Force Motion Research Articles

Generalization of the Den Hartog model and rule-of-thumb formulas for optimal tuned mass dampers

In recent years, the need of improving safety standards for both existing and new buildings against earthquake and wind loads has created a growing interest in the use of the so-called tuned mass dampers, exploited to control, in active or passive way, the dynamic response of structures. To design and optimize tuned mass damper systems, the effective analytical procedure proposed by Den Hartog in his seminal work (Den Hartog, 1985) has been widely adopted over the years, without including damping of the main structure. However, in many cases of engineering interest, the damping of the primary system plays a key role in the overall mechanical response, with the result of an increase in complexity of the related optimization problem, which are in fact solved in the vast majority by means of ad hoc numerical procedures. In the present work, we recover the classical optimization strategy by Den Hartog and generalize it by including the main system’s damping, providing new analytical solutions whose results are consistent with the few ones obtained through alternative mathematical methods by Thompson (1981) and Krenk (2005) and subsequently by Fang et al. (2019). In particular, some closed-form solutions and helpful rule-of-thumb formulas for the optimal setting of the design parameters are derived, by considering two types of incoming excitations, i.e. the force acting on the main mass and the ground motion input, both of interest for engineering applications. Finally, theoretical outcomes are compared with consolidated data from the literature. • Generalization of the Den Hartog model and analytical derivation of optimal tuning frequency ratio and damping of the absorber in Tuned Mass Dampers subjected to force or ground motion inputs. • Definition of rule-of-thumb formulas for design purposes. • Comparison of results from proposed analytical approach and numerical analyses to show advantages and effectiveness of the method, also for design parameters out of classical ranges. • Explicit expressions for optimal Tuned Mass Damper configurations in cases of stochastic ground motion input.

Experiments on the localized interaction at the interface fuel rod/spacer grid in pressurized water reactors

The release of fissile material into the coolant caused by fretting of the fuel rods at the interface with spacer grids is a significant safety issue and cause of financial losses in the operation of Pressurized Water Reactors (PWRs). Each fuel rod is kept in position inside spacer grids through friction from the preload exerted by retaining elements (springs and dimples). Fretting of the fuel rods occurs at the contact with the springs and dimples. In severe fretting cases the integrity of the fuel rod cladding is compromised and fission byproducts enter the primary coolant circuit. The reciprocating motion at the contact interface of the fuel rods and spacer grids resulting in material fretting is due to the Flow-Induced Vibrations (FIV) of fuel rods, caused by the unstable surrounding coolant flow, which in PWRs is predominantly parallel to the length of fuel rods (axial flow). Under specific flow conditions, fretting develops rapidly. The vibrations of fuel rods, as well as the relationship of fretting wear mechanisms with several factors associated with the fission process and coolant flow dynamics and stability (vibration amplitude, preload, oscillating loads, irradiation, axial slip, spring relaxation, temperature, oxidation, material of spacer grids and fuel rods), have been considered in the literature. However, direct experimental measurements of the contact force and axial slip during FIV have not been treated in the literature, likely because of the absence of suitable measurement methods. This gap in experimental measurement techniques is addressed in this work, specifically for the analysis of PWR fuel assemblies, by installing a piezoelectric stack and aiming laser Doppler vibrometers on a one-meter-long fuel rod, supported by two full-scale spacer grids, in-air or immersed in quiescent water. In the presence of small- and large- amplitude forced vibrations, the signal of the piezoelectric force transducer increases with the amplitude of vibration, but it is also affected by vibrations perpendicular to the excitation, which appear for large-amplitude excitations. The axial motion of the fuel rod at the spacer grid has a complex evolution and is significant for large-amplitude vibrations only. At any rate, the time histories of contact force and axial motion display the effects of impacts and slips, particularly during the tests in water. The measurement system shows that the severity of the interaction at the spacer grid interfaces is influenced strongly by the amplitude of the forced fuel rod vibrations. Since fuel rods and fuel assemblies are prone to several nonlinear phenomena, as demonstrated by recent studies, it follows that the usage of nonlinear models will be essential to numerically estimating the severity of fretting.

Dynamic modeling and analysis of large axially deployable spacecraft under gravity gradient

Many spacecrafts are designed with extendible, deployable, or inflatable appendages to achieve various desirable ultra-large configurations in space, which brings new challenges to the dynamic modeling and analysis of large spacecrafts. In this paper, flexible vibration and attitude angle coupling dynamic behavior of an axially deployable spacecraft considering the effects of gravity gradient are investigated. First, an improved spacecraft’s coupled dynamic model is constructed based on the Euler–Bernoulli beam theory and Hamilton’s principle while accounting for the axial motion and gravity gradient for the first time. Then, a practical deployment strategy is adopted to resolve the problem of speed residue. In addition, the effects of gravity gradient force and extension motion on deploying process, long-time evolution of the flexible vibration, and attitude motion of the spacecraft are investigated. The results indicate that the gravity gradient force and the coupling effects may alter the stability of the spacecraft system with a short deploying time, and result in a new absolute minimum value for the flexible vibration. This investigation provides constructive guidance for the attitude adjustment scheme and deployment strategy design of large-scale deployable spacecrafts.

A Simple Model for an Internal Wave Spectrum Dominated by Non-Linear Interactions

Ocean motions at frequencies of the internal wave band are generally associated with freely propagating waves that are supported by stable vertical stratification in density. Previous analyses of yearlong current observations from the Bay of Biscay showed that a finestructure of semidiurnal tidal and near-inertial higher harmonics fills the spectrum. Here, a simple model is presented of forced nondispersive motions with forward energy cascade. The model fits the spectral shape of higher harmonics well within statistical significance and shows that such interactions imply maximum wave steepness in a balance between forcing and turbulent mixing. The single fitting parameter takes a value of approximately one, at which the barotropic tidal flow speed equals the internal wave phase speed. We infer that the barotropic tide sets a non-linear limit to baroclinic current scales without generating non-linear higher harmonics directly.

Trapped-particle microrheology of active suspensions.

In microrheology, the local rheological properties, such as the viscoelasticity of a complex fluid, are inferred from the free or forced motion of embedded colloidal probe particles. Theoretical machinery developed for forced-probe microrheology of colloidal suspensions focused on either constant-force (CF) or constant-velocity (CV) probes, while in experiments, neither the force nor the kinematics of the probe is fixed. More importantly, the constraint of CF or CV introduces a difficulty in the meaningful quantification of the fluctuations of the probe due to a thermodynamic uncertainty relation. It is known that, for a Brownian particle trapped in a harmonic potential well, the product of the standard deviations of the trap force and the particle position is dkBT in d dimensions, with kBT being the thermal energy. As a result, if the force (position) is not allowed to fluctuate, the position (force) fluctuation becomes infinite. To allow the measurement of fluctuations in theoretical studies, in this work, we consider a microrheology model in which the embedded probe is dragged along by a moving harmonic potential so that both its position and the trap force are allowed to fluctuate. Starting from the full Smoluchowski equation governing the dynamics of N hard active Brownian particles, we derive a pair Smoluchowski equation describing the dynamics of the probe as it interacts with one bath particle by neglecting hydrodynamic interactions among particles in the dilute limit. From this, we determine the mean and the variance (i.e., fluctuation) of the probe position in terms of the pair probability distribution. We then characterize the behavior of the system in the limits of both weak and strong trap. By taking appropriate limits, we show that our generalized model can be reduced to the well-studied CF or CV microrheology models.

Reactive Task Adaptation of a Dynamic System With External Disturbances Based on Invariance Control and Movement Primitives

This article proposes a general control framework for robot physical contact tasks. To satisfy the tradeoff between safety and performance in the interaction between robots and the environment, multipriority control is regarded as a preemptive strategy for constraint management when unknown disturbances exist. The equality and inequality constraints related to robot safety are enforced by invariance control, while reference profile tracking is accommodated by dynamic movement primitives without violating the higher priority constraints. With this framework, we complete the unification of force control and motion control in robot task execution. The robot thus acquires the capability for strong disturbance rejection and transferrable intelligence between similar tasks. At the same time, a variant linear–quadratic regulator (LQR) is integrated into the framework, which enables the robot to achieve exponential convergence of the tracking error. The proposed approach is tested and evaluated with two types of physical contact tasks, showing a superior control effect and faster convergence than the existing methods.

Experimental study of two kinds of hard marine growth effects on the hydrodynamic behavior of a cylinder submitted to wave and current loading

The presence of marine growth increases submarine structures diameter and roughness and thus the hydrodynamic loading due to wave and current excitation. In this paper, two kinds of hard roughness (mussels and corals) are studied experimentally. In order to cover a wide range of the dimensionless numbers (Reynolds number, Keulegan–Carpenter number and reduced speed), three kind of trials are carried out: current only, forced motions and a combination of forced motions and current. Two equivalent diameters are used for the calculation of the hydrodynamic coefficients: an equivalent diameter corresponding to the closed volume of the system, where no fluid is permitted, and an equivalent diameter based on the projected area of the colonized structure for the drag coefficient, and on the total volume for inertia coefficients.Results show that these coefficients are up to 4 times higher than those obtained for a reference cylinder. The use of a different specific diameter for inertia and drag coefficient leads to fit all results with the reference cylinder results. This standardization prove that the knowledge of the volume and the projected surface of the cylindrical structure could simplify the forces estimation applied on the system just by knowing the corresponding smooth one.

Numerical study on transient airflows and air exchange induced by door motion in thermally stratified environment

Door motion has been identified as a contribution factor for containment transport between indoor and outdoor, but the combined airflow characteristics due to door motion, ventilation airflow and thermal effects have not been clarified. This paper investigated transient airflow characteristics and amount of air exchange induced by hinged door motions in thermally stratified environment with displacement ventilation using dynamic CFD simulation. The results show that about 40% amount of air exchange occurs in the first phase when door angle β < 30° although the consumed time is only 15% of the whole door motion process. Indoor and outdoor air temperature difference and rotation speed of the hinged door are two important influencing factors. When the door motion is slow enough and temperature difference is above 3 °C, the thermal convective flow could significantly affect the airflow pattern through the doorway. When there is no indoor and outdoor temperature difference, the amount of air exchange increases linearly with door motion speed. Under combined effects of buoyancy force and door motion, a moderate door speed results in minimum air exchange. The door motion only affects the air temperatures near the door. The overall thermal stratification in the displacement ventilated room is not significantly destroyed by a single door open and close cycle. The findings could provide suggestions for reducing door motion induced contaminant transport, and enhance understanding of dynamic disturbance effects in thermally stratified environments.

Kinematic and dynamic investigation of a novel inertial propulsion drive

Today there is a great deal of controversy over the operation of inertial propulsion drives (IPD), as they challenge the laws of Newtonian mechanics. Starting with the last decades of the previous century, many devices that use the centrifugal force to generate linear propulsion were patented. Regrettably, whether we are talking about the initial, or the most recent attempts, only a few of these systems passed the patent stage and were involved for practical applications.The aim of this paper is to present an IPD, developed by the authors, which uses for generating linear motion the kinetic energy of several masses, placed in the articulation points of the links of a chain drive. The masses placed equidistantly along the half-length of the chain perform a complex movement, consisting of the specific displacement of the chain elements and a rotation around an axis, that is parallel to the line which joins the centres of the chain wheels. After deducting the equations of the geometric coordinates of the masses, the total propulsion force was computed. The obtained results are supporting the ability of the IPD to generate propulsive force and linear motion.

Metal transfer behavior during CMT-based Wire Arc Additive Manufacturing of Ti-6Al-4V alloy

CMT-Wire Arc Additive Manufacturing (CMT-WAAM) has the advantages of low heat input and high production efficiency. However, the surface geometric accuracy of the CMT- fabricated sample is inferior, especially for the deposition of titanium alloy. The focus of this study was to analyze the metal transfer behavior during CMT-WAAM of titanium alloys by a high-speed camera. The metal transfer and molten pool behaviors during the single-layer and multi-layer deposition in both CMT and CMT + P modes were compared to optimize the characteristic process parameters. The results showed that the hybrid metal transfer mode, including the short-circuit transition and the globular transition, occurred in the CMT + P mode. The effect of Ip1 on the droplet diameter was more significant than that of tp1. Under these two modes, the size and spread ability of the molten pool increased with the increase of Iboost, tp1 and Ip1. While in the CMT + P mode, Ip1 did not yield a significant influence compared with tp1. Simultaneously, noticeable oxide skin was observed on the surface of the flowing molten pool when Iboost reached 350 A in the CMT mode. Compared with the CMT mode, new spatter types were generated by arc force and droplet free-fall motion in the CMT + P mode. Ultimately, the maximum effective rate of 70.4 % was obtained in the CMT + P mode when the parameters were selected as Ip1 = 400 A and tp1 = 4 ms.

Electroplating technology of suspended diamond particles surface based on rotating electrode

In view of the difficulty of fine-grained diamond surface electroplating, a method of diamond barrel plating based on rotating electrode is proposed, which is to make the cathode rotate during the rolling process. The mechanism of dynamic contact between fine-grained particle in suspension electroplating solution and electrode is analyzed. And the force model and motion equation of diamond abrasive particles in electroplating fluid were established. The single factor experiments were carried out to study the effects of the rotation speed of the plating bottle, the rotation speed of the electrode, and the diameter of the diamond particles on the weight gain rate and the surface morphology of the suspended fine-grained diamond. The results show that the contact time between the suspended particles and the electrode can be increased when the electrode direction is opposite to that of the plating bottle, and the rotation speed should be matched with the flow rate of the plating solution to obtain a good electroplating result. The weight gain rate decreased with the decrease of particle size. For 25–36 μm diamond particles, the optimal process parameters are as follows: the rotation speed of plating bottle is 20 r/min, the electrode speed is 50 r/min, and the electrode turns opposite to the plating bottle. The smallest size range of diamond particles that can be electroplated by this method is 5–10 μm.

Improving Extreme Anchor Tension Prediction of a 10-MW Floating Semi-Submersible Type Wind Turbine, Using Highly Correlated Surge Motion Record

Extreme value prediction of the load-effect responses of complex offshore structures such as the floating wind turbine (FWT) is crucial in ultimate limit state (ULS) design. This paper considers two cases to understand the feasibility of the bivariate correction on the extreme load and motion responses of a 10-MW semi-submersible type FWT. The empirical anchor tension force and surge motion used in this study are obtained from the FAST simulation tool (developed by the National Renewable Energy Laboratory) with the load cases stimulated at under-rated, rated and above rated speeds. Then, the bivariate correction method is applied to model FWT extreme response for a 5-years return period prediction with a 95% confidence interval (CI), based on just 2 min short response record. The proposed methodology permits accurate correction of the bivariate extreme value in case of, for example, corrupted measurement sensor data. Based on the proposed novel method’s performance, it is concluded that the bivariate correction method can offer better robust and precise bivariate predictions of coupled surge motion and anchor tension of the FWT.

Vibrodynamic parameters of radial piston engines with Pencake mechanism

Introduction (problem statement and relevance). The development of calculation methods at the design stage of the balance and vibration activity of multipurpose converting mechanisms of engines differing in the classical crank mechanism is actual.The purpose of the work was to substantiate such a technique for a FSUE “NAMI” three-cylinder radial engine with a Pencake conversion mechanism designed to drive electric generators.Methodology and research methods. To solve the problem, both classical methods of piston engine dynamics and modern methods based on solid modeling and simulation of forced motion were used. Scientific novelty and results. It was found that in the investigated engines a complete balance of the inertial forces of the first-order translational masses and centrifugal forces could be achieved with the help of two counterweights on the crankshaft. The vibration levels of three-cylinder radial and in-line engines assembled from the same links have been compared and the noticeable advantages of the radial star-shaped engine were marked both in terms of the root-mean-square values of vibration velocity and in its spectral vibration.Practical significance. The results of the work can be used in practical development.

System Comparison for Gait and Balance Monitoring Used for the Evaluation of a Home-Based Training.

There are currently no standard methods for evaluating gait and balance performance at home. Smartphones include acceleration sensors and may represent a promising and easily accessible tool for this purpose. We performed an interventional feasibility study and compared a smartphone-based approach with two standard gait analysis systems (force plate and motion capturing systems). Healthy adults (n = 25, 44.1 ± 18.4 years) completed two laboratory evaluations before and after a three-week gait and balance training at home. There was an excellent agreement between all systems for stride time and cadence during normal, tandem and backward gait, whereas correlations for gait velocity were lower. Balance variables of both standard systems were moderately intercorrelated across all stance tasks, but only few correlated with the corresponding smartphone measures. Significant differences over time were found for several force plate and mocap system-obtained gait variables of normal, backward and tandem gait. Changes in balance variables over time were more heterogeneous and not significant for any system. The smartphone seems to be a suitable method to measure cadence and stride time of different gait, but not balance, tasks in healthy adults. Additional optimizations in data evaluation and processing may further improve the agreement between the analysis systems.

Analysis of transient longitudinal dynamic behavior of tire on μ-step road

In this paper, the variation of tire longitudinal force and vehicle motions is studied when vehicle passing through the boundary of two road surfaces with different friction coefficient. The critical longitudinal slip of total sliding on the front and back roads is obtained by theoretical analysis. Then the variation of longitudinal force in different range of longitudinal slip is analyzed and a mathematical model is established to describe the transient force characteristics of tire. The longitudinal force, the longitudinal slip, the forward speed, and the angular velocity of the wheel on μ-step road are tested experimentally for different initial longitudinal slips, compared the tested results with those calculated by mathematical model. The results show that the initial longitudinal slip before passing through the road boundary is directly related to the change of longitudinal force and vehicle motions. The larger the initial longitudinal slip is, the more obvious the transient characteristics of the tire will be. For the vehicle driving from high-adhesion-road to low-adhesion-road. When the initial longitudinal slip is small, the longitudinal force decreases rapidly at first, and then quickly returns to the original value and remains constant on the low-adhesion-road. When the initial longitudinal slip exceeds the maximum recoverable longitudinal slip, the reduced longitudinal force cannot be recovered or can only be partially recovered on the low-adhesion-road. For the case of low-adhesion-road to high-adhesion-road, the longitudinal force will continue to increase as the tire passes through the boundary, and then gradually decrease to the original value when contact area passes through the boundary completely. In generally, the increased initial slip rate will not cause the longitudinal force irrecoverable. The relevant conclusions can provide theoretical references for vehicle dynamics and ABS control.

Numerical computation of effective thermal equilibria in stochastically switching Langevin systems.

Stochastically switching force terms appear frequently in models of biological systems under the action of active agents such as proteins. The interaction of switching forces and Brownian motion can create an "effective thermal equilibrium," even though the system does not obey a potential function. In order to extend the field of energy landscape analysis to understand stability and transitions in switching systems, we derive the quasipotential that defines this effective equilibrium for a general overdamped Langevin system with a force switching according to a continuous-time Markov chain process. Combined with the string method for computing most-probable transition paths, we apply our method to an idealized system and show the appearance of previously unreported numerical challenges. We present modifications to the algorithms to overcome these challenges and show validity by demonstrating agreement between our computed quasipotential barrier and asymptotic Monte Carlo transition times in the system.

Calculated estimation of influence of convection rate of molten working and heating medium during hardening of restored parts

The paper presents a computational and mathematical assessment of the convection rate of the molten working and heating medium during the strengthening of the restored parts. The calculated estimate is based on the theory of multidimensional heat and mass transfer processes occurring in the electrode furnace during the strengthening of the restored parts. Computational modeling is carried out based on the choice of initial data and characteristics. The calculation results made it possible to establish the effect of the convection rate of the molten working and heating medium on the hardening of the restored parts. The theoretical description of the conditions for the onset of convective motion of a molten continuous medium is based on the Rayleigh–Bénard, Navier–Stokes, and Lorenz equations for the flow of a viscous continuous medium using the Oberbeck-Boussinesq approximation. The description of the internal space of the tank furnace is carried out by a system of differential equations of the balances of elementary volumes into which it is divided. Transformations into a system of differential equations are carried out on the basis of the Galerkin method. The use of this transition method leads to the fact that the sought functions are represented in a variable-separated form that exactly satisfies the boundary conditions. The introduction of assumptions and boundary conditions made it possible to obtain the equations of motion of mass forces and a viscous medium in a polar coordinate system. A formula describing the configuration of the temperature field is obtained.

Exploration of Thermophoresis and Brownian motion effect on the bio-convective flow of Newtonian fluid conveying tiny particles: Aspects of multi-layer model

This research deals with the analysis of bioconvection caused by the movement of gyrotactic microorganisms. The multi-layer immiscible Newtonian fluid flowing through the vertical channel conveying tiny particles is accounted. The immiscible fluids are arranged in the form of a sandwich where the middle layer has a different base fluid that does not mix with the base fluid of the adjacent fluid layer. This separation of the fluid layers gives rise to the interface boundary conditions. Such flows have found applications in electronic cooling and solar reactors processes. Buongiorno’s model has been incorporated to design the mathematical model that describes the three-layer flows of Newtonian fluid conveying tiny (metal/oxide) particles under thermophoretic force and Brownian motion. The model thus formed is in the form of the ordinary differential system of equations that are solved using the DTM-Pade approximant after non-dimensionalization. The limited results have an excellent comparison with the existing literature results. The results are discussed through graphs and tables. It is seen that thermophoresis enhances the temperature and particle concentration of the fluid whereas, the Brownian motion is found to enhance the temperature and decrease the concentration. The presence of bioconvection helps in achieving enhanced energy and mass transportation. Moreover, the heat transfer occurring between the different base fluids helps to maintain the optimum temperature in the systems.

Wind-Induced Instability Mechanism of Old Tacoma Narrows Bridge from Aerodynamic Work Perspective

Postflutter limit cycle oscillations (LCOs) are typical nonlinear aeroelastic phenomena for bridge girders. An H-shaped section with a roughly 5:1 aspect ratio, treated as a simplified section of the Old Tacoma Narrows Bridge, was chosen for wind-induced instability re-evaluation, considering its vibration amplitude-dependent aerodynamics characteristics and nonlinear structural damping effects from the energy perspective of aerodynamic work. Forced vibrations at large torsional amplitudes in a wind tunnel were realized with the help of an improved forced motion apparatus (FMA), and synchronous measurements of forces and displacements on the FMA were achieved. Self-excited forces (SEFs) were extracted, and an energy map showing quantitative relationships between vibration amplitude, reduced velocity, and aerodynamic work acting on the section were established. Furthermore, the postflutter LCOs phenomena originating from the energy balance between nonlinear aerodynamic work input and energy consumption by structural damping effects were reillustrated, and nonlinear structural damping effects of prototype bridges are therefore discussed. Moreover, the instability paths of the bridge were investigated by the energy map, considering its vibration amplitude-dependent aerodynamics and structural damping effects from an aerodynamic work perspective. The results show that LCO velocity basically increases with vibration amplitude at different structural damping ratios in torsional degree of freedom, characterizing postflutter LCOs phenomena. The structural damping ratio at the bridge’s collapse is also re-estimated as about 0.0115 with better coincidence of on-the-spot observation and theoretical analysis. In addition, both the aerodynamic damping ratio considering nonlinear characteristics of the SEFs and the structural damping ratio basically increasing with vibration amplitude contribute to postflutter LCOs phenomena of the Tacoma Bridge. The instability paths of the bridge essentially rely on the competitive relationships between structural damping ratios, structural stiffness degeneration, and oncoming wind velocities in the process of collapse.

Level of Conceptual Understanding Among Secondary Students on Topic of Forces and Motion Using Half-Length Force Concept Inventory (HFCI)

This study aimed to identify the level of understanding of secondary school students on the topic of forces and motion as a whole as well as based on different genders. A total of 73 students from one of International School was selected as respondent. This survey study used the Half-Length Force Concept Inventory (HFCI) model. Data were analyzed using the IBM Statistical Package for Social Science (SPSS) Statistics version 26. The study found that the level of understanding of secondary school students on forces and motion topic was at low level. The misconception found in the aspect of force motion related to Newtonian concept of force. There was a significant difference in term of level of conceptual level of understanding in forces and motion topic between male and female students (M = 43.88, p =.001) which is less than .05. Results showed that the students having low level of conceptual understanding in forces and motion topic. This also will give some insights to teacher at secondary level towards identifying weakness among students on topic of forces and motion as well as improving method of approach in teaching and learning to students.