Damped Solution Research Articles

Piezoelectric Shunt Damping for a Planar Motor Application under Cryogenic Conditions

For several decades, Moore’s law has driven the semiconductor industry, with computational power and production costs as the main drivers. Such drivers have enabled several technological innovations in the mechatronics and dynamics architecture of photolithography machines, used for semiconductor circuits manufacturing. Among current investigations, the use of superconductive magnets would enable higher accelerating stages and, thus, higher throughput and lower manufacturing costs. However, this involves a complex magnet structure that needs to operate at cryogenic temperatures and mechanical resonances at relatively low frequencies as a result of the thermal architecture of the system. The damping options are also limited due to the very low temperature. This paper explores the use of shunted piezoelectric transducers for damping the internal modes of the magnet mass. A classical resistive and inductive RL shunt is considered. The study was conducted both numerically and experimentally on a demonstrator of a superconductive magnet plate concept, where piezoelectric transducers are incorporated to support the superconducting coils. The study demonstrates the effectiveness of piezoelectric shunts as a damping solution at very low temperatures, with limited impact of the temperature variation on the performance.

Data‐driven variational method for discrepancy modeling: Dynamics with small‐strain nonlinear elasticity and viscoelasticity

AbstractThe effective inclusion of a priori knowledge when embedding known data in physics‐based models of dynamical systems can ensure that the reconstructed model respects physical principles, while simultaneously improving the accuracy of the solution in the previously unseen regions of state space. This paper presents a physics‐constrained data‐driven discrepancy modeling method that variationally embeds known data in the modeling framework. The hierarchical structure of the method yields fine scale variational equations that facilitate the derivation of residuals which are comprised of the first‐principles theory and sensor‐based data from the dynamical system. The embedding of the sensor data via residual terms leads to discrepancy‐informed closure models that yield a method which is driven not only by boundary and initial conditions, but also by measurements that are taken at only a few observation points in the target system. Specifically, the data‐embedding term serves as residual‐based least‐squares loss function, thus retaining variational consistency. Another important relation arises from the interpretation of the stabilization tensor as a kernel function, thereby incorporating a priori knowledge of the problem and adding computational intelligence to the modeling framework. Numerical test cases show that when known data is taken into account, the data driven variational (DDV) method can correctly predict the system response in the presence of several types of discrepancies. Specifically, the damped solution and correct energy time histories are recovered by including known data in the undamped situation. Morlet wavelet analyses reveal that the surrogate problem with embedded data recovers the fundamental frequency band of the target system. The enhanced stability and accuracy of the DDV method is manifested via reconstructed displacement and velocity fields that yield time histories of strain and kinetic energies which match the target systems. The proposed DDV method also serves as a procedure for restoring eigenvalues and eigenvectors of a deficient dynamical system when known data is taken into account, as shown in the numerical test cases presented here.

Explicit solution framework and new insights of 3-DOF linear flutter considering various frequency relationships

Different engineering structures, e.g., long-span bridges, bundled conductors, and cable-supported photovoltaic modules, exhibit various frequency relationships among different degrees of freedom (DOFs). Despite extensive research, the initiation mechanisms of flutter remain somewhat ambiguous for a 3-DOF system considering heaving-lateral-torsional motions, especially when frequencies are close among different DOFs. This study introduced an explicit eigenvalue solution framework for tackling the 3-DOF linear flutter problem by utilizing matrix perturbation methods, enabling the extraction of modal damping and frequency solutions for all possible frequency scenarios. These solutions explicitly clarified the influence mechanism of all flutter derivatives (aerodynamic damping and stiffness), structural frequencies, and mechanical dampings. Important flutter derivatives, flutter risk level, and sensitivity level to mechanical damping and to frequency detuning were summarized in a table for all frequency scenarios, providing a panoramic perspective on flutter instability and the coupling mechanism. Numerical studies were conducted on a thin plate, the Akashi Kaikyo Bridge, and an eight-bundled conductor to examine the proposed explicit solutions. The results showed that approaching frequencies can amplify the coupling effect among different DOFs by half an order, but this does not necessarily mean the system is more prone to flutter. A system where the torsional frequency approximates the heaving/lateral frequency is expected to face a higher flutter risk if given significant torsional-related aerodynamic stiffness (H3*, P3*). Evidently, this high risk exhibits insensitivity to mechanical damping and small frequency-detuning. Though usually ignored in bridge flutter analysis, drag force and lateral motion could exert noticeable influence in a minority of cases, e.g., more than 10 m/s decrease of critical wind speed for the Akashi Kaikyo Bridge at large angles of attack. The proposed explicit solution framework provides a systematic view and new insights into the flutter initiation mechanism, serving as a reference in the design and studies of various engineering structures with different frequencies and coupling features.

Phase-space evolution of quasiparticle excitations in electron gas

In this research, we use the dual lengthscale quasiparticle model for collective quantum excitations in electron gas to study the time evolution of the Wigner function. The linearized time-dependent Schrödinger–Poisson system for quasiparticles is used to study the dynamics of initial known stationary and damped solutions in an electron gas with arbitrary degree of degeneracy. The self-consistent potential in the Schrödinger–Poisson model is treated in a quite different manner in this analysis due to the effective coupling of the electrostatic field to the electron density, which leads to a modified Wigner function. It is shown that the modified Wigner function in the absence of external potential evolves similar to the system of free particles, a feature of collective quantum excitations which is quite analogous to freely evolving classical system of particles in the center of mass frame in the absence of external forces. The time evolution of the modified Wigner function reveals a grinding effect on large-amplitude density structures present at initial states, which is a characteristic feature of the Landau damping in plasmas. It is further shown that linear phase-space dynamics of spill-out electrons (damped quasiparticles) can be described similar to free quasiparticles with imaginary momentum. The later predicts the surface electron tunneling via the collective excitations of spill-out electrons at the half-space boundary, which is closely related to the Heisenberg's uncertainty principle. Current research can have applications in plasmonics and related fields.

Damped Kadomtsev Petviashvilli equation for magnetosonic waves in a dissipative OH plasma in the ionospheric F-Layer

In this paper we study the linear and nonlinear dynamics of magnetosonic waves in a dissipative Oxygen-Hydrogen (OH) plasma. It is shown that such waves can propagate nonlinearly as solitary structures for both super and sub, acoustic and Alfvenic regimes. We use the hyperbolic tangent method to solve the collisional Kadomtsev-Petviashvili (KP) equation and obtain a damped solitary wave solution. Both compressive and rarefactive damped solitary structures are obtained and are significantly affected by the oxygen ion-neutral collision frequency, temperature, propagation angle, and ambient magnetic field present in the F-layer of Earth’s ionosphere.

Modified Chameleon Swarm Optimization Algorithm to Improve the Power System Stability

Power system stability has been difficult due to the occurrence of low frequency oscillation in the modern power system. Oscillation is mainly due to sudden changes of frequency, load, voltage, active power and reactive power. In this paper we provide a damping solution to oscillate the low frequency by using modified chameleon optimization algorithm. Damping performance and stability analysis of system is done by proposed modified chameleon Swarm Algorithm compared with conventional chameleon Swarm algorithm and Genetic algorithm with different operating condition in terms of Real power, Reactive power and Load disturbances. The comparative results confirmed that the proposed controller exhibit higher damping ratio, and better damping of deviations in speed and power angle to improve the stability of the system.

Optimization of a structural Acoustic Black Hole embedded in a stringer-stiffened composite laminate panel

Many modern airframes are made of composite laminate materials due to their low mass but strong loadbearing capability. Carbon fiber composite laminates allow for a strong and lightweight aircraft, but create unhealthy levels of disruptive and uncomfortable noise within the fuselage. This work looks at the possibility of a structural Acoustic Black Hole (ABH) as a passive vibration damping solution for a common stringer-stiffened airframe panel. A 1-D symmetrically damped ABH was integrated vertically into the cross section of a stringer stiffener of a composite laminate plate. A multi-objective evolutionary algorithm was employed to search for the optimal ABH dimensions in terms of the tradeoff between weight, axial linear buckling load, and integrated vibration response. Computational results predicted the ability for damped ABH-stiffeners of a certain dimension to have less vibrational response than others with comparable linear density and axial strength. Mass normalized, non-tapered and ABH-tapered preliminary panels were manufactured and tested. These results showed a capability of ABH stiffeners to decrease vibrational response in the attached skin, more prominently above their cut-on frequency. Stiffened panels were manufactured to optimized specifications and their experimental results validate the presence of an optimal ABH dimension to achieve passive vibration damping in a system with mass and structural constraints.

Damped harmonic oscillator revisited: The fastest route to equilibrium

Theoretically, solutions of the damped harmonic oscillator asymptotically approach equilibrium, i.e., the zero energy state, without ever reaching it exactly, and the critically damped solution approaches equilibrium faster than the underdamped or the overdamped solution. Experimentally, the systems described with this model reach equilibrium when the system's energy has dropped below some threshold corresponding to the energy resolution of the measuring apparatus. We show that one can (almost) always find an optimal underdamped solution that will reach this energy threshold sooner than all other underdamped solutions, as well as the critically damped solution, no matter how small this threshold is. We also comment on one exception to this for a particular type of initial condition, when a specific overdamped solution reaches the equilibrium state sooner than all other solutions. We experimentally confirm some of our findings.

Sonic horizon formation for two-dimensional Bose–Einstein condensates with higher-order nonlinear interaction

Based on the Gross–Pitaevskii equation model that incorporates higher-order nonlinear interaction, we studied sonic black hole and sonic horizon formation involved in nonlinear dynamical evolution for Bose–Einstein condensates with higher-order nonlinear interaction. On the basis of the modified variational method and the scenario where the system starts dynamic evolution from ground state, we derived the typical system distribution width function, which is analytically formulated as periodic oscillation solution and monotonically damped variational oscillation solution under different parametric settings. We also calculated the criteria formula for sonic black hole horizon formation with regard to the two evolution modes: oscillation mode and monotonically decay mode, pictorially demonstrating the time interval of sonic horizon appearance. The theoretical results obtained here can be used to guide relevant experimental studies of sonic horizon and sonic black hole formation for Bose–Einstein condensates incorporating the higher-order nonlinear interaction effects.

Design of energy harvesting magneto-rheological fluid damper for vehicle

Modern vehicles must include dampers in the suspension system in order to absorb vibration energy while driving. Passive dampers have dominated the market for many years. To increase the passenger comfort levels, suspension systems with controlled dampers that can adjust to uneven road profiles are needed. Semi-active suspensions have emerged as one of the most popular modern damping solution types due to their ability to manage damping force. The semi-active suspension system of the car uses magneto-rheological (MR) dampers for vibration control. The MR damper consumes low energy, has quick response, and better controllability of the damping force. A part of the energy lost in vehicle dampers can be recovered due to developments in energy-harvesting devices. This regenerated energy can be used in vehicles to power a number of extra systems, such as lighting, heating and air conditioning, and other things. This research attempts to develop an MR fluid damper with energy-harvesting rack and pinion system. The purpose of this study is to design a suspension system that combines an MR fluid damper and an energy-harvesting rack and pinion system. The design calculation involves setting the design parameters for the system that harvests energy and the MR fluid damper. Also, static structural analysis is carried out for both systems using finite element analysis software.

Nonlinear Damping and Field-aligned Flows of Propagating Shear Alfvén Waves with Braginskii Viscosity

Braginskii magnetohydrodynamics (MHD) provides a more accurate description of many plasma environments than classical MHD since it actively treats the stress tensor using a closure derived from physical principles. Stress tensor effects nonetheless remain relatively unexplored for solar MHD phenomena, especially in nonlinear regimes. This paper analytically examines nonlinear damping and longitudinal flows of propagating shear Alfvén waves. Most previous studies of MHD waves in Braginskii MHD have considered the strict linear limit of vanishing wave perturbations. We show that those former linear results only apply to Alfvén wave amplitudes in the corona that are so small as to be of little interest, typically a wave energy less than 10−11 times the energy of the background magnetic field. For observed wave amplitudes, the Braginskii viscous dissipation of coronal Alfvén waves is nonlinear and a factor around 109 stronger than predicted by the linear theory. Furthermore, the dominant damping occurs through the parallel viscosity coefficient η 0, rather than the perpendicular viscosity coefficient η 2 in the linearized solution. This paper develops the nonlinear theory, showing that the wave energy density decays with an envelope . The damping length L d exhibits an optimal damping solution, beyond which greater viscosity leads to lower dissipation as the viscous forces self-organize the longitudinal flow to suppress damping. Although the nonlinear damping greatly exceeds the linear damping, it remains negligible for many coronal applications.

Self-Attenuation of Drillstring Torsional Vibrations Using Distributed Dampers

Summary During drilling operations, drillstring vibrations cause many downhole dysfunctions, resulting in underperformance, equipment failure, and possibly wellbore damage. Current drillstring vibration mitigation solutions are generally located at a single site, either at the topdrive or close to the bit. However, because the sources of vibration excitation are distributed along the whole drillstring, these single-point vibration damping solutions do not succeed in removing all vibration modes. A distributed vibration damping solution is investigated, wherein damping subs are placed at intervals along the drillstring. The drillpipe rotates on bearings inside the damping subs, thereby reducing mechanical torque. The damping sub has a slightly larger diameter than the neighboring tool joints, lifting the drillstring off the borehole wall and thus eliminating most of the mechanical friction between the damping subs. Viscous friction is introduced in the form of rotary eddy current brakes within the damping subs, which cause the damping of torsional oscillations. The damping sub moves axially on spur wheels supported by bearings, thereby reducing drag forces. The decoupling of rotary and axial movement is a key element for removing a source of excitation. Simulations made with a 4n degree-of-freedom (DOF) transient torque and drag model confirm the expected results. The results of simulations for a use case based on a complex 3D trajectory are presented. With damping subs every 30 m and a damping coefficient of 20 N·s/rd, the topdrive torque is reduced to 40% of that of a plain drillstring, and torsional stability is obtained across the topdrive speed range of 60 to 180 rev/min. By comparison, conventional nonrotating pipe protectors (NRPPs) would have reduced the topdrive torque to 30%, but torsional stability would have not been achieved because the expected damping coefficient was less than 0.02 N·s/rd. The design of the damping sub relies on readily available technological components that can sustain very high pressures and temperatures. The damping subs are therefore compatible with high-pressure/high-temperature applications, including geothermal drilling.

3D joint interpretation of potential field, geology, and well data to evaluate a salt dome in the Qarah‐Aghaje area, Zanjan, NW Iran

AbstractAs geophysical parameters are not always functionally related, treating multiple geophysical data sets to have a realistic geological model is not straightforward. An effective strategy to derive a geological interpretation is a combination of several geophysical methods with geological and well observations, each with its advantages and limitations. Gravity and magnetic methods are encouraging tools to investigate salt domes due to enough density and susceptibility contrasts between salt minerals and the background sedimentary rocks. In this paper, the dome‐shaped salt unit in the Qarah‐Aghaje area in Zanjan, located in the northwestern part of Iran, is investigated through the integration of 3D inversion models obtained from gravity and magnetic data and geological and well information. The 3D inversion of both data sets is made using a weighted damped minimum length solution for which model weighting is constructed from multiplying depth weighting and compactness constraints. At first, a synthetic case with a high degree of similarity to the real case is considered to evaluate the efficiency of the adopted inverse algorithm. Then, the inversion algorithm is implemented on the collected gravity and magnetic methods, and interpretation is made utilizing 3D obtained inverse models and geologic and well data. The result shows a dome‐shaped potash‐bearing salt unit that starts from a depth of 12 m and continues to the depth of 200 m. The drilled well in the centre of the main source of the salt (Well 3) demonstrates a depth range of 11–115 m.

Multimode vibration control of stay cables using pseudo negative stiffness MR damping system

At present the vibration control of stay cable suffers from low damping effectiveness in single mode vibration caused by the limitation of damper installation position as well as the poor modal compatibility, that is, a rapid degradation performance when the actual mode deviates from the designed optimal mode. In this paper, one practical semi-active magnetorheological (MR) damper based control solution is proposed to address the problems faced in multi-modal vibration control of stay cables. The semi-active pseudo negative stiffness (PNS) control strategy takes full account of the MR damper’s mechanical characteristics and the demands of the stay cable vibration control. Compared with the linear equivalent model, the proposed time-varying model exhibits more details of the damping force and the nonlinear response of the damped stay cable, which shows its essential role in the optimal design of MR-PNS scheme. Then the optimal design method of MR-PNS multi-modal vibration control for stay cable is summarized by taking the first three modes vibration control of the J20 cable in Nanjing Baguazhou Yangtze River Bridge as simulation examples. The simulations of cross-modal, multi-modal and wind-induced vibration cases are conducted respectively, while the results show that the optimal designed multi-modal MR-PNS scheme can simultaneously exceed the passive maximum modal damping ratio within first three modes. The advantages of the proposed MR-PNS method in high damping efficiency and modal compatibility could be verified by comparing with the passive multi-modal damping solution.

On the Effect of Frequency Separation, Mass Ratio, Solidity, and Aerodynamic Resonances in Coupled Mode Flutter of a Linear Compressor Cascade

Abstract At a low mass ratio of structure to air, the work-per-cycle approach, or better known as the energy method, will lead to nonconservative results as aerodynamic coupling of modeshapes acts destabilizing. Using the p–k method to solve the aeroelastic stability equation, the effects of various structural aspects are investigated for a two-dimensional compressor cascade in subsonic and transonic flow conditions. The investigated key parameters are frequency separation, mass ratio, and solidity. Furthermore, the effect of a high frequency dependency of the aerodynamic forces is presented. Such phenomena can happen in case of aerodynamic or acoustic resonances. If the resonance peaks are close to the aeroelastic frequency, a discontinuous behavior of the frequency or damping solution can lead to a rapid destabilization of the system, once the aeroelastic frequency moves from one side to the other of the peak. In these regimes, it is crucial to have a high quality representation of the frequency-dependent generalized aerodynamic forces (GAFs) for an accurate prediction of the flutter onset.

Qualitative analysis of bounded traveling wave solutions to Nagumo nerve conduction equation and its approximate oscillatory solutions

In this paper, we study the bounded traveling wave solutions to the Nagumo nerve conduction equation by using the theory of dynamical system and undetermined assumption method. We make a detailed qualitative analysis on the dynamical system corresponding to the traveling wave solution to this equation and obtain a threshold value c∗ that when the wave velocity is less than c∗, the bounded traveling wave solution to Nagumo equation exhibits oscillatory and damped properties, and when the wave velocity is higher than c∗, it usually takes the form of a wavefront solution. In addition, we obtain several new pulse solutions and wavefront solutions to Nagumo equation by using undetermined assumption method. In particular, we obtain the approximate oscillatory damped solutions when the wave velocity less than the threshold c∗. Further, by establishing the integral equation between the approximate solution and the exact solution, and examining the asymptotic state of the solution at infinity, the error estimation between the approximate solution and the exact solution of the oscillatory solution is obtained as an infinitesimal quantity decreasing exponentially. Finally, we compare the approximate solutions of the oscillatory solutions with the numerical solutions, and they are in agreement.

Active Damping Control for LCL Filters With Inverter-Side Current Feedback Only

In the past decade, extensive active damping solutions based on state variable feedback have been proposed to damp <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> resonance. In this letter, an innovative control strategy, which can achieve overcurrent protection, injected power control, and active damping at the same time, is proposed with the inverter-side current feedback only. Moreover, to avoid the mathematical limitations when solving characteristic roots of a third-order system, the damping-factor-based design method is proposed for the first time, by analyzing its equivalent circuit. The optimal damping factor, which is recommended to be positive and as large as possible, is searched to achieve superior resonance suppression effect. Finally, the proposed control and design method is verified by experimental results and shows good robustness both in stiff and ultraweak grid conditions.

Explanation of wind gusts induced by pressure changes. Turbulence in the air

The paper researches wind gusts that are caused by changes in pressure on a flat surface. To describe this phenomenon the equations of the state of a continuous medium are used. In the stationary case, these equations in the air are the equation of the decreasing exponent for the pressure gradient. Consequently, the volume force in the air cannot act permanently. It decreases at a distance of about a kilometer. This exponential damping solution is due to wind gusts. The paper concludes that the periodic dumping of volumetric forces leads to turbulence in the air. These disruptions or turbulence are also observed when the air rotates in cyclones and anticyclones. In the water, pressure fluctuation leads to periodic waves.

Improved Active Damping Stabilization of DAB Converter Interfaced Aircraft DC Microgrids Using Neural Network-Based Model Predictive Control

The stability problem induced by constant power loads (CPLs) is becoming more prominent in more electric aircraft. In this article, the stabilization issue of dc distribution bus with dual-active-bridge (DAB) converters was investigated. On the basis of voltage regulation, an active damping solution based on model predictive control (MPC) was proposed by explicitly incorporating a stabilization term into a cost function. In this solution, to ensure the output voltage performance with a smaller steady-state error and a dynamic voltage overshoot, an adaptive weighting factor was adopted with a stray resistor taken into account. A theoretical design of the weighting factors was performed using the artificial neural network (ANN) method. The proposed approach could supply stiff load voltage and provide good dc-link voltage stabilization, as well as load voltage overshoot clamping. These findings were verified through the computer simulations and practical experiments of an 800-W converter prototype with a switching frequency of 20 kHz, an input voltage of 270 V, and an output voltage of 270 V.

Combined Damped Sinusoidal Oscillation Solutions to the (3 + 1)-D Variable-Coefficient Generalized NLW Equation in Liquid with Gas Bubbles

This paper investigates the combined damped sinusoidal oscillation solutions to the 3 + 1 -D variable-coefficient (VC) generalized nonlinear wave equation. The bilinear form is considered in terms of Hirota derivatives. Accordingly, we utilize a binary Bell polynomial transformation for reducing the Cole-Hopf algorithm to get the exact solutions of the VC generalized NLW equation. The damped sinusoidal oscillations for two cases of the nonlinear wave ordinary differential equation will be studied. Using suitable mathematical assumptions, the novel kinds of solitary, periodic, and singular soliton solutions are derived and established in view of the trigonometric and rational functions of the governing equation. To achieve this, the illustrative example of the VC generalized nonlinear wave equation is provided to demonstrate the feasibility and reliability of the procedure used in this study. The trajectory solutions of the traveling waves are shown explicitly and graphically. The effect of the free parameters on the behavior of acquired figures of a few obtained solutions for two nonlinear rational exact cases was also discussed. By comparing the proposed method with the other existing methods, the results show that the execution of this method is concise, simple, and straightforward.