Rigid Body Research Articles

Reverberation ray matrix analysis for wave propagation in beam structures with rigid components

The method of reverberation-ray matrix (MRRM) is modified for the dynamic response analysis of beam structures with rigid components. The wave expressions for the beam structures are derived based on the Timoshenko beam theory, and the MRRM formulations are obtained through the compatibility conditions of displacements and joint coupling equations by considering the effects of rigid components. An application of this method is considered in the context of a phononic crystal with spring-mass-like resonators. The proposed resonant unit consists of a large mass-like central component connected to thin beams that serve as springs. The large central component can be approximated as a rigid body. Using the MRRM and the finite element method (FEM), the band diagrams and the transmission spectrums are calculated. The innovative cell offers the advantage of producing lower and wider bandgaps when compared to traditional lattice structures. The accuracy of the MRRM is verified with the FEM. The current research provides a vibration analysis approach for beam structures with rigid components and the analysis of phononic crystals serves as a reference for structural design.

A computationally efficient method for dynamic response analyses of accessory drive systems using harmonic balance method together with alternating frequency/time domain technique

Serpentine belt accessory drive system (SBADS) is a typical coupled vibration system with rigid body vibrations and continuum vibrations. Vibration behaviors of a SBADS consist of rotational vibrations of pulleys and tensioner arm and transverse vibrations of belt spans. In modeling of a SBADS, transverse vibration of a belt span consisting of time and space coordinates is discretized into multiple degrees of freedom with only time variable. As a result, number of degrees of freedom of a SBADS is large, and computational efficiency of dynamic responses of a SBADS is low. To solve this issue, a calculation method for nonlinear dynamic characteristics of a SBADS is proposed based on the harmonic balance method with alternating frequency/time domain technique in the paper. An engine front end accessory drive system is taken as a study example, the coupling vibration model of the SBADS is established, and hysteretic behavior of the tensioner is considered in the model. In addition, a dimensionality reduction method for the dynamic matrix is proposed based on local nonlinearity of the model. A calculation method for nonlinear dynamic responses of the SBADS is subsequently developed by combining the harmonic balance method and alternating frequency/time domain technique. Nonlinear dynamic responses estimated by the proposed method are validated by comparing with numerical simulations. Finally, amplitude-frequency responses of the SBADS are calculated using arc-length continuation method, and influences of nonlinear tensioner on frequency domain responses and internal resonance phenomena of the SBADS are analyzed.

The principal bundle structure of continuum mechanics

In this paper it is shown that the structure of the configuration space of any continua is what is called in differential geometry a principle bundle. A principal bundle is a structure in which all points of the manifold (each configuration in this case) can be naturally projected to a manifold called the base manifold, which in our case represents pure deformations. All configurations projecting to the same point on the base manifold (same deformation) are called fibers. In this paper, it is shown that each of these fibers is then naturally isomorphic to the Lie group SE(3) representing pure rigid body motions. Furthermore, it will be shown that it is possible to define intrinsically (coordinate free), what is called a connection and this allows to split any continua motion in a rigid body sub-motion and a deformable one in a completely coordinate free way. As a consequence of that it is then possible to properly define a pure deformation space on which an elastic energy can be defined and this will be related to other literature on intrinsic strain which has not shown the geometric structure which will be presented in this work. This will be shown using screw theory and Lie groups. Screw theory is vastly used in the analysis of rigid body mechanisms but is not normally used to analyse continua. The paper will also relate known concepts of continua like helicity and enstrophy to screw theory concepts which will become evident by the presented construction.

Evaluation of trunk muscle coactivation predictions in multi-body models

Musculoskeletal simulations with muscle optimization aim to minimize muscle effort, hence are considered unable to predict the activation of antagonistic muscles. However, activation of antagonistic muscles might be necessary to satisfy the dynamic equilibrium. This study aims to elucidate under which conditions coactivation can be predicted, to evaluate factors modulating it, and to compare the antagonistic activations predicted by the lumbar spine model with literature data.Simple 2D and 3D models, comprising of 2 or 3 rigid bodies, with simple or multi-joint muscles, were created to study conditions under which muscle coactivity is predicted. An existing musculoskeletal model of the lumbar spine developed in AnyBody was used to investigate the effects of modeling intra-abdominal pressure (IAP), linear/cubic and load/activity-based muscle recruitment criterion on predicted coactivation during forward flexion and lateral bending. The predicted antagonist activations were compared to reported EMG data.Muscle coactivity was predicted with simplified models when multi-joint muscles were present or the model was three-dimensional. During forward flexion and lateral bending, the coactivation ratio predicted by the model showed good agreement with experimental values. Predicted coactivation was negligibly influenced by IAP but substantially reduced with a force-based recruitment criterion.The conditions needed in multi-body models to predict coactivity are: three-dimensionality or multi-joint muscles, unless perfect antagonists. The antagonist activations are required to balance 3D moments but do not reflect other physiological phenomena, which might explain the discrepancies between model predictions and experimental data. Nevertheless, the findings confirm the ability of the multi-body trunk models to predict muscle coactivity and suggest their overall validity.

On the Trajectory of a Light Small Rigid Body in an Incompressible Viscous Fluid

In this paper, we study the dynamics of a small rigid body in a viscous incompressible fluid in dimension two and three. More precisely we investigate the trajectory of the rigid body in the limit when its mass and its size tend to zero. We show that the velocity of the center of mass of the rigid body coincides with the background fluid velocity in the limit. We are able to consider the limit when the volume of the rigid bodies converges to zero while their densities are a fixed constant.

Constructing a game engine: A proposed game engine architecture course for undergraduate students

This paper presents a structured series of lessons for teaching undergraduate computer science or game development students how to construct a game engine using C++ and standard graphics APIs such as OpenGL or DirectX. Our proposed course content discusses rendering topics, game object management, scene management, and rigid body physics where learners are tasked to incorporate them into a fully functional prototype scene editor. By incorporating actual coding into the course, students can gain a better understanding of low-level engine features and also hone their programming skills. In addition to the learning content, we provide recommended assessment methods. We include discussions about our teaching experience in handling a game engine architecture course, titled GDENG03, which 36 students have passed. Our paper stands out from related works by providing a framework for interested educators on how to write a 3D game engine and how to teach the same in class. Based on our actual delivery of GDENG03, all 36 students achieved high scores of >80% out of 100 which demonstrates the effectiveness of our learning content. We received positive student feedback, such as a better appreciation of game engines, while suggestions for course improvement were raised, such as using simpler terminologies and better workload management. Based on student scores and feedback, we can attribute the success of our students’ learning to our inclusion of practical coding examples and discussions, highlighting their relevance to mainstream game engines. The learning materials and accompanying source code can be accessed in the following link: .

Vibration Characteristics of Asymmetric Flexible Cantilever Beams Connected to a Central Rigid Body

A satellite with two solar wings can be modeled using a pair of symmetric flexible cantilever beams connected to a central rigid body. Due to certain reasons, the symmetric flexible cantilever beams may be turned into asymmetric ones, which will inevitably influence the vibration properties of the structural system. By changing the structural sizes and adding local mass on one side of the two beams, a structural system with asymmetric mass distribution is obtained and its vibration characteristics are investigated. Hamilton’s principle with the assumed mode method is employed to establish the equation of motion of the asymmetric structural system. The natural frequencies, mode shapes, frequency response curves and displacement time histories of the system are calculated, and they are compared with those of the structural system with a symmetric mass distribution. The correctness and feasibility of the present analytical method are verified by means of the finite element method (FEM) and a vibration experiment. The analytical results show that the mass asymmetry of the two beams leads to the mode localization phenomenon, and the coupling effect between the two beams and the central rigid body is enhanced. The larger the mass asymmetry is and the closer the position of the added local mass to the end of the cantilever beam is, the more obvious of the mode localization phenomenon is and the more obvious of the coupling effect between the two beams and the central rigid body is. The present investigation results are helpful for the dynamic analysis and design of spacecraft structures composed of flexible solar wings and a central rigid body.

Uzay Hareketinde Bir Katı Cismin Kinematik Diferansiyel Geometrisi

Bu çalışmanın iki bölümünden birincisi; diğer bölümün daha iyi anlaşılabilmesi için temel kavramları olan diferansiyel geometri ve kinematikle ilgilenir. İkinci bölümde ise bir düzlem yüzeye komşu bir nokta tanımlanmıştır. Belirtilen noktanın sabit olması için gerekli ve yeterli koşullar sunulmuştur. Regle yüzeye adjoint bir A noktasının geometrik yeri olan eğrinin özellikleri, regle yüzeyin özellikleriyle bağdaştırılarak incelenir.

Investigating the dispersion characteristics of symmetric and asymmetric modes in rails: A theoretical and experimental study

The propagation law of ultrasonic guided waves in waveguide structures is determined by their dispersion characteristics, and the number of guided waves in symmetric and antisymmetric modes in rails is significant, so the dispersion characteristics are very complex. In order to study the dispersion characteristics of symmetric and antisymmetric modes in rails, this paper derives the wave equation based on the SAFE method with higher order elements, and the correctness of the wavestructure calculation in the SAFE model is verified using the FE method. This paper focuses on the wavestructure state at 0 kHz and the wavestructure changes during mode crossing through and repulsive deflections, and for the first time experimentally verifies the phenomenon of wave structure exchange in rails. The main conclusions are that the dispersion curves between modes with the same symmetry show repulsive deflection, and the dispersion curves between modes with opposite symmetry show crossover; the wavestructure of the rail is mainly rigid body translation and rigid body rotation at frequencies close to 0 kHz; the guided wave at the intersection of symmetric and antisymmetric modes transforms into a fading wave that cannot be continuously propagated in rails; when the dispersion curves are close, the wavestructures between the two modes are linearly superimposed, and when the dispersion curves are deflected by repulsion, the wavestructures of the two modes are exchanged.

Method of generating speckle patterns for digital image correlation based on modified Conway's Game of Life.

The measurement accuracy of digital image correlation (DIC) is influenced by the quality of the speckle pattern. Although various models for generating random speckle patterns have been well discussed, obtaining appropriate speckle images with isotropic quality and performance could be a challenging issue in DIC. In this paper, we propose a novel (to our knowledge) method for generating speckle patterns based on modified Conway's game of life (GoL). By sequentially assembling the speckle patterns generated from the modified GoL, we produced the GoL speckle image. Then, verification and comparison experiments were conducted through pure in-plane translations. The results show that the generated speckle image which was resized with k s=6& k r=2 processing and subsequently fuzzified using a Gaussian filter, produces the best accuracy for DIC measurement. Furthermore, based on the rigid body in-plane rotation displacement tests in the physical experimental results of three different speckle images, the GoL speckle generated from our proposed method shows the smallest measurement error. This indicates that the proposed speckle patterns generating method could provide a new type of speckle pattern with better quality and accuracy.

Co-rotational 3D beam element using quaternion algebra to account for large rotations: Formulation theory and static applications

This paper presents a co-rotational beam element based on quaternion algebra as a means of parameterizing large rotations. This co-rotational framework is based on a decomposition of beam kinematics into a rigid element frame, which follows the element and its pure deformation. Once the decomposition between rigid body motion and deformation is obtained, the principle of virtual work allows calculating the element response projected onto large displacements and rotations. This 3D co-rotational element lies within the framework of incremental formulations. The special feature of this formulation pertains to the decomposition of kinematics to extract the rigid body motion and pure deformations through use of quaternion algebra by solving an internal nonlinear kinematic equation. Thus, from the 2 quaternions defining global rotations and the 2 displacement vectors at the ends of the beam, this method is able to extract: 1 quaternion and 1 displacement vector parameterizing the rigid body motion, plus 2 other quaternions defining the internal rotations and beam elongation. The proposed formulation based on quaternion algebra therefore constitutes an alternative to the literature’s treatment of large-rotation kinematics using a quaternion algebra. The operators are also linearized in order to obtain the algorithmic stiffness operator. Eleven distinct static numerical applications are presented, along with comparisons from the literature in the aim of demonstrating the efficiency of this proposed element.

Sensitivity Study Using Synthetic 3D Image Datasets to Investigate the Effect of Noise Artefacts on Digital Volume Correlation

BackgroundThe potential effect of image noise artefacts on Digital Volume Correlation (DVC) analysis has not been thoroughly studied and, more particularly quantified, even though DVC is an emerging technique widely used in life and material science over the last decade.ObjectiveThis paper presents the results of a sensitivity study to shed light on the effect of various noise artefacts on the full-field kinematic fields generated by DVC, both in zero and rigid body motion.MethodsVarious noise artefacts were studied, including the Gaussian, Salt & Pepper, Speckle noise and embedded Ring Artefacts. A noise-free synthetic microstructure was generated using Discrete Element Modelling (DEM), representing an idealistic case, and acting as the reference dataset for the DVC analysis. Noise artefacts of various intensities (including selected extreme cases) were added to the reference image datasets using MATLAB (R2022) to form the outline of the parametric study. DVC analyses were subsequently conducted employing AVIZO (Thermo Fisher). A subset-based local approach was adopted. A three-dimensional version of the Structural Similarity Index Measure (SSIM) was used to define the similarity between the compared image datasets on each occasion. Sub-pixel rigid body motion was applied on the DEM-generated microstructure and subsequently “poisoned” with noise artefacts to evaluate mean bias and random error of the DVC analysis.ResultsWhen the local approach is implemented, the sensitivity study on zero motion data revealed the insignificant effect of the Gaussian, Salt & Pepper, and Speckle noise on the DVC-computed kinematic field. Therefore, the presence of such noise artefacts can be neglected when DVC is executed. On the contrary, Ring Artefacts can pose a considerable challenge and therefore, DVC results need to be evaluated cautiously. A linear relationship between SSIM and the correlation index is observed for the same noise artefacts. Gaussian noise has a pronounced effect on the mean bias error for sub-pixel rigid body motion.ConclusionsGenerating synthetic image datasets using DEM enabled the investigation of a variety of noise artefacts that potentially affect a DVC analysis. Given that, any microstructure – resembling the material studied – can be simulated and used for a DVC sensitivity analysis, supporting the user in appropriately evaluating the computed kinematic field. Even though the study is conducted for a two-phase material, the method elaborated in this paper also applies to heterogeneous multi-phase materials also. The conclusions drawn are valid within the environment of the AVIZO DVC extension module. Alternative DVC algorithms, utilising different approaches for the cross-correlation and the sub-pixel interpolation methods, need to be investigated.

Nonlinear modeling of wave–structure interaction for a flexible floating structure

We present a coupled high-fidelity numerical approach for accurately modeling the fully nonlinear wave–structure interaction of a floating highly-flexible structure in waves. The methodology combines numerical methods that solve the Navier–Stokes equations for viscous-flow dynamics with a free surface, and formulates the nonlinear dynamics of the flexible floating structure as a set of differential–algebraic equations. A verification study was conducted for numerical wave generation and propagation, and the discretization error was quantified. The validation was performed against experimental measurements of a flexible structure subjected to regular waves, where its upstream edge was constrained to the vertical equilibrium location. Our comparisons with the experimental data showed a favorable agreement. This study specifically focused on comparing the wave-driven hydroelasticity of a constrained and a freely floating flexible structures. It provided insights into the effects of rigid body motions on its structural deformations in waves. Developed as an open-source tool, our study demonstrates the potential of the coupled methodology for accurately modeling the wave–structure interactions of flexible floating structures in various nonlinear sea states.

Exploring the influence of friction in the puncture mechanics of soft solids

AbstractFriction is an ever-present force in our lives, affecting the interaction between objects in numerous ways. The common hypothesis of frictionless contact between a foreign rigid object (needle) and a target material during puncturing leads to a constant penetration force. However, experimental observations reveal a linear increase in penetration force as the needle tip delves deeper. This force increment arises from the interplay of friction and adhesion at needle-solid interface. The present work provides an insight into the measure of friction and adhesion quasi-static characteristics at the needle-solid interface through puncture experiments. To this end, an axisymmetric hyperelastic model is presented to describe the expansion of a cavity under the contact pressure of the penetrating needle. In addition, the competing mechanisms of cavity expansion and mode I cracking during needle penetration in a soft solid are discussed.

3D printer-driven design of a non-assembly titanium surgical instrument using compliant lattice flexures

Metal additive manufacturing is a promising technology for the production of functional medical products, due to its high shape complexity and resolution, and ability to withstand sterilization temperatures. This study explores the possibility of designing a completely non-assembly steerable surgical instrument using Selective Laser Melting. Despite its advantages for medical devices, the rough surface quality of unfinished parts can be problematic for non-assembly designs, leading to increased friction and wear in rigid body mechanisms and tendon-actuated mechanisms. We investigated printing of rolling contact joints with crossed flexures as low-friction joints, adjusted for printing in titanium for the design of the instrument. Grid-based lattice structures were incorporated as miniature flexures, and we explored the influence of various grid sizes on the flexibility and bending stiffness of the lattices. Based on this exploration, we altered the rolling joint configuration from two crossed flexures to a single straight flexure for our design. The resulting steerable surgical instrument design is completely non-assembly, including its actuation, facilitates easy removal of support structures, and requires no surface finishing steps. It has a diameter of less than 20 mm, facilitates opening and closing of a grasper, and steering of the grasper by 20 degrees.

Evaluation and implementation of Lie group integration methods for rigid multibody systems

AbstractAs commonly known, standard time integration of the kinematic equations of rigid bodies modeled with three rotation parameters is infeasible due to singular points. Common workarounds are reparameterization strategies or Euler parameters. Both approaches typically vary in accuracy depending on the choice of rotation parameters. To efficiently compute different kinds of multibody systems, one aims at simulation results and performance that are independent of the type of rotation parameters. As a clear advantage, Lie group integration methods are rotation parameter independent. However, few studies have addressed whether Lie group integration methods are more accurate and efficient compared to conventional formulations based on Euler parameters or Euler angles. In this paper, we close this gap using the $\mathbb{R}^{3}\times SO(3)$ R 3 × S O ( 3 ) Lie group formulation and several typical rigid multibody systems. It is shown that explicit Lie group integration methods outperform the conventional formulations in terms of accuracy. However, it turns out that the conventional Euler parameter-based formulation is the most accurate one in the case of implicit integration, while the Lie group integration method is computationally the more efficient one. It also turns out that Lie group integration methods can be implemented at almost no extra cost in an existing multibody simulation code if the Lie group method used to describe the configuration of a body is chosen accordingly.

Internal dissipation in the Dzhanibekov effect

The Dzhanibekov effect is the phenomenon by which triaxial objects like a spinning wing bolt may continuously flip their rotational axis when initially spinning around the intermediate axis of inertia. This effect is closely related to the Tennis Racket theorem that establishes that the intermediate axis of inertia is unstable. Over time, however, dissipation ensures that a torque free spinning body will eventually rotate around its major axis, in a process called precession relaxation, which counteracts the Dzhanibekov effect. Euler’s equations for a rigid body effectively describe the Dzhanibekov effect, but cannot account for the precession relaxation effect. A dissipative generalization of Euler’s equations displays two dissipative mechanisms: orientational diffusion and viscoelasticity. Here we show through numerical simulations of the dissipative Euler’s equations that orientational diffusion, rather than viscoelasticity, primarily drives precession relaxation and effectively suppresses the Dzhanibekov effect.

Crystal Polymorph Search in the NPT Ensemble via a Deposition/Sublimation Alchemical Path.

The formulation of active pharmaceutical ingredients involves discovering stable crystal packing arrangements or polymorphs, each of which has distinct pharmaceutically relevant properties. Traditional experimental screening techniques utilizing various conditions are commonly supplemented with in silico crystal structure prediction (CSP) to inform the crystallization process and mitigate risk. Predictions are often based on advanced classical force fields or quantum mechanical calculations that model the crystal potential energy landscape but do not fully incorporate temperature, pressure, or solution conditions during the search procedure. This study proposes an innovative alchemical path that utilizes an advanced polarizable atomic multipole force field to predict crystal structures based on direct sampling of the NPT ensemble. The use of alchemical (i.e., nonphysical) intermediates, a novel Monte Carlo barostat, and an orthogonal space tempering bias combine to enhance the sampling efficiency of the deposition/sublimation phase transition. The proposed algorithm was applied to 2-((4-(2-(3,4-dichlorophenyl)ethyl)phenyl)amino)benzoic acid (Cambridge Crystallography Database Centre ID: XAFPAY) as a case study to showcase the algorithm. Each experimentally determined polymorph with one molecule in the asymmetric unit was successfully reproduced via approximately 1000 short 1 ns simulations per space group where each simulation was initiated from random rigid body coordinates and unit cell parameters. Utilizing two threads of a recent Intel CPU (a Xeon Gold 6330 CPU at 2.00 GHz), 1 ns of sampling using the polarizable AMOEBA force field can be acquired in 4 h (equating to more than 300 ns/day using all 112 threads/56 cores of a dual CPU node) within the Force Field X software (https://ffx.biochem.uiowa.edu). These results demonstrate a step forward in the rigorous use of the NPT ensemble during the CSP search process and open the door to future algorithms that incorporate solution conditions using continuum solvation methods.

Development of TPACK-Based Physics Magazine as Teaching Material for High Schools: A Study on Rotational Dynamics and Rigid Body Equilibrium

This study aims to develop a physics teaching magazine based on Technological Pedagogical and Content Knowledge (TPACK) for senior high school students, focusing on rotational dynamics and equilibrium of rigid bodies. Employing a Research and Development (R&D) approach with the 4-D model, the process encompassed definition, design, and development stages. The magazine's content and media aspects were validated by experts, achieving feasibility scores of 94% and 87.9%, respectively. The magazine was evaluated by students of SMAN 1 Lembah Seulawah Aceh Besar, with results indicating strong acceptance and effectiveness as a learning medium. While the study confirms the potential of TPACK-based interactive learning materials in science education, its limited scope and sample size suggest caution in generalizing the findings. Future research should expand the scope, involve larger samples, and integrate diverse technological tools. This research contributes to the discourse on digital competencies in science education, emphasizing the need for innovative materials and continuous professional development.

Numerical study to investigate the effect of sample size sensitivity on porous materials with respect to different geometrical parameters

Porous materials play a crucial role in various industrial applications, where precise determination of geometric parameters like dynamic tortuosity, as well as viscous and thermal characteristic lengths, is essential for optimizing acoustical performance. Up to this point, there has been no published size sensitivity test that recommends the ideal sample size for analyzing these parameters in an industrial environment. The present article analyzes different reconstructed porous material samples using conventional CFD and coupled FEA-CFD simulations and suggests optimal sample size and specific simulation setup optimized for industrial purposes, which grant high accuracy and reasonable computational cost. The present paper analyzed several samples, which were reconstructed by micro-CT and analyzed in Star-CCM+ simulation environment. It was found that the optimal sample size (1.5×1.5×1.5 mm or 2.5×2.5×2.5 mm) is different for specific average pore sizes. It was proven through various numerical simulations based on reconstructed porous material samples that running only one coupled CFD-FEM simulation is satisfactory to directly determine all investigated parameters. It was demonstrated that the computationally demanding numerical model could be simplified in specific cases using a rigid body and highlight the limitations.