Rigid Body Research Articles

The water bottle flipping experiment: a quantitative comparison between experiments and numerical simulations

Abstract The water bottle flip experiment is a recreational, non-conventional illustration of the conservation of angular momentum. When a bottle partially filled with water is thrown in a rotational motion, water redistributes throughout the bottle, resulting in an increase of moment of inertia and thus a decrease in angular velocity, which increases the probability of it falling upright on a table as compared with a bottle filled with ice. The investigation of this phenomenom is accessible to undergraduate students and should allow them to gain better understanding of combined translational and rotational motions in classical mechanics. We report a series of detailed experiments that are quantitatively compared with numerical calculations based on a simple theoretical framework in which the water volume is decomposed into thin slices of a rigid body that are subjected to fictitious forces in the non-inertial frame of the spinning bottle. This model also allows us to capture and predict other experimental configurations. Finally, we discuss additional counter-intuitive effects that contribute to bottle stabilization on landing.

Seismic response prediction for buildings with sliding live loads using neural networks

The seismic response of primary structures (PS) can be significantly influenced by live loads, particularly when these loads consist of stacked bodies that are capable of sliding during seismic events. Conventional design methods often fail to account for the energy dissipation resulting from such sliding, leading to overly conservative structural estimates. This study examines the effects of sliding live loads on the seismic response of a PS, where two rigid bodies, referred to as secondary bodies (SBs), are stacked as live loads on a PS. The interaction between the lower SB and the PS, as well as between the SBs, is modelled using Coulomb's friction model. The governing equations are solved using the fourth-order Runge-Kutta method. Seismic Zones III and V from IS 1893:2016 are considered as hazard levels. A parametric investigation explores the impact of varying dynamic parameters of both the PS and SBs on the seismic response. The results demonstrate significant energy dissipation within the stack due to sliding, which, if not considered, results in conservative displacement estimates. The study also evaluates how friction coefficients, mass ratios, and excitation levels affect the stack's energy dissipation capacity. A novel method to compute the modified primary structural period (Tnew) for design purposes is proposed, and an artificial neural network (ANN) model is developed, achieving a high prediction accuracy (R2 = 99 %). Sensitivity analysis is performed to assess the influence of input parameters on the output. This research highlights the need to include sliding loads in seismic design.

A hybrid method for aeroacoustic computation of moving rigid bodies in low Mach number flows

A hybrid method for aeroacoustic computation of moving rigid bodies in low Mach number flows

Peak factors of wind load for main frame design of rooftop structures

ABSTRACT Technology is being developed to unitize structures installed on apartment rooftops during construction. The rooftop is located at the top of a high-rise building with a flexible structure. However, the rooftop structure itself is close to a rigid body and is not integrated with the building. Therefore, it is difficult to calculate the gust effect coefficient of the rooftop structure. The peak factor provided by the Korean Design Standard (KDS) uses an equation for general buildings and may be inaccurate to a certain extent when used to calculate the wind load on rooftop structures. Therefore, in this study, wind pressure tests were conducted on three research models to calculate the appropriate peak factors for rooftop structures. For each model, the peak factor trend was analyzed according to the wind pressure coefficient, and the peak factor was presented. When the evaluation time was 10 min, the positive pressure peak factor converged to three and the negative pressure peak factor converged to four. Additionally, a formula for calculating the peak factor of rooftop structures based on the wind load evaluation time is proposed. Hence, the peak factor of rooftop structures can be calculated based on various evaluation times.

Steerable ultrasonic propulsion of rigid objects based on circular pressure modulation of a focused sectorial transducer array

As a common disease of human urinary system, the high prevalence and incidence rate of renal calculus have brought heavy burden to society. Traditional ultrasonic lithotripsy struggles with the comprehensive elimination of residual fragments and may inadvertently inflict renal damage. Although focused ultrasound can propel stones by the acoustic radiation force (ARF) with minimal tissue damage and enhanced passage rate, it is still lack of the accurate control for calculi at different locations. A circular pressure modulation approach for steerable ultrasonic propulsion of rigid objects is developed based on a sector-array of focused transducers. The ARF exerted on on-axis rigid spheres (stones) is derived based on acoustic scattering. It is proved that the ARF of focused fields exhibits an axial distribution of increasing followed by decreasing with the peak slightly beyond the focus. As the sphere radius increases, the ARF exerted on spheres at the focus increases accordingly with a decreasing growth rate. Inclined propulsion can be realized by the circular binary pressure modulation with the deflection increased by expanding the angle of power-off sector sources. The maximum deflection angle approaching 60° is determined by the F-number and element number of the sector-array. Experimental propulsions of steel balls are conducted using an 8-element sector-array with motion trajectories captured by a high-speed camera. Distributions of the motion speed and acceleration for steel balls of different radii are calculated through image processing. The ARF of mN level and the deflection angle of 12° are demonstrated by the successful propulsion of steel balls. This research provides an effective and flexible approach of steerable stone propulsion using an ultrasonic power supply without the complex control in amplitude or phase and the high-precision motion of the sector-array, hence promoting the practical application in non-invasive treatment of stones.

The elliptope and bounds in the rotational dynamics of rigid bodies

The elliptope and bounds in the rotational dynamics of rigid bodies

Investigation of dynamic effect of rapid impact compaction

Dynamic compaction is a soil improvement technique which involves the repeated application of an impact load to a contact area of the soil surface induced by heavy weights. Experimental measurements were prepared for evaluation of the ground wave propagation induced by the rapid impact compaction. Influence of increase of subsoil stiffness during compaction and terrain configuration were investigated. When the shear strength of soil is exceeded during the penetration of the compaction footing, increase of peak particle velocities is slower but still clearly visible along the measurement line. The peak particle velocity is damped by the subsoil below 5 mm s−1 within 40–50 m from the source of excitation. Attenuation radius is affected by the terrain configuration, when terrain elevations cause the increase of acceleration amplitudes. Rigid bodies in the ground, such as foundation structures, could have similar influence. Dominant frequencies are in the interval from 20 to 40 Hz regardless the distance from the source of excitation or the density of the treated subsoil. Obtained results are preferably related to the given boundary conditions. However, wave propagation pattern and change of its characteristics during densification of the subsoil are applicable at another construction sites considering their particularities.

Fast mobility analysis for generative design applications through a real vector space representation of mobilities

During the early stages of design, mechanisms are commonly modeled as perfect joints assembled with infinitely rigid bodies. This representation enables the prediction of the system’s mobilities through a mobility analysis. However, traditional mobility analysis tools can be computationally expensive or lack critical information, such as the type or direction of mobilities. It hinders the generation of topology and configuration through generative design schemes.In this paper, we propose an alternative approach to mobility analysis based on a real vector space representation of mobilities. Our method provides relevant information for early design steps while being computationally effective through a novel formulation of series and parallel assembly topological operations. A benchmark on four selected use cases highlights an acceleration of 3 to 4 orders of magnitude compared to traditional approaches. Additionally, design rules on the joints’ positions can be automatically generated with our approach. It enables the automation of the complete design process, including topology and configuration. As such, we provide guidelines to develop a generative design scheme dedicated to the synthesis of guiding mechanisms.

The added value of diffusion tensor imaging with systematic bias correction for the assessment of liver morphology and physiology.

Diffusion-weighted images of the human liver are prone to artifacts from bulk motions, poor SNR, non-uniformity of magnetic field gradients, and non-optimal choice of diffusion weightings. These factors markedly affect diffusion tensor imaging (DTI) metrics such as mean diffusivity (MD) and fractional anisotropy (FA). This work presents a simple preprocessing pipeline for enhanced magnetic field gradient non-uniformity calibration and analysis of the systematic bias removal attained in each correction step. Liver DTI scans were conducted in two isotropic phantoms and one healthy volunteer. Diffusion tensor was calculated for the original data and after denoising, B1 correction, rigid body registration, and magnetic field gradient non-uniformity correction applying the B-matrix spatial distribution (BSD) method and then, compared with the standard approach (sDTI). MD and FA were determined in three segments of the right lobe from DTI using four different combinations of b-values from the set 0, 400, and 800 s/mm2. Results showed that the proposed preprocessing and BSD methods have a significant impact on MD and FA values in off- and iso-centered isotropic phantoms. The applied corrections applied to the human liver resulted in a 11% change in MD and a - 64% change in FA. By manipulating the b-values used in the diffusion tensor calculation, DTI metrics that reflect only morphology or additional information about liver tissue physiology can be obtained. Accurate quantification of the human liver by diffusion requires appropriate preprocessing and carefully chosen b-value. Noise, B1 inhomogeneity, mis-registration, and non-uniform magnetic field gradients significantly change distributions of DTI metrics in isotropic phantoms and the human liver. Basic preprocessing and the B-matrix spatial distribution (BSD) method perform differently for off-center and isocenter locations. In the human liver, they removed systematic bias of FA and MD by up to -63% and 11%, respectively. Visible variability of FA and MD among b-value sets indicates the possibility of DTI sensitization to different liver compartments.

Characterisation of the Rigid Body Vibration Spectra of Road Transport Vehicles

ABSTRACTFor decades, numerous attempts at re‐creating realistic (vertical) vibrations that purport to represent typical conditions during road transport have been proposed and published. This has and continues to result in a significant number of target power density spectra (PDS) for use in laboratory simulation of vibrations despite the fact that the underlying parameters that influence the vibrations (road surface unevenness and vehicle dynamics) remain largely unchanged. This paper seeks to address this situation by analysing published and measured PDS (129 in total) from a variety of vehicles and road types with the aim of establishing typical PDS. Through the analysis of the frequency of the first natural mode of these PDS, it was found that there exist five typical response PDS (three for steel leaf suspension and two for air ride suspension) that can be considered as representative vibration response PDS for road transport in general. These representative PDS were matched with a two degree‐of‐freedom quarter‐car model representing the heave response of the rigid body motion of the vehicles. The analysis suggests that the higher frequency content of the measured data is not related to rigid body motion but emanates from drivetrain and, in some cases, structural vibrations. These usually comprise numerous harmonics of fixed and varying frequencies as well as transients. As these vibrations are impossible to classify based on vehicle type, it is recommended that the five quarter‐car representative spectral models proposed in this paper—namely, for steel leaf spring suspended vehicles with heavy, moderate and light loads and air ride type vehicles with heavy and light loads—be used for laboratory simulation for the purpose of evaluating the vibration resistance of products and packaged systems. It is suggested that, for most packaged product, this is sufficient to test their ability to survive road transport vibrations. These will yield more realistic vibrations than those endorsed by standards organisations and should have a positive impact on the optimisation of packaging designs and a corresponding reduction in packaging waste. Finally, the need for further work aimed at developing methods to identify and extract fixed and varying discrete frequency vibration as well as transient vibrations was identified.

Numerical Investigation of Wake Characteristics for Scaled 20 kW Wind Turbine Models with Various Size Factors

Wind energy is essential for sustainable energy development, providing a clean and reliable energy source through the wind turbine. However, the vortices and turbulence generated as wind passes through turbines reduce wind speed and increase turbulence, leading to significant power losses for downstream turbines in wind farms. This study investigates wake characteristics in wind turbines by examining the effects of different scale ratios on wake dynamics, using both experimental and numerical approaches, utilizing scaled-down models of the Aeolos H-20 kW turbine at scales of 1:33, 1:50, and 1:67. The experimental component involved wind tunnel tests in an open-circuit tunnel with adjustable wind speeds and controlled turbulence intensity. Additionally, Computational Fluid Dynamics (CFD) simulations were conducted using STAR-CCM+ (Version 15.06.02) to numerically analyze the wake characteristics. Prior to the simulation, a convergence test was performed by varying grid density and y+ values to establish optimized simulation settings essential for accurately capturing wake dynamics. The results were validated against experimental data, reinforcing the reliability of the simulations. Despite minor inconsistencies in areas affected by tower and nacelle interference, the overall results strongly support the methodology’s effectiveness. The discrepancies between the experimental results and CFD simulations underscore the limitations of the rigid body assumption, which does not fully account for the deformation observed in the experiment.

Hydrodynamic response analysis of the aquaculture net under the combined action of irregular waves and currents

ABSTRACT The hydrodynamic response of fishing nets is crucial in aquaculture. During service, due to severe sea states and collisions with large fish, potentially resulting in net damage. Analyzing this damage is complex due to the large number of net meshes. This study establishes a mathematical model of the net system under wave-current coupling based on the rigid-body kinematics and the lumped-mass method. An analysis was conducted to investigate how various environmental conditions and types of damage affect net deformation and force. Results indicate that maximum force occurs at the connections to the rigid frame and the midpoint of the net. Among various types of net damage, the nodes motion increased exclusively around the periphery of the damaged area, while the netting twine force significantly decreased only in the direction of the damage. Notably, damage to the upper net has the greatest impact on both netting twine force and deformation.

Dynamic balance of circles with one support point on pommel horse exercise

Double-leg circles on pommel horse exercises require a high degree of dynamic balance. However, theoretical conditions for maintaining dynamic balance are unclear. The purpose of this paper is to propose a simple theoretical model of the dynamic balance of the circles, and to illustrate its qualitative properties. To this end, the body of a gymnast is simply modeled as one rigid body with one support point, and symmetric and constant-velocity circles are assumed in most analyses. The condition that the torques of wrist and shoulder joints are zero is assumed as a dynamic balance condition with minimum strength. A control law is proposed to demonstrate the motion. Various properties of the dynamic balance condition are analyzed as follows. In the symmetric circles, (1) as the period of a circle decrease, the heights and the radius of the toes increase, and (2) the rotation of the body around its longitudinal axis in the double-leg circle has the effect of lifting the toes. (3) The shoulder and wrist torques can change the pose around the dynamic balance condition. In asymmetric circles, (4) the radius of the center of mass (CoM) increases as the angular velocity of the CoM around the support point decreases, and (5) the body angle with respect to the horizontal plane increases as the upward acceleration of the CoM increases. Moreover, mechanical principles of the circles are discussed as follows. (6) The CoM motion during the symmetric circles of the simple model can be related to the conical pendulum. In the simple model, (7) the pommel reaction force should be parallel to the arm segment when the wrist torque and the shoulder torque are equal or zero, and (8) to change the vertical component of the angular momentum of the body around the support point, the wrist torque around the vertical axis is needed. These results provide theoretical and qualitative insights into understanding and improving pommel horse exercise.

Basic Principles of Deformed Objects with Methods of Analytical Mechanics

Analytical mechanics is the most fundamental discipline in this field. The basic principles of analytical mechanics should also be applicable to deformed objects. However, the virtual displacement principle proposed by analytical mechanics is only applicable to particle systems and rigid body systems, and not to general deformed objects. In this study, the basic principle, which includes the virtual displacement principle and d’Alembert–Lagrange principle (also called the virtual displacement principle of dynamics), of general deformed objects (such as, elastic, plastic, elasto-plastic, and flexible objects) is derived using analytical mechanics. First of all, according to the method of analytical mechanics, the external force, internal force, constraint reaction force and elastic recovery force of the deformed object system under the equilibrium state are analyzed, and the concepts of virtual displacement, ideal constraint and virtual work are introduced, and the virtual displacement principle (also called virtual work principle) of deformed objects is proposed; secondly, vector form, coordinate component form and generalized coordinate form of generalized virtual displacement principle of deformed object are given; thirdly, Introduce inertial force and use analytical mechanics to derive the d’Alembert–Lagrange principle of dynamic systems; fourthly, as application of the principle, the virtual displacement principle of deformed objects in plane polar coordinate system, space cylindrical coordinate system and spherical coordinate system are given; fifthly, the constitutive relationship between the gravitational strain of elastic–plastic materials was introduced, and an example of the application of the d'Alembert–Lagrange principle in elastic–plastic objects was given; finally, a brief conclusion is drawn. This study unifies the virtual displacement principle of elastic objects, plastic, elastoplastics, deformed object systems and rigid object systems using the basic analytical mechanics method. This is a basic principle for dealing with the static problems of deformed objects. This work also lays the foundation for further study of the dynamics of deformed object systems.

Rheology modification in a subduction channel due to eclogite facies metasomatism (Rocky Beach Metamorphic Mélange, Port Macquarie, Australia)

The rheological properties of the interface between the down-going and overriding plates in subduction zones provides insight into how plate convergence is accommodated and the controls on seismic and aseismic slip. This interface is known as the subduction channel and exhumed examples provide the only direct information on deformation mechanisms and the impact of metamorphism on rheology. The Rocky Beach Metamorphic Mélange in eastern Australia is one such exhumed subduction channel, composed of eclogite, blueschist and greenschist facies blocks within a mélange matrix. Previous phase equilibria modelling indicates that high pressure blocks were subducted to ca. 100 km depth and then retrogressed during return flow and exhumation. We found that the rheology of blocks is modified by metasomatism, consistent with studies on other subduction channels. However, through comparison of blocks from different metamorphic grades we found that the effect of metasomatism on rheology varied depending on the pressure and temperature conditions of metasomatism. While unmetasomatised eclogites behaved as rigid objects in the mélange matrix, rocks with mineral assemblages that equilibrated during eclogite facies metasomatism accumulated significant strain, forming isoclinal folds and refolded folds. Deformation of these blocks began at eclogite facies and continued during return flow and retrogression to blueschist facies. At blueschist facies, metasomatised blocks developed mm-scale isoclinal folds with shearing parallel to fold limbs forming rootless isoclinal folds. At the transition between blueschist and greenschist facies, pressure solution became important, preferentially focusing along layers of lawsonite, dissolving it from the rock. At greenschist facies, dissolution-precipitation processes caused significant mass loss, producing mm-spacing between pressure solution seams and cuspate folds, analogous to dewatering structures in sediments. In the RBMM eclogite facies metasomatism reduces the competence of rigid blocks, reducing overall subduction channel heterogeneity during return flow. We suggest that subduction channels that experience widespread eclogite facies metasomatism may be less likely to generate seismic slip during return flow, since the proportion of rigid blocks and block strength are both reduced.

TorqTwin—An open-source reference multibody modeling framework for wind turbine structural dynamics

This paper presents an open-source multibody modeling framework for wind turbine structural dynamics, namely TorqTwin (Torque Towards wind). The multibody formulation includes both rigid and flexible bodies. For flexible bodies, such as towers and blades, the floating frame of reference formulation and modal reduction approaches are applied. The TorqTwin tool relies on Kane’s method and the symbolic Python library SymPy. The multibody formulation in TorqTwin is validated using the OpenFAST-ElastoDyn module and the commercial software Bladed. For both the fixed-bottom and floating IEA 15MW reference wind turbines, the rigid motions and flexible deflections calculated by TorqTwin are compared to those by ElastoDyn. Also, blade deflections predicted by TorqTwin are compared to those of the commercial software Bladed. The overall very good agreement between TorqTwin and other software validates the multibody formulation in TorqTwin. The strength of TorqTwin is that it contains the full functionality of the state-of-the-art open-source ElastoDyn module and includes other modeling capabilities of commercial software, such as the bend-twist coupling effect of blades and more flexible modes. TorqTwin is designed to benefit both the wind energy research community and industry, as it helps understand and verify the theory behind the ElastoDyn module, provides a reference for formulating more complicated configurations, such as multi-rotor turbines, and helps to develop aeroelastic simulation tools.

Numerical study on the motion characteristics of free fall lifeboats entering calm water and rough sea

As ocean engineering operations extend into deeper seas, the working environment becomes increasingly complex, making free fall lifeboats (FFLBs) more vital for maritime disaster rescues. Unlike traditional davit-launched lifeboats, FFLBs are propelled into the water at a specific velocity and angle, engaging in a complex motion process of launch, impact, submersion, and resurfacing. Therefore, to assess the safety of FFLBs, this paper regarding the lifeboat as a rigid body aims to investigate the six-degree-of-freedom motion characteristics of lifeboat entering the water with different entry angles θ and wave environment, with a specific focus on analyzing the primary causes of capsizing. The numerical simulations of water entry with various θ, wave heights H, and relative entry positions are carried out by combining large eddy simulation and overset mesh technology. The free surface is captured by the volume of fluid method, and the attitude change, acceleration change, motion trajectory, and free surface evolution law of lifeboats are analyzed. The findings suggest that lifeboats can enter calm water safely at θ of 20°–50° and maintain a stable posture. Moreover, in extreme conditions where θ is either 0° or 90°, there is a high risk of entry failure due to excessive vertical acceleration and poor motion attitude, respectively. Furthermore, when facing waves, lifeboats experience reduced horizontal displacement when entering at peak and downward zero point compared to calm water conditions, which poses challenges for avoiding potential dangers.

Mechanism analysis of burn-up failure for needle roller bearing at high-speed gear in manual transmission

Adequate lubrication conditions of needle roller bearings are crucial for the normal operation of transmission. Addressing the burn-up and adhesion failures of needle roller bearings during transmission bench trials, two rigid body rotation physical models were developed to analyze and model the lubrication effect on the inner and outer surfaces of needle roller bearing. Through theoretical analysis and lubrication simulation, it was found that under the critical condition of d/D=0.553, the centrifugal force F on the outer ring surface of the needle bearing was related to the density of lubricant, rotational speed, as well as the angle and size of oil hole, rather than the position of the oil holes; Moreover, the centrifugal force F on the needle roller bearing at input shaft was related to the speed of transmission gear and was also associated with the clearance size between needle roller and cage. Theoretical analysis, simulation, and experimental results have demonstrated that the lubrication performance of needle roller bearings during operation at lower rotary speed gears was inferior to that at higher speed gears, and the lubrication was also less effective when the cage clearance was narrower. Employing angled oil inlets (holes), appropriately enlarging the diameter of oil inlets (holes), and increasing the clearance width between needle roller and cage will contribute to the improvement of lubrication effect.

Self-chemophoresis in the thin diffuse interface approximation

Self-chemophoresis is an appealing and quite successful interpretation of the motility exhibited by certain chemically active colloidal particles suspended in a solution of their ‘fuel’: the particle has a phoretic response to self-generated, rather than externally imposed, inhomogeneities in the chemical composition of the solution. The postulated mechanism of chemophoresis is the interaction of the particle (via an adsorption potential) with the chemical inhomogeneities in the surrounding medium. When the range of this interaction is much smaller than any other relevant scale in the system, the (translational and rotational) phoretic velocities can be described in terms of a phoretic coefficient and a slip fluid velocity at the surface of the particle. Using the case of a spherical particle as a simple and physically insightful example, here we exploit an integral representation of the rigid-body motion to critically re-examine this framework. The systematic analysis highlights two steps in the approximation: first the thin–layer approximation (very large particle size), and subsequently a lubrication approximation (slow variation of the adsorption potential along the tangential direction). We also discuss how these approximations could be relaxed and the effect of this on the particle's motion.

Experimental analysis of the cyclic behavior of rammed earth walls reinforced with arundo donax natural fiber

This experimental study analyzes the seismic behavior of rammed earth walls with Arundo donax natural fiber inclusions, also called "caña brava” (REWC), and without inclusions (REW). The experimental program consists of two stages: physical and mechanical characterization of materials, where properties such as particle size, density, Atterberg limits, and compressive and flexural strength were determined; and dynamic tests, which included compressive and cyclic load tests on REW and REWC walls. The walls were subjected to cyclic loading with derivatives between 0.2 % and 1.4 % in-plane combined with a constant vertical compressive stress of 13 kPa to simulate seismic forces in the presence of gravity loads. The results regarding loading, hysteretic response, energy dissipation, stiffness degradation, and failure mode are compared. In addition, the envelope curves of the load-displacement hysteretic responses are analyzed using a capacity spectrum approach. It is observed that the inclusion of Arundo donax natural fiber negatively affects the mechanical properties of the walls and their hysteretic response. It is also observed that the energy dissipation is affected by the inclusion of Arundo donax natural fiber. However, the stiffness behavior is similar in all the walls. Rigid body failure modes are identified in all the walls, but the walls, including Arundo donax natural fiber, form failure planes that divide the wall into two bodies.