Optimal Damping Research Articles

Dynamics of a double pendulum with viscous friction in the joints. II. Dissipative oscillation modes and optimization of damping parameters

This paper is a continuation of the article "Dynamics of a double pendulum with viscous friction in the joints. I. Mathematical model of motion and construction of the regime diagram", in which a linear mathematical model of the motion of a double mathematical pendulum with identical parameters of links and end loads in the presence of viscous friction in both articulations was given, and a diagram of dissipative regimes of its motion was also constructed. The question of a particular variant of proportional damping is considered, in which the oscillation modes of a dissipative system are not distorted by friction forces, and basic formulas are given that describe the dynamics of the system in this situation. For the general case of damping, through a rational combination of analytical and numerical research methods, all key quantities characterizing the motion of the system on each of the dissipative oscillation modes are identified and determined. In addition, several problems of optimal damping of system oscillations are considered, and the best dissipative parameters are selected based on the criterion of the maximum degree of stability. The obtained results are accompanied by a series of graphical illustrations, which make it possible to establish their dependence on the damping coefficients and note their main qualitative and quantitative features. The solutions found can be useful in practice when designing two-link manipulators and studying their dynamic behavior.

Design of Magnetorheological Fluid Damper with Optimal Damping Force

This article focuses on designing and analyzing of an optimal Magnetorheological Fluid Damper (MRFD) having varying piston shape channeled into the piston of the MRFD. A finite element approach has been employed to investigate the impact of piston material, piston shape, MR fluid gap and pole length on the generated magnetic field density, yield stress along with damping force. Taguchi L18 orthogonal array has been exercised to obtain the optimal damping force. The Analysis of Variance (ANOVA) results investigate the contribution of the selected parameters and depict that the MR fluid gap is the most predominant factor which affects the damping force, making a contribution of 77.56%, followed by piston material which contributes 12.40%, pole length with a contribution of 8.23% and piston shape has negligible contribution of 0.07%. Taguchi predicts the optimized model for the selected parameters as A2B2C1D3 which has been validated by carrying out the analysis using ANSYS Maxwell software v. 16. The damping force of 1053 N has been obtained for the optimal MR damper model which is based on the prediction of the Taguchi results.

Stochastic Optimization of Electromagnetic Inertial Mass Dampers in Nonlinear Hybrid Base Isolation Systems Under Seismic Excitations

Recently developed inerter-based dampers have been installed at the base layer to reduce base displacement and simultaneously improve the superstructure’s performance. However, in the existing research on optimizing damper parameters, the nonlinear property of base isolation is simplified and stochastic linearization technique is introduced to approximate such nonlinearity, which would inevitably introduce errors. In this paper, an improved method is proposed for stochastic optimization of electromagnetic inertial mass dampers (EIMD) in nonlinear hybrid isolation systems subject to seismic excitations. First, a stochastic seismic excitation is represented by one elementary random variable adopting the dimension-reduction spectral representation method. Then, statistical moments of nonlinear base-isolated structural responses are estimated using two-point estimation method (2PEM). Finally, the EIMD optimal parameters are obtained via the modified directional bat algorithm (MDBA) recently proposed by the authors through minimizing base layer response moments. This proposed improved method could fully consider the base isolation nonlinearity compared with the previous stochastic linearization technique. Moreover, the proposed stochastic optimization of the EIMD only requires two dynamic analyses to achieve its efficiency. A seven-story base-isolated frame building equipped with an EIMD is investigated in the numerical simulation, and results indicate that EIMD optimized by this proposed method obviously outperforms the results by the stochastic linearization technique and the conventional viscous damper (VD) in the base layer displacement reduction.

Traveling-wave vibration modelling for thin-walled gear with ring damper

The harmful resonances of the thin-walled gears for aviation high-speed gear transmission systems, especially the traveling-wave vibration (TWV), frequently occur under complex excitations. The ring damper is an excellent and widely used damping technology for TWV reduction. However, lacking the TWV predictive method, there are few theoretical bases for the damper optimization. In this paper, firstly, assuming that the external input energy, the gear damping energy dissipation, and the ring damper energy dissipation form an energy balance, a novel model of TWV response based on energy dissipation (TRED) is proposed for the thin-walled gear with ring damper. Secondly, to solve the complex nonlinear TRED model, using the Rayleigh damping theory, the discrete expression of TRED model is innovatively given instead of traditional equation solving methods. Considering that the TRED model is established based on the vibrational displacement, a method for the conversion of gear vibration strain and displacement is given under different TWV directions and vibration strain measurements, and the solving method is proposed for the TRED model based on the above established theories. Finally, to validate the TRED model and its solutions, the speed-up experiments are conducted, and the experimental results are compared with the TRED prediction. Results show that the experimental and theoretical results are consistent, and the maximum predictive error is 8.7 %, which validates the feasibility of the proposed theories and methods.

The martensite/strain-glass crossover composition region of Ni-Co-Mn-Ga ferromagnetic strain glass system

The ferromagnetic strain glass within the martensite/strain-glass crossover composition region has been reported to exhibit optimal damping performance. The construction of a crossover composition region in ferromagnetic strain glass systems has great potential to optimize their functional properties. The transforming properties of the Ni55-xCoxMn20Ga25 (x = 8.2–9.2) system is detected to construct the crossover composition region. The results reveal that Ni55-xCoxMn20Ga25 (x = 8.4, 8.6, 8.8, 9.0, and 9.2) alloys undergo two-step transitions, i.e., austenite to strain glass and strain glass to martensite transition. Based on the experimental results, the phase diagram with a crossover composition region of Ni55-xCoxMn20Ga25 ferromagnetic strain glass system was established. This guide explores the relevant functional properties of alloys within the martensite/strain-glass crossover composition region.

Discrete viscous dampers for multi-mode vortex-induced vibration control of long-span suspension bridges

Multi-mode vertical vortex-induced vibrations have been observed on several long-span suspension bridges, where several vertical modes of stiffening girder are excited in turn with increasing of wind velocity. This paper proposed a discrete viscous dampers solution and its optimization targeting multi-mode vortex-induced vibration control for long-span suspension bridges. The minimal modal damping ratio was used to evaluate the performance of the damper system. The wind tunnel test verified that the modal damping ratio is an alternative to the resonance response amplitude and can be obtained by complex modal analysis. The ternary search algorithm was adopted to find the optimal damper parameter for the Yingwuzhou Yangtze River Bridge, which is a suspension bridge that suffered excessive vortex-induced vibrations. Using linear damper elements to connect the bridge tower and the bridge girder directly turned out to be a feasible method of increasing multiple modal damping ratios. Four torsional eddy current dampers have been installed in the Yingwuzhou Yangtze River Bridge, based on the numerical optimization results calculated in this paper. Although the measured modal damping ratios were smaller than the numerical results, the structural damping increased by three times after dampers were installed, and the requirement of the current specification was satisfied.

Selection of the optimal design for a vibro-impact nonlinear energy sink

The efficiency of a vibro-impact nonlinear energy sink (VI NES), that is, a vibro-impact damper, is largely determined by its design. The optimal damper design can be found through optimization procedures. However, the result of their work is ambiguous, their various options show different values of the optimal damper parameters. A thorough analysis of the obtained parameters values allow you to select the best option according to a certain criterion. While carrying out this analysis, we observe many interesting phenomena, namely, the synergistic effect of multiple parameters, rich complex dynamics of the VI NES, the presence of direct impacts between the damper and the main body, the dependence of the total energy on the exciting force parameters.The analysis also allows us to formulate the limitations of the VI NES. All these problems are reflected in this article.

Numerical study on weakening vortex-induced vibration of semi-ring diversion type component

Conventional spoiler components are commonly employed to mitigate vortex-induced vibration (VIV), but their effectiveness varies significantly. Therefore, detailed comparative studies should be made between different components and a more comprehensive suppression method will be proposed. In this paper, numerical simulations are conducted to explore the weakening effect of hydrodynamic shapes on VIV of structures. Different spoiler components, including rectangular spoiler, fairing, and fin plate are investigated, and for further optimization, a novel concept of semi-ring diversion type component is proposed. The attenuation effects of different components on vibration are compared. In addition, sensitivity analyses of the diversion component, including slit width (XW), front angle (α), and nozzle size (BL), are conducted at various reduced velocities to determine the optimal sizes. Results indicate that traditional spoiler components have inherent shortcomings in terms of weakening efficiency, which can only reduce the maximum resonance value (Ay(max)) to 50%–77%, extend the dimensionless critical velocity (Ucr) by −0.5–1.5, and shorten the length of frequency lock-in interval to 2.5–3, compared to the bare cylinder. The diversion component effectively reduces the frequency of vortex shedding around the cylinder. The optimal vibration damping effect is achieved when XW = 0.03, α = 60°, and BL = 0.11. Compared to the bare cylinder, the structure shows a substantial reduction in resonant frequency by 69%, a threefold decrease in the length of the frequency lock-in interval, a 68.2% reduction in Ay(max) and a delay in Ucr of 2.65, demonstrating a potential mitigation device for VIV.

Design and Control of Hydraulic Power Take-Off System for an Array of Point Absorber Wave Energy Converters

The development of wave energy converter (WEC) arrays is an effective way to reduce the cost of levelized energy and facilitate the commercialization of WECs. This study proposes a hydraulic power take-off (PTO) system for an array of point absorber wave energy converters (PA-WECs) and designs a control system using a novel algorithm called the improved simplified universal intelligent PID (ISUIPID) controller and the adaptive matching controller including an improved artificial gorilla troops optimizer (IGTO) to improve and stabilize the output power of PA-WEC arrays. Simulations under varying irregular wave states have been carried out to verify the validity of the mathematical model and the control system. The results show that the designed IGTO has faster convergence speed and better convergence accuracy in solving the optimal linear damping coefficient of the generator, and the proposed ISUIPID controller provides superior performance in tracking the speed of the hydraulic motor under the changing sea states. In addition, the capture power and output power of the array of PA-WECs are improved and the electrical energy can be output stably under the designed control system. The array of PA-WECs with the proposed control system will become an independent, stable, efficient, and sustainable power supply system.

Analiza mehanizma disipacije energije međukatno izolirane konstrukcije utemeljena na zaostajanju u fazi

Owing to the existence of the isolation layer, a phase lag phenomenon occurs between the superstructure and substructure of a story isolation structure. This phenomenon causes a phase difference between the superstructure and substructure; furthermore, the generated phase difference has a significant impact on the structural damping effect. To study this effect, we established a two-mass model of an inter-story isolated structure, derived the phase difference formula, analysed the impact of the phase difference on the damping effect of the modelled inter-story isolated structure and obtained the optimal phase difference to achieve the best damping effect; in addition, we combined the principle of minimum base shear and optimal phase difference to optimise the damping of the structural isolation layer with different mass ratios. Based on the optimal damping, an energy balance equation was established from the viewpoint of energy. The energy transfer and consumption under different phase differences were analysed to further discuss the relationship between phase differences and the damping effect of the inter-story isolated structure.

A technique for modeling and optimizing the design of wave energy conversion devices

With the continuous development of society and the economy, energy shortages have become increasingly prominent. As an important marine renewable energy source, wave energy holds significant theoretical significance due to its widespread distribution and vast storage potential. In this paper, we employ differential equation theory, numerical optimization methods, and optimization techniques to model and design algorithms for investigating the energy conversion mechanisms of wave energy devices. Due to the complex situation, we decided to simplify that into two scenarios. As to the first scenario, the essence of energy output in wave energy devices lies in the relative velocity between the floater and the oscillator. Firstly, the product of the damping force and the instantaneous relative velocity is integrated over time and divided by the period to obtain the average output power. Maximizing the average output power, with the damping coefficient as the decision variable, establishes a nonlinear optimization model. Secondly, a stepwise optimization approach is applied to control the damping coefficient, resulting in optimal damping coefficients of 33600, . Finally, a genetic algorithm is employed to validate the results as to the next scenario. After adding rotational dampers and torsion springs to the wave energy device, the relative velocity and relative angular velocity between the floater and the oscillator jointly contribute to energy output. The objective is to maximize the sum of the average output power of linear dampers and rotational dampers. The decision variables are the linear damping coefficient and the rotational damping coefficient. A nonlinear optimization model is established. A stepwise optimization approach is applied to optimize both types of coefficients, and the results are validated using a genetic algorithm. The optimal solution is found to have a linear damping coefficient of 60135.7781 N·s/m and a rotational damping coefficient of 4244.90358 N·s·m for the rotational dampers.

Experimental investigation of a dual-pontoon WEC-type breakwater with a hydraulic-pneumatic complementary power take-off system

Floating offshore multi-purpose structures have recently attracted much attention worldwide in terms of sharing costs, enhancing efficiencies and reducing environmental impacts. In this paper, hydrodynamic experiments are conducted to examine the accessibility of wave energy absorption by a dual-pontoon floating breakwater integrated with hybrid-type wave energy converters (WECs). The main structure and the air chamber between the two pontoons are designed as an Oscillating Buoy (OB) and an Oscillating Water Column (OWC), respectively. Two power take-off (PTO) systems, including a hydraulic system and a Wells turbine, are selected to extract wave energy from structural motion and chamber airflow. To investigate the hydraulic-pneumatic complementary effects, PTO damping coefficients of two systems are adjusted both individually and synchronously. Besides, the hydrodynamic comparison among different geometrical parameters, are further studied. The breakwater-integrated hybrid WEC system led to a larger optimal pneumatic damping for the OWC while the optimal hydraulic damping for the OB is not affected. Additionally, the internal air pressure is acting as a resistive force to pontoons, hence the pontoon motion is smaller, and part of the kinematic energy from pontoons is extracted by the OWC. Correspondingly, the wave attenuation capacity is enhanced by multiple harvesting manners, especially for long-period waves.

Design, analysis and optimization of a hybrid fluid flow magnetorheological damper based on multiphysics coupling model

Magnetorheological (MR) dampers are widely used in industrial applications due to its simple structure, fast response and adjustable damping performance. However, the volume of the MR damper will be limited by the installation space, which hinders the application to some extent. In this paper, a hybrid fluid flow MR damper which can be used in antiseismic building is designed to achieve better damping performance under constrained volume size. The multiphysics coupling simulation model and circuit simulation model are also established. Numerical results show the output damping force is 6.367 kN, the dynamic adjustable range is 50.768, and the current input time is 31 ms under the applied current of 2.0 A. In order to improve the dynamic performance of the designed MR damper under constrained volume size, a multi-objective structural optimization method based on theoretical calculation model is proposed. Experiments are also conducted to investigate the dynamic performance of the initial and optimal MR damper. Compared with the initial MR damper, the output damping force and the dynamic adjustable range of the optimal damper are improved by 6.6 % and 46.3 %, while the energy consumption is reduced by 10.7 %, respectively.

Optimal Energy Extraction of Non- Buoyant Type Wave Energy Converter Using Grey Relation Analysis

The wave energy converters involved in ocean wave energy harvesting are subjected to various natural calamities and thus obtaining the optimal energy extraction is a challenging task. It is normally noted that the energy extraction is maximum when the frequency of the ocean waves matches the natural frequency of the device. The natural frequency of the converter can be modified by tuning its dynamics, but it is intricate to perform in the ocean environment, so an alternative method should be adopted. In this work, the optimal electrical damping is performed to modify the frequency of the system to match the natural frequency of the incident wave. The grey relation analysis is carried out to find out the optimal damping value. Further, the obtained results are subjected to experimental verification and it is observed that the energy extraction is significantly improved. This approach is less complex and effective when compared with the other methods.

Advancing flow-duct noise control: Examples of innovative silencers

Two examples of innovative silencers for advanced duct noise control are presented. The first example is related to using metamaterials and the so-called ‘slow sound' to create a compact virtual Herschel-Quincke tube [1]. The second example revolves around a concept called the ‘modal filter' [2], which is designed to selectively damp a single propagating mode. For plane waves, optimal propagational damping is achieved by a wall impedance equal to the Cremer impedance. We will demonstrate how to compute the Cremer impedance, even for low frequencies, at which the classical solution is invalid [3]. Such an arrangement efficiently dampens both the plane (0,0) and the first radial mode (0,1). To further dampen the first two circumferential modes (1,0) and (2,0), a section with the Cremer impedance can be combined with a modal filter made of micro-perforated plates. These plates are inserted parallel to the flow direction and positioned at modal velocity maxima in the duct cross-section. We anticipate that both examples can be useful in industries requiring compact noise mitigation solutions in flow ducts. [1] https://doi.org/10.1016/j.jsv.2019.115045. [2] https://doi.org/10.1121/2.0000473. [3] https://doi.org/10.1121/1.5136952

Application of nonlinear stiffness mechanism on energy harvesting from vortex-induced vibrations

This study investigates the potential of vortex-induced vibration (VIV) as a renewable energy source, achieved when fluid flow interacts with a bluff body, inducing self-sustained oscillations through vortex shedding in the wake. While VIV research has traditionally focused on understanding its mechanisms and mitigating detrimental effects, interest in VIV energy harvesting has surged as a means to convert marine hydrokinetic (MHK) energy into usable electrical power. The nonlinear effects of two linear oblique springs on VIV energy harvesting are explored using the wake oscillator model, encompassing bistable and Duffing hardening stiffness. The study examines the response and energy harvesting performance while considering the impact of undeformed spring length, structural damping, and initial conditions on VIV energy conversion. Findings show that nonlinear stiffness application in the VIV system can broaden the synchronization bandwidth or reduce the VIV initiation flow speed. Bistable stiffness may broaden the synchronization velocity range, while Duffing hardening stiffness efficiently reduces the VIV initiation speed with small energy harvesting loss. Combining both stiffness types with appropriate control strategies presents a promising approach for achieving a broad synchronization VIV bandwidth and low initiation flow speed. Key parameters, such as the nondimensional parameter defining spring system obliquity and the ratio between undeformed spring length and cylinder diameter, significantly influence VIV response and energy harvesting. Moreover, optimal structural damping is vital to maximize energy harvesting efficiency, and understanding and controlling initial conditions are crucial for optimizing VIV synchronization bandwidth and energy harvesting efficiency for both bistable and Duffing hardening stiffness. This study provides valuable insights into VIV system dynamics and energy conversion potential with nonlinear springs, offering promising avenues for enhancing energy harvesting efficiency and inspiring further applications of nonlinear effects in VIV energy converters.

A numerical approach for determining the optimal position of a single damper for damping a distinct eigenfrequency of multi‐body systems

AbstractIn this paper the damping optimization of a multi‐body oscillator with arbitrary n degrees of freedom is considered. The main contribution is a theoretical result for the optimal position of a single damper in a structured optimization. For that purpose the optimization criterion based on the average total energy is considered. As the damping optimization by means of the chosen optimization criterion in general is not a straight‐forward task, a numerical approach based on the formula of Veselić is introduced in this contribution. This approach can be used for efficiently calculating optimal damping for medium‐size problems with .

The synergistic effect of the multiple parameters of vibro-impact nonlinear energy sink

This article studies the dynamics and efficiency of a vibro-impact damper (single-sided vibro-impact nonlinear energy sink—SSVI NES) depending on the exciting force parameters. The damper is coupled with a linear oscillator—the primary structure. It is shown that the damper is quite effective in a wide range of the exciting force amplitude and in the range of its frequency, which are higher than the resonant frequency; damper efficiency in these regions is fairly stable. The dynamics of the vibro-impact system “primary structure—SSVI NES” is rich and complex, which, however, does not impair the damper efficiency. In complex oscillatory regimes, the damper makes bilateral impacts: it hits both an obstacle and directly against the primary structure, which actually turns a single-sided NES into a double‐sided one. The optimization procedure and the choice of optimal damper parameters play a very important role in damper design. Optimizing multiple damper parameters instead of three shows a synergistic effect and provides better results.

Improving cable-stayed bridge longitudinal aseismic capability via fluid viscous damper parametric optimization and experimental investigation

The seismic vulnerability of Cable-stayed Bridges (CSBs) in high-earthquake intensity areas can be of significant concern to structural safety and resilience. A promising design practice for CSBs depends on decoupling the girder from the girder-pylon connection and involving energy dissipation devices such as fluid viscous damper (FVD) to mitigate the seismic responses. However, the parametric damper optimization algorithm and experimental validation on the FVD of a longitudinal aseismic system for CSB is still limited. In this study, three longitudinal aseismic systems (a semi-floating system with an elastic or damper connection, and a pylon girder consolidation system with a rigid connection) were investigated and compared based on the actual bridge Xigu Yellow River CSB erected in Lanzhou, China. The non-linear time history methodology was implemented to analyze the pylon and girder’s displacement and internal force responses, and the fluid viscous damper (FVD) aseismic system was the optimal choice considering the oval seismic performances. The optimal damping parameters were obtained by conducting parametrical analysis based on qualitative analysis and non-linear multi-function optimization in the pylon-girder and auxiliary pier-girder connections. A full-scale FVD model was designed and manufactured to conduct low velocity, constitutive law, and damping efficiency tests. The experimental results indicate that FVD achieved good energy dissipation capability and stability. FVD damping parameters were deduced according to the constitutive law test. The optimal analytical FVD damping parameter agreed well with the experimental results. Furthermore, the optimization was implemented in the final bridge design, referencing longitudinal aseismic systems for CSBs.

A comprehensive Cosserat rod drill-string model for arbitrary well geometry that includes the dynamics of the cutting and lateral contact

In this paper, a comprehensive continuous Cosserat rod model is developed to study the dynamics of a drill-string. The model presents the following features: (1) it can simulate the 3-D dynamics of the system, including lateral, axial and torsional motion; (2) it includes damping effects by adopting a Kelvin–Voigt material; (3) it uses a velocity-independent bit-rock interaction formulation in which the forces and torques at the bit are obtained by considering the dynamics of the cutting blades and the evolution of the soil profile, which is simulated with the help of an advection equation; (4) lateral contact is also included. In this paper, two application cases are analysed. The first one deals with a vertical borehole. It includes four simulations that are used to further investigate the hypothesis that low-dimensional lumped formulations are not able to capture the dynamics of a drill-string and, while doing so, evaluate the effect of the damping in the system’s response. The predictions are compared with those given by two other models: the first one considers a 2-degrees-of-freedom (DOF) formulation, with 1-axial and 1-torsional DOF; the second one is a semi-discrete approach, with 1 DOF for the axial dynamics and a continuous formulation for the torsional one. Divergences between the predictions are found, associated with the presence of higher frequencies in the signals obtained with the Cosserat model, which reassures the hypothesis that the new continuous approach can capture aspects of the dynamics that cannot be modelled with low-dimensional representations. The efficiency of the drilling is also assessed for the simulations obtained with the new model. The highest performance was observed in those simulations where only axial oscillations occurred, while a performance drop was seen when those vibrations were accompanied by torsional stick–slip, suggesting that an optimum damping value associated with the best drilling performance could be found, were damping controllable. Finally, the second application case is used to illustrate the full potential of the new model to tackle the 3-D lateral, axial, and torsional dynamics in a curved borehole.