Weak Damping Research Articles

Observation of Standing Slow Magneto-acoustic Waves in a Flaring Active Region Corona Loop

Intensity fluctuations are frequently observed in different regions and structures of the solar corona. These fluctuations may be caused by magneto-hydrodynamic (MHD) waves in coronal plasma. MHD waves are prime candidates for the dynamics, energy transfer, and anomalous temperature of the solar corona. In this paper, analysis is conducted on intensity and temperature fluctuations along the active region coronal loop (NOAA AR 13599) near solar flares. The intensity and temperature as functions of time and distance along the loop are extracted using images captured by the Atmospheric Imaging Assembly (AIA) instrument onboard the Solar Dynamics Observatory (SDO) space telescope. To observe and comprehend the causes of intensity and temperature fluctuations, after conducting initial processing, and applying spatial and temporal frequency filters to data, enhanced distance-time maps of these variables are drawn. The space-time maps of intensities show standing oscillations at wavelengths of 171, 193, and 211 Å with greater precision and clarity than earlier findings. The amplitude of these standing oscillations (waves) decreases and increases over time. The average values of the oscillation period, damping time, damping quality, projected wavelength, and projected phase speed of standing intensity oscillations are in the range of 15–18 minutes, 24–31 minutes, 1.46″–2″, 132″–134″, and 81–100 km s−1, respectively. Also, the differential emission measure peak temperature values along the loop are found in the range of 0.51–3.98 MK, using six AIA passbands, including 94, 131, 171, 193, 211, and 335 Å. Based on the values of oscillation periods, phase speeds, damping time, and damping quality, it is inferred that the fluctuations in intensity are related to standing slow magneto-acoustic waves with weak damping.

Voltage stability control strategy for DC microgrid based on adaptive virtual DC motor

The large-scale integration of distributed energy sources and power electronic devices results in the DC microgrid exhibiting significant low inertia and weak damping characteristics. This, in turn, leads to inevitable fluctuations in the DC bus voltage, which endanger the stable operation of the DC system. Energy storage devices can provide equivalent inertia. To enhance the inertia and response speed of the DC bus interface converter, this paper proposes a power allocation parameter adaptive virtual DC motor control strategy based on a hybrid energy storage unit. The strategy introduces power allocation control to regulate the energy storage converter on the basis of virtual inertia parameter adaptive control, thereby enabling the energy storage converter to simulate the inertia and damping characteristics of a DC generator. The small-signal stability of the system is analyzed by establishing a small-signal model of the photovoltaic energy storage system and utilizing the impedance ratio criterion. Finally, the proposed control strategy is validated through simulation. The results demonstrate that the strategy effectively mitigates the fluctuations in bus voltage under varying photovoltaic power and sudden load changes, ensures the power distribution in the hybrid energy storage system, and enhances the dynamic response of the system.

Capsize criteria in beam seas: Melnikov analysis vs. safe basin erosion

We study the problem of capsizing of a rolling ship in harmonic and random beam seas, by means of the Melnikov method and safe basin calculations. In the random excitation case, we consider an integro-differential Cummins-type model equation that takes into account the hydrodynamic memory. The non-linear restoring moment is modeled by a high-order polynomial and the Melnikov criteria are evaluated numerically. We also examine a variant of the classical Melnikov method in which the damping terms are incorporated into the unperturbed system and the perturbation takes a modified form. We compare the theoretical predictions with direct (Monte-Carlo) simulations of the safe basins for two existing ships. In the random excitation case, we quantify the erosion by means of a mean integrity index. For weak damping, the classical and modified Melnikov curves coincide and are in good agreement with the onset of the safe basin erosion. As damping increases the Melnikov curves become less and less conservative with respect to the onset of erosion. Finally, the potential of the Melnikov method to provide a ship classification tool is discussed.

Optimized coordinated control method with virtual inertia based on fractional impedance model for charging stations

Due to the EV (Electric Vehicles) charging stations are characterized by weak damping and low inertia, the EV with a high degree of uncertainty can easily have an impact on the stability of the charging station system. Therefore, this paper proposes an optimization control method to improve the system inertia effect based on the fractional order impedance model of the charging station. This paper presents a study on establishing a fractional impedance model for charging stations, using the deviation between theoretical impedance spectra and actual measurements as a criterion. The goal is to enhance system inertia and optimize the parameters of the fractional-order controller to improve the supporting capacity of the charging station system and enhance its dynamic response. Initially, considering the fractional characteristics of the EV load, a fractional impedance model of the charging station is established. The analysis demonstrates that the fractional-order capacitor provides inertia to the system, enhancing its inertia support capability. In addition, a virtual inertia control strategy based on fractional-order PID (FOPID) is designed. Finally, an improved particle swarm optimization algorithm is utilized to optimize the control parameters. Through experimental verification under different operating conditions, it has been demonstrated that the fractional-order control strategy can achieve a dynamic response time of approximately 0.025s and limit the voltage deviation within 5%. Furthermore, the rotational inertia can rapidly increase to the maximum value satisfying the objective function within 0.05s. The results indicate that this control method effectively suppresses the DC voltage and power oscillations in the distribution grid.

Modification of the transfer matrix method for the sonic black hole and broadening effective absorption band

Sonic black hole (SBH) is capable of the concentration for the sound energy by the shrinking duct and appropriate wall admittance. However, the concentrated energy cannot be dissipated due to the weak air damping. Meanwhile, when the inserted rings are insufficient, the accuracy of the conventional transfer matrix method (TMM) is less than satisfactory for the simulation of the original SBH. In this study we commit to modify this simulation method and broaden the effective absorption band by using porous materials. First, we derived the acoustic transfer relationship of the conical cavity and the acoustic admittance of the toroidal cavity, via formulating the basic equation. After combining with the two method, the modified TMM (MTMM) results show excellent agreement with the finite element results. The applicability of the derived wall admittance is analyzed in detail. The MTMM has also been applied to obtain the sound absorption of a SBH configuration with embedded porous materials (PMSBH). The proposed PMSBH can effectively dissipate the concentrated sound energy, leading to the ultra-low cut-on frequency of near-perfect absorption. Specifically, the cut-on frequency of the PMSBH is 387 Hz, with the corresponding wavelength being 8.8 times than the structural length. In addition, the parametric analysis shows the near independence of the absorption performance of the PMSBH on the damping loss, so that the PMSBH can achieve excellent absorption without adding other acoustic materials. These appealing characteristic could promote the application of the PMSBH in noise control.

Well‐posedness for a class of wave equations with nonlocal weak damping

Well‐posedness for a class of wave equations with nonlocal weak damping

Suspension Bridge Estimation Method using the Fokker-Planck Model

The failure of the suspension bridge has been known since the beginning of the bridge collapse. Most of these failures form the basis of current engineering knowledge. One of the factors of failure is human-made factors related to the calculation of the bridge estimate. This paper presents an indirect estimation method using numerical simulation using finite elements by analyzing the Fokker-Planck model when dynamic excitation is associated with bridge loads. The results show that the Fokker-Planck model's homogeneous form can take into account the solution for the bridge analysis approach. It leads to a stable state when giving mass variations to the model. The indirect estimation method using finite elements can estimate the cable tension with controllable weak damping. It can be concluded that the method in this study is more accurate and convenient for the application technique.

Large-scale vortex formation in three-dimensional rotating Rayleigh-Bénard convection

Numerical experiments are performed on three-dimensional thermal convection between parallel plates in a rotating system with a larger horizontal region than in previous studies. It is confirmed that a large-scale vortex (LSV) with positive vorticity (cyclonic) is formed over a significant part of the region and its horizontal size increases if the horizontal region is extended. The correlation analysis in the vertical direction shows that the small-scale motion has a typical structure of the baroclinic vortex of thermal convection in the rotating system, whereas the large-scale motion is a barotropic vortex that is not associated with thermal convection. A horizontal spectral analysis of the individual terms in the kinetic energy equation reveals that the nonlinear effect of the small-scale vortex motion caused by the buoyancy force induces a large-scale toroidal component, and that the LSV is maintained by the balance between the nonlinear effect and the viscous dissipation of the large-scale motion. The results of this analysis indicate the importance of kinetic energy damping mechanism for the appearance of LSVs. When weak damping operates at larger scales, it is expected that the maximum extent of the vortex appears even if the horizontal region is extended further. On the other hand, the emergence of LSVs will be prevented when strong enough damping is effective at larger scales.

Faulty feeder detection based on the fluctuation characteristics of inflection point dense area for DC distribution network

A flexible direct current (DC) distribution network based on modular multilevel converter (MMC), with the advantages of no phase change failure and fewer current conversion links. It has gradually become the development trend of future medium voltage distribution networks. However, when a single-pole ground fault occurs in the feeder, the converter's low inertia and weak damping characteristics lead to a fast-rising fault current with a high peak value, which is harmful to the system. In this paper, for the difficulty of accurately selecting the faulty feeder when a single-pole ground fault occurs in a radial DC distribution network, a detection method based on the zero-mode current within the inflection point dense area (IPDA) for the fluctuation characteristics of concave and convexity (FCCC) is proposed. Firstly, the zero-mode current of each feeder is processed using a low-pass filter to select the eigen-components; Then, taking second order derivatives of the eigen-components, and the IPDA is established, to find a period in micro measurement to achieve accurate direction correspondence with opposite directions; Again, the data within IPDA is normalized; the criterion is constructed by determining each feeder's FCCC. Finally, the simulation model is built by Power Systems Computer Aided Design to verify that the method can identify the faulty feeder in various situations. Compared with existing methods, the fault detection method proposed in this paper has good stability and can withstand large grounding resistances.

Dual Virtual Series–Parallel Emulation with Inertial Voltage Feedforward Controller for DC Microgrid

The impacts of nonlinearities from the I–V curve cause large oscillation and fluctuation occur in the PV attached DC voltage, BDC, load current, and solar current during low penetration of irradiance. PV system nonlinearities, weak damping, and lack of inertia causes lead to stability issues for DC microgrids. The stability of the system has been shifted to an unstable region during low penetration discussed for traditional controllers. In this paper, dual virtual series and parallel emulation with inertia feedforward controller have been introduced to mitigate fluctuations, initial DC notching, and damping issue for the DC microgrid system. This control method simulates the characteristics of the DC machine's robust and versatile method of DC/DC converter. The crossover frequency of the system has been reduced during low penetration with SPIEC which is not sufficient to prevent the oscillation and notching of the system. The system stability is enhanced through the proposed controller during low penetration analysed by pole-zero plots. During low penetration, the system pole has been shifted to a stable region towards the left side of the s-plane by the proposed controller to the traditional controller. The transient performance like oscillation, overshoot, and DC initial notching is resolved by the feed-forward current controller. However, the steady-state error is resolved by the voltage restoration controller. The proposed controller aims to enhance the power sharing among the energy storage and PV system under constant/variable loads. The oscillation, overshoot, and DC initial notching of the energy storage and PV have been discussed and made fast dynamic response by the proposed controller.

General stability of a triple layer beam with time-varying delay and weak internal damping

Analyzing a triple layer Rao–Nakra beam model which has time-dependent weight function and delay, weak internal damping, with thermal dissipation elements, is our focus. Heat conduction from Fourier’s law was adopted to regulate the thermal dissipation. It is known that when the three equations of the Rao–Nakra beam is directly and globally damped, an exponential stability is achieved. Weak internal damping leads to prolonged resonance, extended vibrational amplitudes and periods, as well as delayed energy dissipation. In this work we will rigorously demonstrate that despite weak internal damping and delay term in the bottom layer’s equation, we can obtain a general stability for the Rao–Nakra beam model. As a result, exponential and polynomial decay can be deduced as particular instances.

A method combining active control with passive regulation to enhance the vibration suppression capability of linear motor-driven aerostatic stage

The Linear Motor-Driven Aerostatic Stage (LMDAS) has been extensively applied in high-precision measuring instruments and precision equipment requiring exceptional velocity and acceleration performance. This is attributable to its low friction, high precision, and high dynamic performance. Nevertheless, the LMDAS is vulnerable to external disturbances due to weak damping of the aerostatic guideway's gas film. This weakness directly affects the positioning accuracy and dynamic characteristics of the system and results in its flutter. This paper proposed a method for improving the overall damping of the system and its ability to suppress vibrations by enhancing the damping of the driving direction via combining active control and passive regulation. The active control algorithm based on the active disturbance rejection controller and the passive regulation technology based on the linear motor were presented, respectively. Both numerical and experimental studies demonstrated that this approach was superior to the traditional PID controller, commonly employed in LMDAS, regarding steady-state performance, dynamic response, and vibration suppression. In particular, this method demonstrated a significant improvement in reducing the maximum vibration acceleration of the LMDAS in all three directions, achieving a 50 % reduction compared to the conventional PID controller.

Research on Sub-Synchronous-Oscillation Energy Analysis and Traceability Method Based on Refined Energy

At present, most studies use the direct method to analyze the oscillation problem of modern power systems. However, these studies often only simplify the external characteristics of the wind turbine and lack an in-depth understanding of its internal refined energy structure. In this paper, based on the direct-drive permanent magnetic synchronous generator’s detailed model (D-PMSG), combined with the dynamic energy of its port, layers of analysis are performed on the wind turbine’s internal connections, and a detailed model of the energy structure is created. Then, the interaction mechanism of each control link in the wind turbine is analyzed by combining the energy function of the wind turbine with the improved perturbation method. Finally, this paper constructs a sub-synchronous oscillation (SSO) scenario of weak damping and a forcing type and proves the accuracy and effectiveness of the traceability method based on the refined energy of D-PMSG. This traceability method based on refined energy is expected to provide a new solution to the stability problem caused by the integration of new energy.

Existence of polynomial attractor for a class of extensible beams with nonlocal weak damping and critical nonlinearity

The goal of this paper is to study the long time behavior of the extensible beams equation with the nonlocal weak damping . In the case of critical growth of the nonlinearity, the polynomial attractor which can quantitatively describe the attractive rate of attractors for the equation is studied. The work generalizes and improves previous results for the extensible beams equation.

Infinite time blow-up of solutions for a plate equation with weak damping and logarithmic nonlinearity

This paper considers a plate equation with weak damping and logarithmic nonlinearity, which can be used to model the deformations and internal forces of an elastic plate under external factors such as lateral loads. We prove the solution blows up at infinity with subcritical and critical initial energies. Moreover, we establish the infinite time blow-up result at arbitrarily high initial energy. These results complement earlier results in the literature.

Data-driven model reduction approach for active vibration control of cable-strut structures

The cable-strut structures have the features of low stiffness and weak damping, resulting in large vibration response under dynamic excitation. The vibration response of the cable-strut structures can be reduced by active control methods. However, many traditional active control methods need to build a state-space model (SSM) based on finite element model (FEM), and solving the active control force for the high-dimensional SSM is time-consuming. In this paper, the dynamic mode decomposition with control (DMDc) method is proposed to achieve a data-driven reduced-order SSM for active vibration control of cable-strut structures. This proposed method only uses the data of structural response and control force input to build reduced-order SSM and does not rely on the FEM. Linear quadratic regulator (LQR) design using the DMDc-based reduced-order SSM (DMDc-LQR) is more computationally efficient than that using the FEM-based SSM (FEM-LQR). The relationship between the design parameters of the DMDc-LQR controller and the FEM-LQR controller is established, which ensures that the control performance indexes of the DMDc-LQR controller and the FEM-LQR controller are equal. The effectiveness of the proposed DMDc-LQR method is validated using numerical Kiewitt cable dome and tensegrity grid under wind and seismic loads. The results show that the DMDc-LQR controller maintains similar control effect to that of the FEM-LQR controller and has advantage of high computing efficiency as well. In addition, the influence of critical parameters (i.e., data noise and model order) on vibration control effect is comprehensively explored. It is found that increasing the model order is effective to mitigate the noise influence on the DMDc-based reduced-order SSM and ensures the effectiveness of the DMDc-LQR controller.

Global solutions and blow-up for a coupled system of nonlinear hyperbolic equations with weak damping

Global solutions and blow-up for a coupled system of nonlinear hyperbolic equations with weak damping

Asymptotic behavior for a class of logarithmic wave equations with Balakrishnan-Taylor damping, nonlinear weak damping and strong linear damping

<abstract><p>In spaces with any dimension, a class of logarithmic wave equations with Balakrishnan-Taylor damping, nonlinear weak damping and strong linear damping was considered</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ {u_{tt}} - M(t)\Delta u + \left( {g * \Delta u} \right)(t) + h({u_t}){u_t} - \Delta {u_t} + f(u) + u = u\ln {\left| u \right|^k} $\end{document} </tex-math></disp-formula></p> <p>with Dirichlet boundary condition. Under a set of specified assumptions, we established the existence of global weak solutions and elucidated the decay rate of the energy function for particular initial data. This contribution extended and surpassed prior investigations, as documented by A. Peyravi (2020), which omitted the consideration of Balakrishnan-Taylor damping and strong linear damping while being confined to three spatial dimensions. Our findings underscored the pivotal role of these overlooked damping factors. Furthermore, our demonstration underscored that Balakrishnan-Taylor damping, weak damping and strong damping collectively induced an exponential decay, although the precise nature of this decay was contingent upon the differentiable function associated with the memory damping term $ {\zeta (t)} $. Consequently, the absence of the damping term in reference by A. Peyravi (2020) was unequivocally shown not to augment the decay rate. This insight enhanced our understanding of the nuanced dynamics involved and contributed to the refinement of existing models.</p></abstract>

Dynamics of the non-autonomous wave equations with nonlocal weak damping and critical nonlinearity

Dynamics of the non-autonomous wave equations with nonlocal weak damping and critical nonlinearity

Lamé system with weak damping and nonlinear time-varying delay

Abstract This article is concerned with the stability and dynamics for the weak damped Lamé system with nonlinear time-varying delay in a bounded domain. Under some appropriate assumptions, the global well-posedness and asymptotic stability are shown in the case where the delay coefficient is upper dominated by the damping one. Moreover, the finite dimensional global and exponential attractors have also been presented by relying on quasi-stability arguments. The results in this article is an extension of Ma, Mesquita, and Seminario-Huertas’s recent work [Smooth dynamics of weakly damped Lamé systems with delay, SIAM J. Math. Anal. 53 (2021), no. 4, 3759–3771].