A tethered-net is a promising method for space debris capturing. However, its deployment dynamics is complex because of the flexibility, and its dependency of the deployment parameters is ...insufficiently understood. To investigate the deployment dynamics of tethered-net, four critical deployment parameters, namely maximum net area, deployment time, traveling distance and effective period are identified in this paper, and the influence of initial deployment conditions on these four parameters is investigated. Besides, a comprehensive study on a model for the tethered-net based on absolute nodal coordinates formulation (ANCF) is provided. Simulations show that the results based on the ANCF modeling method present a good agreement with that based on the conventional mass–spring modeling method. Moreover, ANCF model is capable of describing the flexibility between two nodes on the net. However, it is more computationally expensive.
•The influence of initial deployment conditions on four critical parameters of tethered-net is investigated.•An innovative modeling method for the tethered-net, based on absolute nodal coordinates formulation (ANCF), is proposed.•The ANCF modeling method is more capable to describe the flexibility of the tethered-net as compared to the mass–spring method.
•Fracture delay effect is considered.•Crack initiation problem is studied using incubation time approach.•Linear oscillator failure due to pulse loads is investigated.•Analogies between the two ...problems are drawn.•Importance of threshold load cases is highlighted.
The incubation time fracture criterion (ITFC) is used to analytically investigate dynamic crack initiation under short pulse loads. Particular attention is paid to the phenomenon of delayed fracture – a fundamental fracture effect which can be observed in experiments with short pulse loads. The effect can be described in the following way: the material failure occurs after local stresses reached their maximum values, meaning that the fracture takes place at a drop stage of the local stress field and thus delay is present. It is shown that the fracture delay effect manifests itself when minimal required critical loads are applied to the system. Such loads are called threshold loads being a key tool for experimental investigation of the dynamic fracture effects. It is found that the experimentally registered fracture delay can be clearly explained within the incubation time framework. The conditions for the delay are found, threshold load parameters are evaluated and the corresponding analytical formulas are given. Additionally, a simple analogy based on a mass-spring model is discussed. Analytical formulas available for the oscillator model are used to find some non-obvious similarities between the crack instability under short pulse loads and the oscillator failure when analogous loads are applied: the dynamic fracture process in the crack vicinity appears to exhibit inertial behavior.
Display omitted
The linearized Cartesian elastodynamics model of mechanical systems with flexible links is introduced in this paper to simplify its counterpart n-dof generalized model. The stiffness is represented ...by means of Lončarić’s 6 × 6 Cartesian stiffness matrix (CSM), the inertia by what von Mises termed the inertia dyad, i.e., the 6 × 6 Cartesian mass matrix (CMM). This model applies to a mechanical system with compliant components. Furthermore, the Cartesian frequency matrix (CFM) is defined as a congruent transformation of its stiffness counterpart, the transformation matrix being the inverse of the square root of the positive-definite CMM. The CFM thus defined is dimensionally-homogeneous, symmetric and at least positive-semidefinite. Upon the eigenvalue decomposition of the same matrix, the natural frequencies and the corresponding natural modes, i.e., the eigenscrews of the system, are obtained. The physical meaning of the CFM, together with that of its eigenvalues and eigenscrews, are given due interpretation in the paper, within the context of screw theory. This matrix is intended to serve as a useful tool for the elastodynamics analysis and design of a large class of multibody systems with flexible components, especially at the early design stages.
•Cartesian elastodynamics modeling of mechanical systems with flexible links.•Definition of the Cartesian frequency matrix for the Cartesian mass–spring model.•Properties, physical meaning and applications of the Cartesian frequency matrix.
Inspired by the advantages of the hexagon lattices and auxetic metamaterials, the typical two-dimensional (2D) hexagon-type elastic metamaterials (EMs), that is, the concave, the convex, and the ...rectangular hexagon-type EMs, are presented for investigating the dynamic behavior systematically. Firstly, the lumped mass-spring models are used to construct the band structures, and the eigenmodes are obtained by solving the eigenvalue problem of motion equations to unveil the formation mechanisms of bandgap (BG). Note that the specific dispersion branches are characterized by eigenfrequencies with the eigenmodes presenting similar vibrational forms, rather than just ranking the eigenfrequencies from low to high. Furthermore, the dependence on the main structural parameters of the lumped mass-spring models is investigated to achieve tunability of the bandgap characteristics. Then, the continuum models are also established to study the formation of bandgaps as well as the propagation of waves based on eigenmodes and transmission. The comprehensive study of the physical mechanics of the unit cells is carried out, encompassing the analysis of iso-frequency contours, deformation fields, and mesh-independent analysis. Finally, both the numerical analysis and experimental validation demonstrate the effect of vibration attenuation on in-plane elastic waves, which has the ideal great agreement with the prediction of the band structures (the values of the frequency response functions are much less than -20 dB within the ranges of BGs). This research is expected to provide valuable insight into the design of vibration isolators, beams, plates, and other devices that are being renewed.
Owing to heavy criticisms of nearshore fish farming for causing environmental pollution and encroaching on sea space used for shipping, boating, recreational sea activities and marine eco-tourism, ...offshore fish farming has now being seriously considered. Moreover an offshore site provides more pristine water and greater space for increased fish production. However, offshore fish farming poses challenges such as a more energetic sea environment. A higher sea current can lead to large deformation of fish net and hence a net volume reduction which compromises fish welfare. With the view to identifying the effects of various important parameters on net volume reduction of a gravity-type open-net fish cage, this paper adopts a mass-spring model for the dynamic analysis of current-induced net deformations of cylindrical fish nets with discrete weights hanging at the bottom edge of the nets. In this model, the net mesh comprises knot nodes and bar nodes connected by tension-only massless springs. The spring stiffness is determined from the net bar diameters and material properties. The current-induced loads are applied to each node and calculated based on Morrison’s equation. The governing equation system for nodal motions can be established according to Newton’s second law, and solved by using the Runge-Kutta method for the real-time net deformations. The effects of net string reinforcements, weight distributions and net shapes on the net volume reduction are studied with the view to shed insights into how one may improve fish cage designs to effectively mitigate net deformation under high sea current speeds in offshore fish farming sites.
Display omitted
•Failure of the mass-on-spring system is discussed.•Fracture delay and strength increase for high rates are studied.•The oscillator model is calibrated to address three sets of ...experimental data.•Analogies between the oscillator model and the incubation time model are shown.
The work considers failure of a linear oscillator (a mass-on-spring system) and the corresponding simple engineering approach to dynamic fracture of solids. The system is studied when subjected to two distinct types of load: a short pulse load and a linearly increasing load. These two cases are used to reveal two key dynamic fracture effects observed in dynamically loaded media: the fracture delay and increase of the system strength for high-rate loading. The inertia of the mass helps to capture these effects and thus to clearly show inapplicability of standard strength models when dynamic loads are considered. The linear oscillator is shown to be a basis for an easy to operate yet capable fracture model which admits “ad-hoc” application to various dynamic fracture cases. In this work the model is calibrated in order to fit known experimental results on dynamic crack initiation in plates and on spallation observed in rods. The model shows good performance despite its simplicity and strength of the made assumptions.
This paper is dedicated to modeling of fuel sloshing dynamics and its effect on the stability and control of the space vehicle. Sloshing due to the liquid movement in the fuel tank of a space ...vehicle's propulsion system can be effective on the vehicle’s control and stability. Force and moment interaction between fuel sloshing and space vehicle’s control system will be appeared as a feedback in the control system. With respect to simplicity of analyzing of a rigid body's equations of motion in comparison with a fluid dynamics equations and as a result reducing computational efforts, it is possible to apply a mechanical model instead. So in this paper fuel sloshing is modelled as a linear mechanical system to investigate its effect on the stability and control of the vehicle. For this purpose, two mechanical models, mass-spring and pendulum systems, are applied to model dynamics of a space vehicle with fuel sloshing and each system’s parameters are evaluated for simulat
Mooring lines and aquaculture nets are important components in fish farm systems. During the design stage of the fish farm systems, a numerical method of high computational performance to calculate ...the structural responses of the mooring lines and aquaculture nets is required. The present study aims to explore the applications of an extended position-based dynamics (XPBD) algorithm to the structural modelling of the mooring lines and aquaculture nets and verify the XPBD by comparing the performances with the mass-spring model and FEM of Code_Aster. Three typical cases about the mooring lines and aquaculture nets, including the twelve mooring lines of a floating dock, the flexible net with three sinkers and the lifting operation of a fish cage are discussed. In these cases, the sensitivity studies on the time-step, number of elements and damping ratio are performed to determine the proper settings of these approaches. The accuracy of the original XPBD is improved by adding correction forces to the nodes associated to the spring constraints. Among all the cases, the present modified XPBD can yield results including the static positions, tensions, lifting forces and dynamic deformations of the mooring lines or aquaculture nets that are comparable in accuracy with the mass-spring method and FEM of Code_Aster. The modified XPBD and mass-spring model require much less computational resources than the FEM of Code_Aster for the cases of the twelve mooring lines of a floating dock and the lifting operation of a fish cage. The present modified XPBD can be effectively applied to lifting operations of fish cages involving current loads. Therefore, the proposed modified XPBD can be a new alternative for the structural modelling of the mooring lines and aquaculture nets.
•The present study will explore a new efficient method named extended position-based dynamics (XPBD) method in simulations of the structural responses of the mooring lines and aquaculture nets.•The original XPBD is not accurate and needs to be corrected. It can be improved by using small time step, but the computational cost thereby increases. The modified XPBD is proposed by adding correction forces to the nodes associated to the constraints.•The performances of three approaches, including mass-spring method, extended position-based dynamics method and finite element method, are evaluated in this study.
PDF
