Damping Elements Research Articles

“Borrow-force-attack-force” by multi-scale elastic metamaterial with nonlinear damping

The powerful energy carried by low-frequency vibration is often challenging to be effectively attenuated using traditional damping materials. If low-frequency vibration can be controlled through the energy carried by the excitation itself, the cost of achieving ultra-wide low-frequency vibration control would be significantly reduced. To this end, this paper constructs a multi-scale elastic metamaterial with nonlinear damping (MEMND) to achieve the efficient suppression of ultra-wide low-frequency vibration through its unique transmission characteristics and the effect of “borrow-force-attack-force” (leveraging the excitation to dampen vibration), which is amplified with increasing external excitation. Theoretical, simulation, and experimental results demonstrate that MEMND can achieve over 10 dB damping enhancement at the expense of losing a small amount of the bandgap effect. It exhibits high sensitivity to external excitation in the low-frequency region, offering a promising opportunity for “borrow-force-attack-force”. This work integrates a natural nonlinear damping element into elastic metamaterials and leverages the nonlinear action mechanism of external excitation, presenting a different approach for nonlinear metamaterial design with potential engineering applications.

Experimental Evaluation of Damping and Stiffness in Optimized Active Sport Utility Vehicle Suspension Systems

On a flat city road, the specificity of the suspension poses a challenge. Sport utility vehicles (SUVs) have less flexibility compared to regular cars, despite providing a firm grip on asphalt and concrete. Constant adjustments to the center of gravity of SUVs are necessary. Surprisingly, they are less reliable and stable in urban settings due to this characteristic. In this study, a mathematical model of the suspension system of SUVs based on the Newtonian approach is introduced and validated with data from experiments carried out by the MTS machine system on the mono-tube (oil/air) mixed damper element. The model accurately predicts the performance of this damper, commonly used in SUVs, across various operating conditions, including different frequencies. A coil spring element, serving as a passive suspension unit with this damper, is also tested experimentally under similar conditions. By integrating passive suspension elements with the active actuator, the proposed modified design reduces the power consumption needed for the actuator to function and ensures a certain level of reliability. The effectiveness and performance of the modified active suspension system in comparison to the traditional passive suspension system are assessed using three different strategies: hybrid PID-LQR, linear quadratic regulator (LQR), and proportional-integral-derivative (PID). The genetic algorithm is utilized to determine the optimal parameter values for each controller by minimizing a cost function, maximizing performance, and minimizing energy consumption. Simulation results demonstrate that the active suspension system controlled by the PID-LQR controller offers significantly improved ride comfort and vehicle stability compared to other systems. This suggests that the performance of the active suspension system is greatly enhanced by the combined application of the hybrid PID-LQR controller compared to other systems.

Inductive mode selective damping of structural vibrations

AbstractStructural vibrations pose significant challenges in various engineering applications and require effective damping strategies to improve the overall performance and longevity of systems. While some oscillations can significantly reduce the longevity of systems, others might contribute positively to the overall system performance. Thus, this contribution presents a novel method of an inductive damping concept, that targets only specific vibrational modes based on their mode shapes. By analyzing the used inductive damping element in the context of a single degree of freedom oscillator, it is shown, that it functions as an ideal viscous damper only if the dynamics of the electric part of the system are neglected. The concept of mode selective damping is presented, using two of these damping elements in an oscillator chain with three masses. By altering the wiring configurations connecting the two damping elements in the electrical domain, the damping behavior can be manipulated to selectively damp only specific modes according to their mode shapes.

Investigating the effect of changing the geometric characteristics on the seismic behavior of the yielding shear panels

The use of different types of shear panels as a large group of yielding dampers has been investigated. Acceptable seismic behavior such as stiffness and high deformation capacity, appropriate lateral resistance, ease of construction, and use in the structure are among the most important. Different types of these dampers have been developed, and yield shear panel device (YSPD) dampers are one of them. This research investigates the effects of changes in the geometric dimensions of this type of damper on their seismic behavior. For this purpose, nonlinear finite element models of dampers under cyclic loading were analyzed. The obtained results showed that the simultaneous use of side plates and stiffeners can create suitable conditions for directly controlling the dimensions of the damper. Local buckling in the side plates may concentrate deformations in this part of the damper element, affecting the hysteresis behavior with pinching. In addition, increasing the thickness of the side plate linearly has increased the yield strength and ultimate strength of these dampers. Finally, it was found that the increase in shear plate stiffness can directly increase the energy absorbed by this type of damper, effectively improving the seismic capacity of YSPD dampers.

Multiple-degree-of-freedom damping characteristics evaluation of dual halbach array eddy current damper for turbopump in cryogenic environment

Liquid hydrogen turbopumps are used in large high-performance rockets. Stable high-speed rotation is required for rocket turbopumps. The damping mechanism of the pump must suppress vibration not only in the radial direction but also in the axial direction. However, conventional damping elements using oil or rubber cannot be used due to the cryogenic temperature of liquid hydrogen. Therefore, the application of eddy current dampers to liquid hydrogen turbopumps is focused on in this paper. Although various structures of eddy current dampers have been developed, the multi-degree-of-freedom damping characteristics of dual Halbach array type eddy current dampers for liquid hydrogen turbopumps have not yet been investigated. The variation of damping characteristics with temperature has also not yet been verified. In this paper, we propose a novel dual Halbach array type eddy current damper for liquid hydrogen turbopumps. The proposed damper can generate high damping force and can be operated maintenance-free at the cryogenic temperature. The analysis results show that the damping characteristics strongly depend on temperature and that the amplitude reduction effect is greater at low temperatures. It was also found that the proposed damper has a higher damping force density than conventional dampers.

Modal analysis and vibration response test of tank body

In order to ensure the safety and stability of the oil tank in the transportation process, the dynamic response of the tank body was simulated, tested and optimized based on the finite element method and vibration testing technology. The modal vibration modes were calculated respectively under the conditions of 50 %, 75 % and 100 % liquid filling of the oil tank, and the influence of the oil content on the overall structure mode was obtained. Under the full load condition, the stress response under continuous and non-continuous impact loads was calculated. Based on the analysis results, the vibration damping elements were arranged, and the optimization effect of vibration reduction was verified and analyzed by vibration testing. The results show that full load is more conducive to the stability of the oil tank, and the vibration damping element can reduce the maximum amplitude by more than 80 %, which has good economic and social benefits.

Computer-aided rotary crane stability assessment

This paper introduces a computer-aided approach for evaluating the stability of rotary cranes. Utilizing the Motion add-in within the SolidWorks package, a comprehensive numerical stability analysis was carried out. The interaction dynamics between the crane’s support system and the ground were modeled employing linear springs, while the rope system was characterized by a blend of linear spring and damper elements. The term “temporary loss of stability” was introduced to describe scenarios wherein one support loses contact with the ground. Furthermore, ramifications of overlapping control signals on crane operational safety were investigated. Validation of the numerical findings was accomplished through experimental tests conducted on an actual crane. This integrated methodology not only enhances the understanding of crane stability but also offers practical insights for optimizing crane operations in real-world settings.

A Graph‐Based Methodology for Optimal Design of Inerter‐Based Passive Vibration Absorbers With Minimum Complexity

Passive vibration absorbers (PVAs) play a crucial role in mitigating excessive vibrations in engineering structures. Traditional PVA design typically begins with proposing a beneficial topological layout, incorporating stiffness, damping, and inertance elements, followed by optimal sizing of each element to minimise specific response of dynamically excited structures. An alternative approach involves first designing the impedance function of a PVA and then identifying a passive mechanical layout that replicates this impedance using network synthesis techniques. However, both methods struggle to identify the most efficient PVA layout using the minimum number of elements (referred to as “complexity”) for a given vibration suppression problem. To this end, this study introduces a graph‐based methodology for designing optimal configurations (i.e., layout + sizing) of two‐terminal spring‐damper‐inerter PVAs that achieve specified performance goals with minimum complexity. In this approach, a PVA is represented as a weighted coloured multigraph, enabling the application of a novel graph‐based enumeration technique to generate the full set of potential layouts from any given number of mechanical elements. This enumeration is followed by a performance assessment of all layouts to pinpoint the optimal absorber configuration for the given problem. The methodology’s automation capability and versatility make it suitable for various civil and mechanical engineering applications. The effectiveness of the proposed methodology is demonstrated through two case studies: a vibration absorber design for a wind‐excited tall building and a suspension design for a road vehicle. In both cases, the proposed methodology successfully identifies innovative PVA layouts that surpass traditional designs with minimum additional elements.

Study on Mechanical Properties of Rubber Damping Element under Cyclic Load

Study on Mechanical Properties of Rubber Damping Element under Cyclic Load

Dynamics of a beam with variable cross-section protected from vibration

In this work, the issue of transverse vibrations of a hysteresistype elastic dissipative characteristic beam with a dynamic absorber is considered. In order to evaluate the effectiveness of the dynamic absorber, i.e., to select its optimal parameters, analytical expression of transfer function is determined. The problem of dynamic damping of nonlinear transverse vibrations of an elastic beam with variable cross-section is solved. In this case, the dissipative properties of the beam material and the elastic damping element of the dynamic absorber are hysteresis type and are taken into account by a nonlinear function of one value. Using the method of harmonic linearization

Turn Compensation Control Development and Analysis for a Self-Propelled Sprayer Chassis Suspension System

Highlights An Experimental sprayer chassis suspension control system was developed and evaluated in headland turns. Turning evaluation performance metrics and methods were conceptualized in the context of sprayers. The Experimental chassis suspension system showed stability and comfort increases during aggressive turns. Boom stability improved significantly after completion of the turn for the Experimental suspension system. Abstract. A challenging economic, environmental, and regulatory landscape causes the need for efficient agricultural machinery. The performance of self-propelled sprayers depends on their ability to deposit chemicals accurately and efficiently, and increased machine sizes and faster driving speeds require consideration for sprayer chassis stability. One method of improving this stability is using variable damping elements in the sprayer chassis suspension system. In this work, an Experimental sprayer chassis suspension system that implemented turning event detection and variable damping control was developed for headland turning events. The Experimental chassis suspension system was tested for a constant speed headland turn maneuver at 10 to 25 m turn radii. The performance of the Experimental system was quantified in terms of operator comfort and operator health, chassis roll and roll rate amplitudes, and boom height sensor standard deviation, and this performance was compared to a Baseline sprayer suspension configuration. From the data collected, the Experimental suspension system improved chassis roll and roll rate stability by 30% to 40% for the entry portion of the turning event regardless of turn radius while also showing a 5% increase in ride quality. The need for tuning the damping level to the chassis yaw rate was identified from decreased comfort performance metrics at larger turn radii. Boom height stability improved significantly for Experimental suspension configurations, particularly after the turning event, showing an 8% to 21% improvement in boom height standard deviation. Further exploration of control parameters and their effects outside turning events should be conducted to ensure optimal control law settings based on machine configurations. Keywords: Chassis suspension, Control, Performance, Self-propelled sprayer, Stability, Turn event, Variable damping.

Vibration Research on Centrifugal Loop Dryer Machines Used in Plastic Recycling Processes

This study investigates the vibrations of centrifugal loop dryer machines used in plastic recycling processes. These machines are characterized by large uncertainties, high vibration, and unmodeled dynamics, making the design and maintenance of real-time state estimators for their operational conditions difficult. The present study includes an analysis of the centrifugal loop dryer machines’ vibration characteristics and their influence on operation results based on vibration analysis, frequency response analysis, and expert advice. Two identical loop dryers installed and operated in parallel in a single recycling line were investigated. Measurements were performed using a two-sample measurement design and based on a one-sample statistical method for estimating uncertainty in repeated measurements of data processing. Additionally, a problem connected with incorrect machine operation during high vibration, resulting in insufficient drying of loaded material, was investigated. This was defined as a situation in which some melted plastic is still too wet after mechanical drying, caused by the incorrect installation of damper elements of the holding elements. Finaly, it is recommended that a correction of the machine installation and a control measurement are carried out to determine whether the vibration in the base of the machine still exists. A simplified theoretical vibration analysis of the rotating machine was also carried out in the present paper.

A physiologically enhanced muscle spindle model: using a Hill-type model for extrafusal fibers as template for intrafusal fibers

The muscle spindle is an essential proprioceptor, significantly involved in sensing limb position and movement. Although biological spindle models exist for years, the gold-standard for motor control in biomechanics are still sensors built of homogenized spindle output models due to their simpler combination with neuro-musculoskeletal models. Aiming to improve biomechanical simulations, this work establishes a more physiological model of the muscle spindle, aligned to the advantage of easy integration into large-scale musculoskeletal models. We implemented four variations of a spindle model in Matlab/Simulink®: the Mileusnic et al. (2006) model, Mileusnic model without mass, our enhanced Hill-type model, and our enhanced Hill-type model with parallel damping element (PDE). Different stretches in the intrafusal fibers were simulated in all model variations following the spindle afferent recorded in previous experiments in feline soleus muscle. Additionally, the enhanced Hill-type models had their parameters extensively optimized to match the experimental conditions, and the resulting model was validated against data from rats’ triceps surae muscle. As result, the Mileusnic models present a better overall performance generating the afferent firings compared to the common data evaluated. However, the enhanced Hill-type model with PDE exhibits a more stable performance than the original Mileusnic model, at the same time that presents a well-tuned Hill-type model as muscle spindle fibers, and also accounts for real sarcomere force-length and force-velocity aspects. Finally, our activation dynamics is similar to the one applied to Hill-type model for extrafusal fibers, making our proposed model more easily integrated in multi-body simulations.

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.

Discrete element models for elasto-plastic wave propagation in nonlinear architected materials

Nonlinear architected materials are known to exhibit a plethora of dynamic phenomena that enhance our capacity to manipulate elastic waves. Since these properties stem from complex, subwavelength geometry, dynamic simulations at high resolutions are often intractable at scales of interest. Therefore, prior studies have turned to effective medium models that capture essential properties in the long-wavelength limit. One class of such models is a periodic structure composed of discrete mass, spring, and damper elements, whose constitutive relationships are computed to match behaviors observed in experiments or fine-scale simulations of representative volume elements. While models of this type have been implemented successfully in many cases, the majority of literature has been focused on recoverable deformation, possibly including linear damping. However, history-dependent effects, such as friction and plasticity, have been much less explored. In this work, we develop a discrete element modeling framework for nonlinear architected materials undergoing plastic deformation. Due to the history- and rate-dependent characteristics of plasticity, the framework generally yields a system of differential-algebraic equations whose computational cost is significantly greater than an elastic system of comparable size. We demonstrate the method using several examples from the literature and explore means to obtain phenomenological plasticity models for general geometries.

Development of Empirical Model for Electromagnetic Damping Coefficient Damper

The significance of the electromagnetic damper in vibration systems has attracted considerable interest from researchers, making it a prominent area of research. Various papers have been consulted to explore the vibration concept associated with electromagnetic dampers and their practical applications. A vibration test rig with a simple electromagnetic damper has been designed and tested to investigate the effect of electromagnetic force. An experimental study on the response of the electromagnetic damper was conducted. A logarithmic decrement method was deployed to find the damping coefficient, c, of a one-degree freedom system (mass spring damper system). A test rig and electromagnetic damper element were introduced as a damper in the system. Design factors included the type of geometry, type of material and the current supply to the system. The testing was conducted using the in-house developed vibration test rig. The data obtained from the experiment has been analysed to determine the electromagnetic damping performance. A factorial analysis was performed to identify the significant factors influencing the damping coefficient of the system. Two empirical models obtained through regression analysis of Excel and Minitab. It was found that the influential effects for the response are the type of material (aluminum), slotted geometry and a bigger amount of current (3 A). The application of a cylindrical conductor and magnet as a damper reduced the vibration response of spring mass damper.

Multimode TED-tuned beam mass damper for low-g capacitive MEMS accelerometers VRE reduction

Capacitive Micro-Electro-Mechanical Systems (MEMS) accelerometers for quasi-static applications are susceptible to vibration rectification error (VRE) when the ambient AC vibration signals get rectified to DC. Studies to mitigate the VRE have relied on the sigma-delta filtering algorithm with closed-loop feedback as well as the adoption of vibration-insensitive frequency modulation (FM) instead of conventional amplitude modulation. In this study, we propose a novel solution to VRE caused by asymmetric railing introducing multimode thermoelastic damping (TED) tuned beam mass damper (TBMD) integrated into the MEMS accelerometer effectively functioning as a compensator. Our contribution breaks through the microfabrication limitation of damping elements by utilizing intrinsic TED in MEMS material. The damper elements were alternately tuned up to the third flexural mode due to MEMS manufacturing constraints. This was done through parametric sweeps in numerical simulations on single-axis capacitive MEMS accelerometer integrated with multimode TED-damped TBMD. According to simulation results, the higher the mode shapes of the TED-damped tuned beam mass damper, the higher the damping effect and the better the vibration rectification factor.

Random vibration analysis of nonlinear structure with viscoelastic nonlinear energy sink

Most engineering structures serve in complex and harsh dynamic environments and suffer from nonlinear vibrations generated by random excitations such as strong winds and waves, which need to be mitigated. To this end, a novel viscoelastic nonlinear energy sink (VNES) device is proposed for the vibration control of structures, whereby the random vibration of a nonlinear oscillator with a VNES device is analyzed in this paper. Specifically, the mathematical model of the structure-VNES is formulated. An approximate technique for the treatment of viscoelastic damping element modeled by the fractional derivative is developed, whereby an equivalent nonlinear system without fractional derivative is derived. The averaged Itô equations associated with the amplitude envelopes are then obtained by resorting to the stochastic averaging method. The closed-form solution of the stationary response is solved from the Fokker–Planck–Kolmogorov (FPK) equation and verified by the Monte Carlo simulation (MCS) data simultaneously. The effects of system parameters and noise intensity on the stationary response are sequentially examined. By comparing the VNES system to the case without attachment and one equipped with the commonly used tuned mass damper (TMD) device, the performance and robustness of the VNES are highlighted. The conclusions of this work may contribute to the efficacy of the application of the VNES in practice.

A configuration-optimisation method for passive-active-combined suspension design

Active control can improve the performance of a passive vehicle suspension, but it comes with a high power consumption and large actuator forces. To balance dynamic performance and power/force needs, both the passive and active parts in the suspension should be designed together and work synergistically. Previous approaches that combine passive and active design have been limited to a narrow range of suspension structures, such as passive-active-parallel layouts. This leaves many other structures unable to be explored (e.g., passive-active-series layouts), and thus the current identified design may be far from optimal. Another limitation is that these previous approaches assume an ideal active part and do not consider the parasitic effects of a physical active actuator and its transmission system, such as backlash, friction and inertia. This simplification would hinder their practical application in real-life situations. To address these two limitations, this work introduces a novel design method for passive-active-combined suspensions. Firstly, it allows for the enumeration of all possible suspension designs consisting of a pre-determined number of stiffness, damping, inertance and active actuator elements. Secondly, the method takes into account the parasitic effects that arise from physical realisation when identifying the optimal suspension design. The effectiveness of this method is demonstrated through a quarter-car case study, where the skyhook controller is adopted as an example control strategy. It is found that compared to the traditional combined suspension, the identified design achieves a significant improvement in the trade-off between ride comfort and required active force. The obtained results are verified experimentally.

Artificial boundary condition for Klein-Gordon equation by constructing mechanics structure

An innovative local artificial boundary condition is proposed to numerically solve the Cauchy problem of the Klein-Gordon equation in an unbounded domain. Initially, the equation is considered as the axial wave propagation in a bar supported on a spring foundation. The numerical model is then truncated by replacing the half-infinitely long bar with an equivalent mechanical structure. The effective frequency-dependent stiffness of the half-infinitely long bar is expressed as the sum of rational terms using Pade approximation. For each term, a corresponding substructure composed of dampers and masses is constructed. Finally, the equivalent mechanical structure is obtained by parallelly connecting these substructures. The proposed approach can be easily implemented within a standard finite element framework by incorporating additional mass points and damper elements. Numerical examples show that with just a few extra degrees of freedom, the proposed approach effectively suppresses artificial reflections at the truncation boundary and exhibits first-order convergence.