the response of single-degree-of-freedom (SDOF) non-linear systems endowed with fractional derivatives subjected to stochastic excitation. The procedure, labeled improved pseudo-force method (IPFM), is developed by extending a step-by-step integration scheme proposed by the second author for the numerical solution of classical differential equations. The IPFM relies on the following main steps: i) to use the Grünwald–Letnikov (GL) approximation of the fractional derivative; ii) to treat terms depending on the unknown values of the response, which result from the GL approximation as well as from the non-linear restoring forces, as pseudo-forces; iii) to handle non-linearities by performing iterations at each time step. The IPFM provides accurate solutions by using time steps of larger size compared to classical step-by-step integration schemes. In this paper, the IPFM is applied within the framework of classical Monte Carlo Simulation (MCS) to evaluate the time domain dynamic response of non-linear fractional systems subjected to the generic sample of a stochastic excitation.

Magnetic susceptibility and response time of isotropic and structured magnetorheological elastomers

The response time of magnetorheological elastomers (MREs) depends on the complex interplay of multiple factors. In this study we investigate the response times of silicone rubber based elastomers containing magnetically soft fillers (iron and magnetite) with isotropic, and two types of anisotropic particle structures. The response times of the elastomers were extracted as the characteristic time constant from the time domain dynamic susceptibility response to ramp excitation in the weak field limit ( H< 10 kAm−1). The MREs with both types of filler materials in all particle configurations showed a positive susceptibility response, while an inverse proportionality was observed between the response times and the slope of the ramp excitation in all cases. The dynamics of the structural change is found to be highly sensitive to the type of the filler material, and the anisotropy of the microstructure. The response times of the iron loaded MREs varied from (4.0 ± 0.3) ms up to (60.5 ± 2.3) ms. The magnetite loaded MREs displayed faster response (between (1.2 ± 0.1) ms and (12.1 ± 1.8) ms), which is attributed to the cross-linking inhibitor effect of the magnetite particles. The anisotropic particle structure also favors a decreased response time, however the remanence of the particles can modify the structural effect.

Dynamic response of the half-space subjected to a moving point load and thermal stress

Dynamic transient response of the half-space subjected to a moving point load and thermal stress is investigated analytically in this study. By employing the Helmholtz decomposition and introducing a moving coordinate system, the corresponding modified partial differential equations of motion for the transient waves in the half-space are firstly obtained. With one-side and two-side Laplace transformation over the new time and space variables, the second-order partial differential equations of motion in the modified system are then simplified as the ordinary differential equations, whose solutions are thereafter obtained when the boundary condition is satisfied. To get the dynamic response in time domain, the analytical solutions in Laplace domain are inverted using the Cagniard-de Hoop method. Some examples are evaluated and discussed in details for the purpose of examining the effect of the moving load and thermal stress on the transient response of the half-space.

Vibration-Based Fault Diagnosis of Helical Gear Pair With Tooth Surface Wear Considering Time-Varying Friction Coefficient Under Mixed Elastohydrodynamic Lubrication Condition

Abstract Based on “slice method,” the improved time-varying mesh stiffness (TVMS) calculation model of helical gear pair with tooth surface wear is proposed, in which the effect of friction force that obtained under mixed elastohydrodynamic lubrication (EHL) is considered in the model. Based on the improved TVMS calculation model, the dynamic model of helical gear system is established, then the influence of tooth wear parameters on the dynamic response is studied. The results illustrate that the varying reduction extents of mesh stiffness along tooth profile under tooth surface wear, in addition, the dynamic response in time-domain and frequency-domain present significant decline in amplitude under deteriorating wear condition.

Analysis of longitudinal coupling dynamic characteristics of deep sea mining vessel and stepped lifting pipe

In deep-sea mining, the coupling dynamic response between the mining vessel and the lifting pipe is a significant problem, which directly affects the structural design of the lifting system and the safety of field operation. The characteristics of coupled motion model have not been fully considered in the existing research. Therefore, this paper uses time-domain coupled numerical model as the research object, considering ocean current, surface wave, pipe dynamics and vessel-pipe contact mechanics, to study the dynamic behavior of the lifting pipe and mining vessel during the process of deep-sea mining using AQWA and OrcaFlex softwares. The response amplitude operator (RAO) is used to compare the measured and simulations dynamic response of the mining vessel. There is a very good agreement in RAO between the experiments and simulations. The coupling simulation results show that the coupling effect has a significant effect on the time domain dynamic response of the lifting pipe, but has little effect on the average effective tension and longitudinal amplitude along the pipe length. The research results of this paper are of great significance to the safety design of deep-sea mining lifting system and the planning of deep-sea operation activities.

An efficient numerical method for dynamic analysis of polygonal plate under moving loads

Plate structures under moving loads are frequently encountered in practical engineering. Over the past decades, the moving-load models for plates are mainly developed for rectangular plates. In this study, an efficient numerical method is developed for triangular and quadrilateral plates, which are the two most representative polygonal plates and also the basic elements to form general polygon plates. To avoid the mismatch between the moving load and nodes that encountered in Finite Element Method (FEM), the entire domain of the plate is firstly mapped into a square domain using the isoparametric shape functions. The domain decomposition method is also introduced to handle the general polygon shaped plates, whereas the penalty function method is adopted to handle arbitrary boundary conditions. The first-order shear deformation theory (FSDT) is used to describe the elastic deflection of the plates, and then the deformation fields in the mapped domain are spatially discretized by using Chebyshev polynomials of the first kind (CPOFK). Afterwards, the governing equations of motion is derived using Lagrange’s equation, in which the inertia force, Coriolis force and centrifugal force due to the interactions between the moving load and supporting plates are taken into account simultaneously. The mode reduction method is employed to reduce the dimension of dynamic equations, and then the first-order generalized-α method is used to solve the dynamic response in time domain. Finally, the correctness and efficiency of the presented method are validated from convergence analysis and comparisons.

Benchmarking Optimisation Methods for Model Selection and Parameter Estimation of Nonlinear Systems

Characterisation and quantification of nonlinearities in the engineering structures include selecting and fitting a good mathematical model to a set of experimental vibration data with significant nonlinear features. These tasks involve solving an optimisation problem where it is difficult to choose a priori the best optimisation technique. This paper presents a systematic comparison of ten optimisation methods used to select the best nonlinear model and estimate its parameters through nonlinear system identification. The model selection framework fits the structure’s equation of motions using time-domain dynamic response data and takes into account couplings due to the presence of the nonlinearities. Three benchmark problems are used to evaluate the performance of two families of optimisation methods: (i) deterministic local searches and (ii) global optimisation metaheuristics. Furthermore, hybrid local–global optimisation methods are examined. All benchmark problems include a free play nonlinearity commonly found in mechanical structures. Multiple performance criteria are considered based on computational efficiency and robustness, that is, finding the best nonlinear model. Results show that hybrid methods, that is, the multi-start strategy with local gradient-based Levenberg–Marquardt method and the particle swarm with Levenberg–Marquardt method, lead to a successful selection of nonlinear models and an accurate estimation of their parameters within acceptable computational times.

Time-Domain Dynamic Modeling and Analysis of Complex Heavy-Duty Gearbox Considering Floating Effect

Expert insights into the time-domain dynamic behavior of heavy-duty gearboxes form the foundations of design evaluation and improvement. However, in the existing lateral–torsional coupling (LTC) modeling method for gearboxes that is normally used for frequency-domain dynamic behavior, the meshing forces are modeled as spring dampers with fixed acting points on the meshing gears to simulate only the transient LTC effect, and thus the steady state characteristic in the time domain cannot be obtained due to the unrealistic distortion of positions and orientations as the gear angles increase. In this paper, a novel and generally applicable LTC modeling method for heavy-duty gearboxes, mainly planetary gear sets with floating components, is proposed by using space-fixed spring dampers with floating acting points on the meshing gears to study the time-domain dynamic response and to support the dynamic design of heavy-duty gearboxes. Based on the proposed method, a LTC model of a 2 megawatt (MW) wind turbine gearbox with floating components considering the time-varying meshing stiffness, bearing stiffness, torsional stiffness, and floating effect was established. The simulated results of representative components were in accordance with experimental results on a test rig, and dynamic behavior was calculated.

Three-Dimensional Aeroelastic Model for Successive Analyses of High-Aspect-Ratio Wings

Abstract Next-generation civil aircraft and atmospheric satellites will have high-aspect-ratio wings. Such a design necessitates successive analysis of static, frequency, and time-domain dynamic responses based on a three-dimensional nonlinear beam model. In this study, a new successive-analysis framework based on an absolute nodal coordinate formulation with mean artificial strains (ANCF-MAS) is developed. While retaining the advantages of other three-dimensional (3D) ANCF approaches, such as constancy of the mass matrix and absence of velocity-dependent terms, ANCF-MAS uses the elastic force of the mean artificial strains to remove cross-sectional deformations that cause locking problems. The equation becomes a differential equation with an easily linearized elastic force that enables not only static and dynamic analyses but also frequency analysis using standard eigenvalue solvers. The solutions converge to the analytical frequencies without suffering from locking problems. A proposed successive-analysis method with model-order reduction reveals that the frequencies vary with the nonlinear static deformation because of the 3D deformation coupling. This reduced-order model agrees well with nonlinear models even when the wing experiences a large nonlinear dynamic deformation.

Blasting induced dynamic response analysis in a rock tunnel based on combined inversion of Laplace transform with elasto-plastic cellular automaton

SUMMARY The dynamic disturbance from explosion, earthquakes and stress impact may induce rock mass damage around the deep-buried tunnel. Here, we show the dynamic responses triggered by blasting load disturbance. In this paper, the theoretical formulae are first derived to evaluate the time-domain dynamic responses based on the wave function expansion method and the inversion of Laplace transform and then a self-developed numerical code, that is, elasto-plastic cellular automaton (EPCA), a module of CASRock, is subsequently employed to simulate the blasting induced elasto-plastic dynamic responses. It can be found from the analytical solutions that tensile stress concentration at two sidewalls occurs, while compressive counterpart at the roof and floor appears. Moreover, the radial velocity vibrations generate concentration at the two sidewalls, while the circumferential counterparts appear at the roof and floor. The numerical simulations indicate that compression-shear and tensile failure are the major mechanism for the rock mass damage around the rock tunnel. The analytical and numerical results help to understand the velocity vibrations and the major mechanism of rock mass damage and provide theoretical basis for the support of rock tunnel.

Risk‐based many‐objective configuration of power system fault current limiters utilising NSGA‐III

The fault current limiter (FCL) has been envisaged as a feasible solution to defend against out-of-range short-circuit currents (SCCs) in power systems. However, the existing studies mainly sited and sized FCLs under deterministic fault scenarios. Moreover, the influences of FCLs on power systems are complex including dynamic aspects, which makes it extremely difficult to configure FCLs optimally. This paper proposes a risk-based many-objective FCL configuration framework. Specifically, a data-driven Proportional Hazard Model (PHM) is developed to evaluate the nodal long-term short-circuit probability considering equipment aging, weather statistics, and surrounding conditions. The risks in terms of out-of-range SCC, abnormal voltage sag, and transient instability are formulated as the objective functions of the FCL configuration model, as well as the overall FCL investment. The time-domain dynamic response process of FCLs is considered in both the SCC limiting and the transient stability simulation process, mainly in the form of a time-varying resistance. The state-of-the-art NSGA-III is deployed to search the Pareto-optimal FCL configuration solutions of the established many-objective FCL configuration problem. The numerical results verify that the risk-based model configures FCLs more economically with a 7.5% decrease of average FCL investment compared with the deterministic model.

Combining FDTD and coupled-mode theory for self-pulsing modeling in coupled nonlinear microring resonators

By means of finite-difference time-domain (FDTD) simulations, the stationary and dynamic responses of coupled optical microring resonators made with a material exhibiting an instantaneous Kerr nonlinearity are numerically investigated. We compare the results with the coupled-mode theory (CMT) and find good agreement. We demonstrate by integrating Maxwell’s equations that this system can show a self-pulsing operation in the normal dispersion regime. Finally, this work shows that FDTD simulations can be combined with a CMT analysis for the purpose of designing optical functions whose operation is based on nonlinear coupled micro-resonators.

Time-domain analysis for dynamic responses of non-classically damped composite structures

A complex mode superposition method based on equivalent viscous damping model (CEV) is proposed for time-domain dynamic responses of non-classically damped composite structures. The damping matrix of hysteretic non-classically damped composite structures can be easily obtained and complex mode superposition method based on hysteretic damping model is directly realized in the physical space. However, hysteretic damping model is not causal, and is only applied in frequency-domain analysis. By the aid of constitutive model of Kelvin-Voigt model, viscous damping model which is equivalent to the hysteretic damping model is obtained based on single degree of freedom system. Combined with complex mode superposition method of hysteretic damping model and mathematical simplicity of equivalent viscous damping model, CEV can be realized. Structural vibration responses of shaking table test under random excitations are measured, which are compared with the corresponding calculation results using CEV and traditional complex mode superposition method based on viscous damping model (CR), respectively. The calculation results obtained by the two complex mode superposition methods are consistent with the test results. Compared with CR, the calculation results of CEV are unique, computationalefficiency of CEV is higher and the problem of choosing reasonable modes has been avoided.