Rigid Body Research Articles

Dynamics Modeling and Motion Evaluation of a Near-Ground Tethered Balloon Cable System under Severe Wind Environments

Weather survival poses a significant challenge for the utilization of tethered balloons. The dynamic modeling of tethered balloon systems presents challenges due to the flexible nature of the cables and the intricate nature of gust forces. The present study introduces a new approach for modeling near-ground tethered balloon systems, which enables the analysis of their dynamic responses and performance evaluation under complex boundary conditions. First, finite cylindrical rigid bodies that are joined together by bushing forces to describe the dynamics of the tethered cable. The properties of the flexible cables under severe bending and translation can be illustrated by the dynamics model. Second, a three-dimensional dynamics model based on the multibody dynamics theory is created to deal with the interaction of the tethered balloon system and flexible cables. The dynamic responses of the tethered balloon system under challenging operating conditions are investigated, focusing on the number of cable segments and the place and direction of gust wind impacts. This model allows for precise assessment and optimization of the system’s overall performance to improve weather resistance. The results show that compared to computational fluid dynamics (CFDs) methods, the multibody system dynamics-based balloon model improved the solution time by 80%, with a pitch angle deviation of only 0.0016°. Moreover, the bushing model effectively reduced cable force and enabled accurate reflection of the system’s motion characteristics.

A novel freemium code SAND (v1.0) for generation of randomly packed beds

The main current approaches for generation of the packed bed models are based on rigid body dynamics (RBD) and Newton's laws (discrete element methods - DEM). This paper deals with the development and analysis of a novel code based on analytical geometry approach for the packed bed generation. The architecture and main algorithms of the novel code are described and clarified. The parameters of the packed bed generated via the novel code are compared with experimental data and packed beds generated via Blender (RBD), Yade (DEM). The novel code demonstrates many advantages, such as good correlation with experimental data, no overlaps between pellets in the packed bed, and a low computational time for packed bed generation. The packed bed model can be directly exported in .step format. Other advantages are also demonstrated and clarified. The novel code is attached to this paper and can be freely used by engineers and scientists.

Determination of the dynamic stiffness matrix of a rail damper and application to vibration decay rate

In this paper, the 6×6 dynamic stiffness matrix of a rail damper seen by a short section of rail is defined based on the force simplification theory, and a method to determine the matrix is presented. According to the method, frequency response functions (FRFs) between specific points on the rail as a rigid body are measured with hammer testing. These FRFs are then used to express the acceleration of the mass center of the rail as well as the rail's angular acceleration. As the third step, the equations of motion of the rail are established based on the laws of momentum and moment of momentum, from which the dynamic stiffness matrix can be worked out. The method is then applied to determine the dynamic stiffnesses of a typical damper, and the determined dynamic striffnesses are combined with an infinite periodic track model to stduy the effect of the damper on the verical and lateral vibration decay rates of the rail.

Low frequency, broadband and thin acoustic metamaterials for acoustic insulation

Elastic and locally resonant metamaterials can be used to improve the acoustic insulation properties of panels, particularly at low frequencies. Among the possible architectures, we are interested in the case of a very soft panel consisting of a porous material in which a periodic distribution of cylindrical inclusions is inserted. It has recently been established (JSV 571 (2024) 118005) that this configuration gives rise to a large and low-frequency transmission dip, explained by the coexistence of an elastic band gap and the destructive interference resulting from the interaction between an elastic resonance mode of the skeleton and a rigid body mode of the inclusions. The paper aims to describe the essential physical mechanisms involved in using a minimal lumped element model, the characteristics of which are extracted from the cell modes. The relevance of the minimal model is validated utilizing a comparison with reference results obtained using the finite element method. This approach focuses on the mechanisms involved and is not constrained by the choice of a particular geometric configuration (exact shape and size of the inclusion), allowing it to evolve.

Observation-based quantification of aerosol transport using optical flow: A satellite perspective to characterize interregional transport of atmospheric pollution

Interregional transport plays a significant role in haze formation with varying and disputable contribution extent. Current research on quantitatively analyzing interregional atmospheric pollution transport has mainly relied on meteorological and chemical models. However, these models are typically affected by uncertainties due to the assumptions and simplifications inherent in the numerical simulations and source emission estimations. In this study, a comprehensive optical flow framework is developed to offer a new perspective on quantitative characterization of interregional transport of atmospheric pollution based on synergistic observations from geostationary and sun-synchronous satellites. In this framework, the high-frequency continuous aerosol observing images are regarded as video in computer vision, and an aerosol dynamic optical flow algorithm is proposed by incorporating aerosol-specific assumptions and constraints, overcoming the limitation that traditional optical flow methods are typically confined to rigid bodies. Results demonstrate that the developed optical flow framework could distinguish the aerosol transport process from other dynamic processes of aerosol development and accurately capture the fast-changing details of transport processes. Moreover, the satellite-based optical flow framework achieves aerosol transport results comparable to those of widely accepted model-based methods, demonstrating the physical interpretation of pixel-based optical flow results and highlighting its effectiveness in quantitative characterization of the atmospheric pollution transport process via the Aerosol Transport Index (ATI). Furthermore, a case analysis of long-term assessments of interregional transport of atmospheric pollution indicates that Beijing acts as a “sink” of atmospheric pollution, and a downward trend could be found from the annually averaged transported aerosol net loadings due to the emission reduction policy. Compared with model-based methods, the satellite-based optical flow framework is directly grounded in observations and does not rely on emission inventories that take years to update. Therefore, it not only helps improve understanding the patterns of atmospheric pollution interregional transport, but also provides a more efficient and economical way to assess the effectiveness of regional joint control policy.

On the nonlinear dynamics of in-contact rigid bodies experiencing stick–slip and wear phenomena

In this paper, the dynamic behavior of one degree-of-freedom oscillator subject to stick–slip and wear phenomena at the contact interface with a rigid substrate is investigated. The motion of the oscillator, induced by a harmonic excitation, depends on the tangential contact forces, exchanged with the rigid soil, which are modeled through piecewise nonlinear constitutive laws, accounting for stick–slip phenomena due to friction as well as wear due to abrasion, already developed by the authors in a previous work. The nonlinear ordinary differential equations governing the problem are derived, whose solution is numerically obtained via a typical Runge–Kutta-based algorithm. The main target of this study is to analyze and discuss the strong nonlinear behavior, descending from the presence of stick–slip and wear phenomena, thus investigating the effect of the different interface modeling. In this framework, the analysis is carried out considering the whole evolution of non-smooth contact laws, starting from the virgin interface.

From the Cosserats mechanics backgrounds to modern field theory

In the paper, yet weekly known, Cosserats’ original four concepts as follow: the four-time unification of rigid body dynamics, statics of flexible rods, statics of elastic surfaces and 3D deformable body dynamics; the intrinsic formulation based on the local, von Helmholtz symmetry group of monodromy; the invariance under the Euclidean group. The concept of a set of low-dimensional branes immersed into Euclidean space are revalorized and explained in terms of the modern gauge field theory and the extended strings theory. Additionally, some useful mathematical tools that connect the continuum mechanics and the classical field theory (for instance, the convective coordinates, von Mises’ “Motorrechnung”, the Grassmann extensions, Euclidean invariance, etc.) are involved in the historical explanation that how the ideas were developing themself.

Research on the influence of rigid body modes on the operating vibration of arc gate

Abstract The 5# arc working gate of Jiangshan Wanyao Reservoir is composed of the suspension system of the gate and the steel wire rope, which has a serious vibration phenomenon when running without water. Firstly, the rigid body modal analysis of the gate suspension system is analyzed, the position size of key components such as gate support hinge shaft, gate motion guide embedded parts, and main beam position state is measured and evaluated on site, and the dynamic stress and vibration of the support arm are tested and analyzed during gate operation. It is concluded that the influence rule and weight of the steel wire rope on the rigid body mode of the gate, the torsional position of the gate, and the uneven operation condition of the side guide lead to the rigid body mode of the gate. It is suggested to improve the twisting state of the gate, adjust the unevenness of the embedded parts, and weaken the factors that induce the modal vibration of the rigid body.

Curvature in plants

Curvatures are ubiquitous in the animal kingdom - the spiral shell of the nautilus and the corkscrew horns of the blackbuck being iconic examples. Dynamic changes in curvature (i.e., curving) are most striking in the locomotion of some animal species - swimming in fishes and mollusks, looping in leeches, undulatory locomotion in snakes and lampreys, and also sperm motility through flagellum beating. When it comes to plants, which are sessile organisms with a rigid body, the terms 'curvature' and 'curving' evoke very different images - leaves of grass swaying in the breeze, a trunk dangerously bent by a powerful gust of wind, a branch sagging under the weight of its own fruits, as well as the frail arabesques of twining plants like the morning glory and the ivy, which were so influential in the Art Nouveau movement and many other artistic traditions. These various vegetal curves not only prompt creative inspiration in the mind of the beholder, they also initiate signaling cascades leading to developmental responses of the plant. Conversely, curvature can result from a biologically active process in response to an internal or external stimulus. Active curving or decurving are indeed important aspects of the plastic interplay of the developmental program of plants and their environment. Although easily accessible to observation, curvature and curving have only recently become the focus of active research in plant development. Lying at the nexus of biology, physics and mathematics, they require an interdisciplinary approach. The aim of this primer is to give readers an intuitive but accurate understanding of what curvature and curving are, as observed in the plant kingdom, then a more formal definition. We will discuss their role in plant development, both as a signal and as a response, and finally the practical issues and solutions involved in measuring plant curvatures.

Design and analysis of extrusion die for T-shaped sheet materials

Abstract The study explores plastic deformation behavior of T-shaped plates using DEFORM™ 3D, a perfect plastic finite element analysis software that considers T-shaped and double T-shaped extrusion dies as rigid bodies and compares effective strain, effective stress, blank temperature, die wear and temperature conditions. Moreover, the study employed the machine learning step descent method to predict effective stress and effective strain. Furthermore, the Pearson product difference correlation was utilized to examine the relationship between effective stress, effective strain, and temperature in T-shaped extrusion. Lastly, META analysis was conducted to synthesize statistical data on effective stress and temperature from various research.

A fast search method of buckling load for telescopic boom structure

The telescopic boom structures are extensively utilized in engineering applications involving large mobile cranes, aerial work platforms of significant height, and similar mechanical devices. These are predominantly fabricated using solid-webbed box types, latticed truss designs, or a combination thereof. Under load, they exhibit pronounced geometric nonlinear effects, with the relationship between load and displacement demonstrating marked nonlinear characteristics. This paper focuses on the geometric nonlinear modeling of slender multi flexible beam structures. The overall structural system is divided into several substructures, and the concept of multi flexible system modeling is borrowed to establish a follow-up connected body foundation on each substructure. By decomposing the node displacement and rotation in the substructure, the large displacement and large rotation of the node are decomposed into rigid body motion of the connected base and small displacement and small rotation relative to the connected base, effectively representing the large displacement and large rotation of the substructure as rigid body motion of the connected base. A modeling method for the geometric nonlinear analysis of slender and flexible multibody beam structures is proposed. By decomposing the nodal displacement and rotation within the substructures, the large displacement and rotation of the nodes are broken down into the rigid body motion of the body-fixed coordinate and small displacement and rotation relative to the body-fixed coordinate. This approach establishes the application conditions for calculating the structure’s virtual power of deformation using traditional beam elements with linear strain. A method for solving the instability load of slender and flexible multibody structures is proposed. This method integrates the characteristics of the system’s nonlinear equilibrium equations with respect to load, by deriving the system equations with respect to a load increment control parameter. This paper converts nonlinear equilibrium equations into first-order ordinary differential equation (ODE). The method proposed in this paper provides a more efficient solution for the buckling load of the telescopic boom. It can be used to systematically and quickly calculate the structure of the telescopic boom.

Didactical proposal for the study of rigid body kinematics using analytical, video-tracking, and simulated cases of a four-bar mechanism

This work used three methods (analytical, simulated, and video-tracking) to analyze the kinematics of a four-bar mechanism. The results obtained were shared and implemented in an engineering dynamics course at the university level to assess the impact of this exercise on motivation and understanding of the course topic. A survey was used to evaluate the exercise. The survey results showed that for the students, the implementation of different methods to tackle the same problem improved their understanding of the concepts and gave them other options for analyzing a mechanical system.

Geometric Attitude Tracking Control for Rigid Body Based on a Novel Attitude Error Dynamic Model on SO(3)

Geometric Attitude Tracking Control for Rigid Body Based on a Novel Attitude Error Dynamic Model on SO(3)

Low-velocity impact behavior analysis on composite double curved-shell reinforced with graphene platelet

ABSTRACT This research investigates the low-velocity impact behavior of a spherical rigid body on a composite shell reinforced with graphene platelets (GPLs), in which GPL have been uniformly dispersed and randomly arranged within each individual layer. The weight proportion of GPL has been altered across the thickness. The modified Halpin Tsai model is employed to analyze the Young's modulus and the effective material characteristics of a composite reinforced with graphene platelets (GPLRC). The mass density and Poisson's ratio of the viscoelastic multilayer composite are determined using the rule of mixture. The material parameters of each layer are defined according to the Kelvin–Voigt model. The governing equations have been derived by applying the first order shear deformation shell theory, Hamilton's principle, and modifying the Hertz contact law. The PDE problems have been transformed into ODE equations through the utilization of the Galerkin method. Subsequently, the ordinary equations have been solved utilizing the Newmark method. A parametric study is conducted to examine the effects of various factors, such as fraction weight, GPL distribution pattern, impactor mass, radius, viscoelastic modulus, and initial velocity, on the low velocity impact response of a composite shell reinforced with GPL.

Safe Iterative Learning for Attitude Tracking of Rigid Bodies Under Nonconvex Constraints

Safe Iterative Learning for Attitude Tracking of Rigid Bodies Under Nonconvex Constraints

On the Energy Budget of Starquake-induced Repeating Fast Radio Bursts

With a growing sample of fast radio bursts (FRBs), we investigate the energy budget of different power sources within the framework of magnetar starquake triggering mechanism. During a starquake, the energy can be released in any form through strain, magnetic, rotational, and gravitational energies. The strain energy can be converted from three other kinds of energy during starquakes. The following findings are revealed: (1) The crust can store free magnetic energy of ∼1046 erg by existing toroidal fields, sustaining 106 bursts with frequent starquakes occurring due to crustal instability. (2) The strain energy develops as a rigid object spins down, which can be released during a global starquake accompanied by a glitch. However, it takes a long time to accumulate enough strain energy via spindown. (3) The rotational energy of a magnetar with P ≲ 0.1 s can match the energy and luminosity budget of FRBs. (4) The budget of the total gravitational energy is high, but the mechanism and efficiency of converting this energy to radiation deserve further exploration.

PERTURBED MOTIONS OF A NEARLY DYNAMICALLY SPHERICAL RIGID BODY WITH A MOVABLE MASS SUBJECT TO CONSTANT BODY-FIXED TORQUE

The problem of motion of a rigid body about a fixed point is one of the classical problems of mechanics. The interest to the problems of the rigid body dynamics has increased in the second half of the XX century in connection with the development of rocket and space technologies. A spacecraft or satellite, while orbiting about its center of mass, experiences torques from forces of diverse physical nature. This includes torques generated by the motion of internal masses, which can arise from factors such as presence of rotating components (like rotors or gyroscopes), and the activities of crew members aboard the crew vehicle. The dynamics of rigid body incorporated moving masses is a significant focal point in classical mechanics. Extensive research is dedicated to investigating the rotation of a rigid body featuring motion of internal masses. It is assumed that the body contains a viscoelastic element that is modeled by a moving mass connected to the body by a strong damper. The moving mass model loosely attached elements in a space vehicles, which can significantly affect the vehicle’s motion about its center of mass during a long period of time. Some cases are considered of the motion of a rigid body containing internal masses connected to the body by means of elastic and dissipative elements. A number of works are devoted to the analysis of various problems of the dynamics of space vehicles containing internal movable masses. The paper develops an approximate solution by means of averaging method to the system of Euler’s equation terms for a nearly dynamically spherical rigid body containing a viscoelastic element under the action of constant body-fixed torque. We obtained the system of motion equations in the standard form which refined in square-approximation by small parameter. Asymptotic approach permits to obtain some qualitative results and to describe evolution of angular motion using simplified averaged equations and numerical solution. The main objective of this paper is to extend the previous results for the problem of motion about a center of mass of a rigid body under the influence of small internal torque (cavity filled with a fluid of high viscosity) or external torque (resistive medium). The importance of the results is in progress of moving mass control motion of spinning projectiles.

Про стійкість обертання вільної системи двох пружно зв’язаних гіроскопів Лагранжа, один з яких має ідеальну рідину

On the basis of the known equations of motion of the system of coupled gyrostats by P. V. Kharlamov and the state function by S. L. Sobolev, the equations of rotation of a free system of two elastically coupled Lagrange gyroscopes were derived, one of which has an arbitrary axisymmetric cavity completely filled with an ideal incompressible fluid. The rigid bodies are connected by an elastic restoring spherical hinge. A transcendental characteristic equation of the perturbed uniform rotation of the mechanical system under consideration is derived. Taking into account the fundamental tone of the fluid oscillation, a characteristic equation of the fifth order is obtained. On the basis of the Liénard – Chipart criterion written in the inor form, the necessary conditions for the stability of the uniform rotation of the Lagrange gyroscopes and the fluid are written out as a system of four inequalities. With respect to the elasticity coefficient, these inequalities have degrees 1, 3, 6 and 8, respectively. Analytical studies of the leading coefficients of these stability conditions are carried out. It is shown that when the center of mass of the first solid body with liquid or the second does not coincide with the common point of these bodies, then at sufficiently large values of the elasticity coefficient the necessary stability conditions will always be satisfied. In the absence of elasticity in the hinge, the characteristic equation has a double zero root and in this case the stability conditions require additional studies. The obtained stability conditions are exact for an ellipsoidal cavity and approximate for other axisymmetric cavities. To clarify the obtained glass conditions for these voids, it is necessary to take into account additional tones of oscillation of an ideal liquid.

Modeling and motion analysis of flexible legged robots using the finite particle method

Robotics with flexible legs have attracted significant attention. Engineers often design and analyze the motion of legged robots from kinematic and biomimetic perspective. However, the influence of flexibility of the feet on robot locomotion is often not given sufficient considerations, which is also very crucial to the motion posture of the flexible legged robots, especially as the soft robots design becomes increasingly popular. The mainly difficulties lies in the traditional numerical methods in handling the dynamic motion analysis with both large rigid motion and large deformation. In this paper, the finite particle method (FPM) is used to simulate the motion and deformation coupled problems of the flexible six-legged robot. A shell-based particle model of a six-leg robot and the contact model between legs and ground are built. Without iterative and modification of the FPM analytical framework, structural nonlinearity is efficiently handled after eliminating rigid body motions by a fictitious reverse motion. The motion and deformation of a single leg with varying leg thickness, locomotion speed, and leg-to-ground friction coefficients were simulated. By analyzing the stress distribution in the leg and the number of contact points with the ground, the mechanical leg was optimized in design. Furthermore, the motion and deformation of the entire six-legged robot were simulated using the FPM. The numerical results' feasibility was validated through comparison with experimental data obtained from robot walking tests. The proposed method effectively simulates the motion and deformation of flexible robots, providing significant insights for the design of soft robots.

Almost-Poisson Brackets for Nonholonomic Systems with Gyroscopic Terms and Hamiltonisation

We extend known constructions of almost-Poisson brackets and their gauge transformations to nonholonomic systems whose Lagrangian is not mechanical but possesses a gyroscopic term linear in the velocities. The new feature introduced by such a term is that the Legendre transformation is an affine, instead of linear, bundle isomorphism between the tangent and cotangent bundles of the configuration space and some care is needed in the development of the geometric formalism. At the end of the day, the affine nature of the Legendre transform is reflected in the affine dependence of the brackets that we construct on the momentum variables. Our study is motivated by a wide class of nonholonomic systems involving rigid bodies with internal rotors which are of interest in control. Our construction provides a natural geometric framework for the (known) Hamiltonisations of the gyrostatic generalisations of the Suslov and Chaplygin sphere problems.