Degree Of Freedom Model Research Articles

Nonlinear dynamics of a flexible rod partially sliding in a rigid sleeve under the action of gravity and configurational force

We investigate various methods of analyzing systems with moving boundaries, using as an example a flexible rod sliding in an ideal frictionless sleeve in the field of gravity. Special attention is paid to the configurational force acting on the rod at the sleeve opening and thus determining the rod’s dynamics. The non-material kinematic description used in simulations is based on the re-parametrization of the Lagrangian arc length coordinate. The variational formulation uses the energy expressions written for the entire rod, comprising the free segment and the one inside the sleeve. A novel finite element scheme is efficient for highly flexible rods, which may undergo complete ejection. A simplified two degrees of freedom model, which accelerates simulations, shows a good agreement as the bending stiffness increases. An analytical study using Hamiltonian mechanics exploits the separation of variables into fast oscillations and slow axial motion. The adiabatic invariant approach leads to approximate closed-form solutions for the slow dynamics and yields the maximum injection depth of the rod into the sleeve.

Degrees of Freedom: Search Cost and Self-consistency

Model degrees of freedom ( df ) is a fundamental concept in statistics because it quantifies the flexibility of a fitting procedure and is indispensable in model selection. To investigate the gap between df and the number of independent variables in the fitting procedure, Tibshirani (2015) introduced the search degrees of freedom ( sdf ) concept to account for the search cost during model selection. However, this definition has two limitations: it does not consider fitting procedures in augmented spaces and does not use the same fitting procedure for sdf and df . We propose a modified search degrees of freedom ( msdf ) to directly account for the cost of searching in either original or augmented spaces. We check this definition for various fitting procedures, including classical linear regressions, spline methods, adaptive regressions (the best subset and the lasso), regression trees, and multivariate adaptive regression splines (MARS). In many scenarios when sdf is applicable, msdf reduces to sdf . However, for certain procedures like the lasso, msdf offers a fresh perspective on search costs. For some complex procedures like MARS, the df has been pre-determined during model fitting, but the df of the final fitted procedure might differ from the pre-determined one. To investigate this discrepancy, we introduce the concepts of nominal df and actual df , and define the property of self-consistency, which occurs when there is no gap between these two df ’s. We propose a correction procedure for MARS to align these two df ’s, demonstrating improved fitting performance through extensive simulations and two real data applications.

Euclid preparation

We investigate the accuracy of the perturbative galaxy bias expansion in view of the forthcoming analysis of the Euclid spectroscopic galaxy samples. We compare the performance of a Eulerian galaxy bias expansion using state-of-the-art prescriptions from the effective field theory of large-scale structure (EFTofLSS) with a hybrid approach based on Lagrangian perturbation theory and high-resolution simulations. These models are benchmarked against comoving snapshots of the flagship I N-body simulation at z = (0.9, 1.2, 1.5, 1.8), which have been populated with Hα galaxies leading to catalogues of millions of objects within a volume of about 58 h−3 Gpc3. Our analysis suggests that both models can be used to provide a robust inference of the parameters (h, ωc) in the redshift range under consideration, with comparable constraining power. We additionally determine the range of validity of the EFTofLSS model in terms of scale cuts and model degrees of freedom. From these tests, it emerges that the standard third-order Eulerian bias expansion – which includes local and non-local bias parameters, a matter counter term, and a correction to the shot-noise contribution – can accurately describe the full shape of the real-space galaxy power spectrum up to the maximum wavenumber of kmax = 0.45 h Mpc−1, and with a measurement precision of well below the percentage level. Fixing either of the tidal bias parameters to physically motivated relations still leads to unbiased cosmological constraints, and helps in reducing the severity of projection effects due to the large dimensionality of the model. We finally show how we repeated our analysis assuming a volume that matches the expected footprint of Euclid, but without considering observational effects, such as purity and completeness, showing that we can get constraints on the combination (h, ωc) that are consistent with the fiducial values to better than the 68% confidence interval over this range of scales and redshifts.

Peak angular momentum of pirouettes by a university-level contemporary dance cohort

Turning movements are an important movement to master in many dance styles. For advanced or professional dancers, the pirouette (completing one or more turns with a specific stylistic form) is difficult to master and increasing the revolutions heightens difficulty further. The purpose of this study was to investigate peak angular momentum generation (PAM) of completing single- and attempting triple-revolution pirouettes for contemporary dance students. Adaptations made by dancers whilst rotating and imbalances within the centre of mass over the base of support were identified. Ethical approval was received. Seven female university-level contemporary dance students completed five successful single-revolution pirouettes en dehors (PeDh) and attempting to complete five successful triple-revolution PeDh whilst being recorded using a three-dimensional VICON motion capture system. PAM and torso lean (TL) and a two-dimensional foot vector (FV) were then calculated using a six degree of freedom model (Visual3D). A one-way ANOVA (P < 0.05) compared mean variance between single-, double-, and triple-revolution pirouettes. Significant effects were determined for all variables in each pirouette condition. A Tukey post-hoc test (P < 0.05) determined overall significant differences between PAM (F2, 37 = 15.8, ⍵² = 0.426), TL (F2, 37 = 3.4, ⍵² = 0.108), and FV (F2, 30 = 4.9, ⍵² = 0.192) for the midpoint turn of each pirouette condition. Independent samples T-Tests (𝛼 < 0.05) were conducted to compare PAM (t11 = 1.8, d = 1.026), TL (t11 = 0.1, d = 0.030), and FV (t6 = 0.6, d = 0.433) between successful and unsuccessful double pirouettes, with no differences reported. This test was repeated for successful and unsuccessful triple pirouettes. Again, no differences were observed for PAM (t15 = −2.2, d = −1.093), TL (t15 = −1.6, d = −0.802), and FV (t15 = −1.3, d = −0.648). This study concluded that PAM increased as the number of pirouette revolutions increased. Furthermore, a minimum threshold for PAM was calculated to produce successful double (0.597 kg·ms2⎺¹) and triple (0.637 kg·ms2⎺¹) pirouettes. Observations from the pirouette trials and FV data illustrated that dancers ‘hop’ when an imbalance is sensed, in an attempt to regain balance and continue pirouette revolutions. However, this method predominately produced unsuccessful pirouettes as the initial PAM was not achieved. This research can be applied to dance coaching as it provides an initial insight into mechanisms to support successful pirouette technique.

Computational and experimental studies of wave–structure interaction: Wave attenuation by a floating breakwater

Interactions between surface gravity waves and a floating rigid body are complex, as waves may reflect from, break on, and be transmitted behind the body. Studies of these phenomena are critically important in improving the safety and functional efficiency of offshore structures. Here, the wave attenuation performance and motions of a type of floating breakwater (FB) are studied through numerical and experimental approaches. A numerical wave tank (NWT) is developed based on the software OpenFOAM and properties of wave channel from a laboratory. In the NWT, the air–water interface is captured by the volume of fluid method. The motions of FB are tracked by the six degrees of freedom model. A mooring system model is developed to simulate the constraints of the FB. Large eddy simulation turbulence modeling is implemented for the wave breaking processes. A model FB with a scale of 1:20 is tested in both the experimental and numerical wave channel. Wave heights at the back/front of the FB and the constraint forces of the mooring wires are measured. The numerical models are validated by comparing the results with experimental measurements. The variations of transmission/reflection coefficients, energy dissipation rate, and maximum mooring force are calculated. Changes of the response amplitude operators with the ratio of FB width to wavelength ( B / L w) and wave steepness are analyzed. The wave transmission coefficient will drop below 0.8 if the value of B / L w is larger than 0.3, but will go over 0.95 if B / L w is less than 0.1. Wave steepness has a large influence on FB motions and the mooring system. The effect of Stokes drift is observed by the shift of position of the FB.

A Comparative Study of Integrated Vehicle–Seat–Human Models for the Evaluation of Ride Comfort

In the literature the value of the driver’s head acceleration has been widely used as an objective function for the modification of the suspension and/or the seat characteristics in order to optimize the ride comfort of a vehicle. For these optimization procedures various lumped parameter Vehicle–Seat–Human models are proposed. In the present paper a Quarter Car model is integrated with three Seat–Human models with different levels of detail. The level of detail corresponds to the number of degrees of freedom used to describe the Seat–Human system. Firstly, the performance of the Quarter Car model, used as a basis, is analyzed in six excitations with different characteristics. Then, the performance of the three lumped parameter Vehicle–Seat–Human models are monitored in the same excitations. The results indicated that in the case of single disturbance excitations the Quarter Car model provided 50–75% higher values of acceleration compared with the eight degrees of freedom model. As far as the periodic excitation is concerned, the Vehicle–Seat–Human models provided values of acceleration up to eight times those of the Quarter Car model. On the other hand, in stochastic excitations the Vehicle–Seat–Human model with three degrees of freedom produced the closest results to the Quarter Car model followed by the eight degrees of freedom model. Finally, with respect to the computational efficiency it was found that an increase in the degrees of freedom of the Vehicle–Seat–Human model by one caused an increase in the CPU time from 2.1 to 2.6%, while increasing the number of the degrees of freedom by five increased the CPU time from 7.4 to 11.5% depending on the excitation.

Research on Yaw Stability Control Method of Liquid Tank Semi-Trailer on Low-Adhesion Road under Turning Condition

To ensure that a liquid tank semi-trailer has good yaw stability and path-following performance on low-adhesion roads under turning conditions, a multi-object PID differential braking-control method is proposed, which takes the tractor yaw rate, semi-trailer yaw rate, and articulation angle as the control parameters. According to the principle of equivalence, the trammel pendulum (TP) model is used to simulate the liquid sloshing effect in the liquid tank, and the Fluent software is used to identify the key parameters of the trammel pendulum model and verify the correctness of its simulation effect. Then, a co-simulation model is built based on TruckSim and MATLAB/Simulink. Based on the simplified six degrees of freedom model and the co-simulation model of a liquid tank semi-trailer, a multi-object PID differential braking-control method is designed, and the vehicle state responses with and without control are compared when it is turning on a low-adhesion road. The simulation results show that the proposed multi-object PID differential braking-control method can effectively improve the yaw stability and path-following performance of the liquid tank semi-trailer when turning on a low-adhesion road.

Advances in Human Biodynamic Modeling for Analysis of Whole-Body Vibrations

Low-frequency road surface or rail track inputs play an important role since humans are most susceptible to whole body vibration when in erect, seated backrest, forward lean postures. Therefore, biodynamic human subject modelling and simulation has been an area of key interest for the researchers in the past. The study reveals that the first lumped parameter single degree of freedom (DoF) model was considered by Cormann in 1962. Since then, several researchers investigated the influence of posture, vibration amplitudes and STH and BTH transmissibility analysis using different lumped parameter models starting from the basic single DoF to a complex 11 DoF models considering all possible human segments for the analysis. This paper acknowledges all those works carried out in the past.

Lateral Dynamic Simulation of a Bus under Variable Conditions of Camber and Curvature Radius

The objective of this paper is to describe a model for the simulation of the lateral dynamics of a vehicle, specifically buses, under variable trajectory conditions, such as camber and radius of curvature; in addition, a variable speed is added as a simulation parameter. The objective of this study is the prevention of vehicle rollover and sideslip. An 8 degrees of freedom model was developed, considering a front and a rear section of the bus with its respective suspension system, and both sections have been connected by a torsion spring that emulates the torsional stiffness of the vehicle chassis. A Panhard bar is also added at the rear as an additional element to the suspension and the behavior of the bus when it is added is analyzed. This model also allows the evaluation of the force on each suspension component, which allows for future controllability of the active suspension components. The results show the dynamic behavior of the vehicle, and some indicators are introduced to show the possible sideslip or rollover. As a conclusion, the influence of the road parameters on the dynamic behavior of the bus and the effect of the Panhard bar on the dynamic behavior of the bus can be pointed out.

Analysis of the Factors influencing Vehicle Handling Stability through Modelling, Equations and Python

Car handling stability means that the car can drive according to the given direction of the driver through the steering system and steering wheel when the driver does not feel too nervous or fatigue. Besides,when the car subject to external interference (uneven road, side wind, cargo or passenger partial load), it can resist interference and maintain a stable driving performance. This is very important to ensure driving safety and driving comfort. This paper mainly through the establishment of two degrees of freedom model, sets out a system of equations, solves the analysis of the change of each angle of inclination on the influence of manoeuvring stability, selected vehicle speed, used python to analyze the relationship between vehicle speed and angle of inclination, so as to analyze the relationship between the angle of inclination and the return torque and manoeuvring stability, and try to use ADAMS/CAR to form a whole vehicle dynamics model. Through the analysis of the data and results, it is achievable that the whole vehicle multi-body system could be optimized, so that the vehicle's handling stability can be significantly improved.

Tip-timing measurements of transient vibrations in mistuned bladed disks

Bladed disks are usually characterized by a rich dynamic response during service due to the occurrence of several mode shapes that vibrate at resonance within the operative range. In particular, during start-ups and shutdowns, the variable speed causes a temporary crossing of resonance that cannot be neglected to determine stress envelope and safety margins of the system during its whole mission. In fact, fluid flow induces fluctuating loads with variable frequencies (non-stationary regime) on the blades being responsible of a dynamic response which does not follow the so-called steady-state (stationary) response. This paper proposes a novel post-processing method for Blade Tip-Timing (BTT) measurements for the identification of the resonance parameters of mistuned bladed disks working in non-stationary operative conditions. The method is based on a two degrees of freedom model (2DOF) and focuses on transient resonances in which two mistuned modes with close resonance frequencies are involved in the dynamic response. In such circumstances, the identification method based on the single degree of freedom (1DOF) model usually fails.To verify the effectiveness of the method, numerical and experimental investigations have been performed. First, a mathematical simulator based on a lumped parameter model of a bladed disk system is used to generate the BTT simulated data. Experimental signals are measured using a commercial BTT system through a set of optical probes mounted circumferentially around a rotating dummy blisk. It is shown that the method produces accurate predictions for the numerical simulation, even in the presence of considerable noise levels. Moreover, experimental results confirm a successful implementation of the method on the actual BTT measurements.

Reactive burn model calibration using high-throughput initiation experiments at sub-millimeter length scales

A first-of-its-kind model calibration was performed using Sandia National Laboratories’ high-throughput initiation (HTI) experiment for two types of vapor-deposited explosive films consisting of hexanitrostilbene (HNS) or pentaerythritol tetranitrate (PETN). These films exhibit prompt initiation, and they reach steady detonation at sub-millimeter length scales. Following prior work on HNS, we test the hypothesis of approximating these explosive films as fine-grained homogeneous solids with simple Arrhenius kinetics burn models. The model calibration process is described herein using a single-step as well as a two-step Arrhenius rate law, and it consists of systematic parameter sampling leading to a reduction in the model degrees of freedom. Multiple local minima are observed; results are given for seven different optimized parameter sets. Each model set is further evaluated in a two-dimensional simulation of the critical failure thickness for a sustained detonation. Overall, the two-step Arrhenius kinetics model captures the observed behavior for HNS; however, neither model produces a good fit to the PETN data. We hypothesize that the HTI results for PETN correspond to a heterogeneous response, owing to the smaller reaction zone of PETN compared to HNS (i.e., it does not homogenize the fine-grained hot spots as well). Future work should consider using the ignition and growth model for PETN, as well as other reactive burn models such as xHVRB, AWSD, PiSURF, and CREST.

Active suspension control strategy of heavy rescue vehicle based on multi-sensor information fusion

This study proposes the active suspension control strategy of heavy rescue vehicles based on multi-sensor information fusion to address the problem of poor ride comfort and stability of heavy rescue vehicles on unstructured pavement. Firstly, an attitude fusion algorithm with acceleration compensation is designed. According to the driving speed, the appropriate cut-off frequency of acceleration filter is selected, and the extended Kalman filter is designed to complete the optimal estimation of position and attitude information. Secondly, the vehicle nine degree of freedom model is established, and the inverse matrix of attitude control is solved to obtain the suspension actuator output. Lastly, an active suspension control strategy based on multi-sensor information fusion is designed. The body attitude information after the information fusion is used for the control of active suspension system to realize the real-time adjustment of body attitude. Test results show that the root mean square values of vertical displacement, pitch angle, and roll angle under active suspension are reduced by 37.01%, 26.96%, and 38.90%, respectively, compared with those under in passive suspension. This reduction improves the ride comfort and stability of the heavy rescue vehicles on unstructured pavement.

Design of an Anti-Windup PID Algorithm for Differential Torque Steering Systems

The EV (electric vehicle) with a wheel hub motor has the advantage of independent driving torque distribution for each wheel, which allows the vehicle performance to be improved. Therefore, a lot of work has been done to investigate the torque allocation algorithm for the mechanical and differential torque integration steering system. To investigate the differential steering process, the 2 DOF (degree of freedom) dual-track reference models with linear and nonlinear tire models are established, and based on the steering process analysis and yaw rate gain calculation, a BP-NN (backpropagation neural network) model is initiated to maintain the accuracy of the calculated yaw rate gain. The limitation of DTSS (differential torque steering system) and the difference of reference models with linear and nonlinear tires are drawn. In addition, an anti-windup variable PID (proportion integration differentiation) controller is designed for the torque distribution. Based on the built 8 DOF model, the vehicle performance indicators are calculated and compared, the gap between the models with linear and nonlinear tires is non-negligible, and a reference model with a nonlinear tire model is recommended for the relevant research. The anti-windup variable PID controller has a better performance than the normal PID controller except for the stability phase plane indicator.

A Three-Dimensional Integrated Non-Linear Coordinate Control Framework for Combined Yaw- and Roll-Stability Control during Tyre Blow-Out.

A tyre blow-out can greatly affect vehicle stability and cause serious accidents. In the literature, however, studies on comprehensive three-dimensional vehicle dynamics modelling and stability control strategies in the event of a sudden tyre blow-out are seriously lacking. In this study, a comprehensive 14 degrees-of-freedom (DOF) vehicle dynamics model is first proposed to describe the vehicle yaw-plane and roll-plane dynamics performance after a tyre blow-out. Then, based on the proposed 14 DOF dynamics model, an integrated control framework for a combined yaw plane and roll-plane stability control is presented. This integrated control framework consists of a vehicle state predictor, an upper-level control mode supervisor and a lower-level 14 DOF model predictive controller (MPC). The state predictor is designed to predict the vehicle’s future states, and the upper-level control mode supervisor can use these future states to determine a suitable control mode. After that, based on the selected control mode, the lower-level MPC can control the individual driving actuator to achieve the combined yaw plane and roll plane control. Finally, a series of simulation tests are conducted to verify the effectiveness of the proposed control strategy.

Full-state modeling and nonlinear control of balloon supported unmanned aerial vehicle

PurposeThe purpose of this study is to provide the full-state mathematical model and devise a nonlinear controller for a balloon-supported unmanned aerial vehicle (BUAV).Design/methodology/approachNewtonian mechanics is used to establish the nonlinear mathematical model of the proposed vehicle assembly which incorporates the dynamics of both balloon and quadrotor UAV. A controllable form of the nine degrees of freedom model is derived. Backstepping control is designed for the proposed model and simulations are performed to assess the tracking performance of the proposed control.FindingsThe results show that the proposed methodology works well for smooth trajectories in presence of wind gusts. Moreover, the final mathematical model is affine and various nonlinear control techniques can be used in the future for improved system performance.Originality/valueMulti-rotor unmanned aerial vehicles (MUAVs) are equipped with controllers but are constrained by smaller flight endurance and payload carrying capability. On the contrary, lighter than air (LTA) aerial vehicles have longer flight times but have poor control performance for outdoor operations. One of the solutions to achieve better flight endurance and payload carrying capability is to augment the LTA balloon to MUAV. The novelty of this research lies in full-order mathematical modeling along with transformation to controllable form for the BUAV assembly.

Efficient seismic risk assessment of irregular steel‐framed buildings through endurance time analysis of consistent fish‐bone model

SummaryThe seismic risk framework of building structures has been presented to reduce earthquake‐induced adverse consequences. In this context, probabilistic analysis of engineering demand parameters (EDPs) is always associated with many uncertainties and high computational demand for use in practical applications. This study has been presented to efficiently estimate the distribution of EDPs in probabilistic seismic risk assessment of irregular steel moment‐resisting frames (SMRFs). For this purpose, the incorporation of the consistent fish‐bone (CFB) model and the endurance time (ET) analysis method has been used. The proposed method (i.e., CFB‐ET) has a substantial impact on reducing the complexities of the new generation of performance‐based earthquake engineering (PBEE) by significantly reducing the degrees of freedom (DOFs) of the original building and the number of required nonlinear time history analyses (NLTHAs). The efficiency of the proposed method has been evaluated using three 3‐, 9‐, and 20‐story SMRFs irregular in bay lengths and three other SMRFs with the same number of stories but irregular in height. In this evaluation, the maximum structural response at all seismic intensity levels up to the collapse stage and also the structural response profile along the building height at service‐level earthquake (SLE), design‐based earthquake (DBE), and maximum credible earthquake (MCE) seismic intensity levels have been investigated. Next, the efficiency of the proposed method in seismic risk assessment is investigated by using seismic fragility and vulnerability curves. The results of these evaluations have been compared with the full incremental dynamic analysis (IDA) of the full DOF model of the building (i.e., SMRF‐IDA) under 44 far‐field ground motions of FEMA P‐695 in terms of computational accuracy and effort. Furthermore, a new approach to estimating the dispersion of the structural response in the ET method has been proposed, whose efficiency has been investigated in the above‐mentioned evaluations. The results show that the proposed method allows for using the new generation of PBEE in engineering applications by significantly reducing computational demand and having sufficient accuracy in the seismic assessment process.

Effect of Damping Components With Slotted Structures on the Instability Induced by Sliding Friction

Experimental tests and numerical simulations are performed to explore the influence of damping components with slotted surface structures in a friction system on the dynamic instability. Damping components with slots at different depths are designed, combined with a special tribological test apparatus to evaluate their ability to stabilize the friction system. The experimental results show that damping components with a slotted structure can dramatically reduce the vibration response of the system and the energy level at the dominant frequency, thus stabilizing the friction system. Specifically, the system containing shallow slots on the leading edge rather than the trailing edge can eliminate the tangential partial wear and show the greatest potential on reducing the unstable vibration, which can be further verified by finite element analysis. Moreover, it is found that the contact inclination angle between the disc and the pad plays an important role in the generation of instability of the system, which can be further explained through a two degree of freedom model with a contact inclination angle.

Multi-objective optimization of vehicle seat suspension with friction under random excitation

A seat suspension contributes greatly to vehicle ride comfort as a result of direct contact with the human body. Friction in a seat suspension produces strong non-smooth nonlinearity in seat dynamics, which makes the simulation-based optimization on the seat suspension’s performance time-consuming. This study tries to address parameter optimization on a vehicle seat suspension with the friction force in an analytical approach. A two degrees of freedom model is firstly established for the human body-seat system with friction and subjected to bandlimited random excitation. The nonlinear model is converted into an equivalent linear model by using Gaussian linearization. The dynamic responses of the linear model have then derived analytically and validated by Monte Carlo simulations. Based on the analytical solution, a multi-objective optimization strategy is proposed for the seat suspension. The acceleration of the human body and the suspension travel are chosen as the objective indexes to evaluate seat performance. Simulation results show that the proposed optimization strategy is efficient, where a global optimum is guaranteed owing to the analytical expression of the objective function. The optimization approach taking advantage of model linearization can be applied to similar mechanical systems with friction.

On the Mathematical Modeling of Slender Biomedical Continuum Robots.

The passive, mechanical adaptation of slender, deformable robots to their environment, whether the robot be made of hard materials or soft ones, makes them desirable as tools for medical procedures. Their reduced physical compliance can provide a form of embodied intelligence that allows the natural dynamics of interaction between the robot and its environment to guide the evolution of the combined robot-environment system. To design these systems, the problems of analysis, design optimization, control, and motion planning remain of great importance because, in general, the advantages afforded by increased mechanical compliance must be balanced against penalties such as slower dynamics, increased difficulty in the design of control systems, and greater kinematic uncertainty. The models that form the basis of these problems should be reasonably accurate yet not prohibitively expensive to formulate and solve. In this article, the state-of-the-art modeling techniques for continuum robots are reviewed and cast in a common language. Classical theories of mechanics are used to outline formal guidelines for the selection of appropriate degrees of freedom in models of continuum robots, both in terms of number and of quality, for geometrically nonlinear models built from the general family of one-dimensional rod models of continuum mechanics. Consideration is also given to the variety of actuators found in existing designs, the types of interaction that occur between continuum robots and their biomedical environments, the imposition of constraints on degrees of freedom, and to the numerical solution of the family of models under study. Finally, some open problems of modeling are discussed and future challenges are identified.