Mass spring models (MSMs) are a popular choice for representation of soft bodies in computer graphics and virtual reality applications. In this paper, we investigate physical properties of the simplest MSMs composed of mass points and linear springs. The nodes are either placed on a cubic lattice or positioned randomly within the system. We calculate the elastic moduli for such models and relate the results to other studies. We show that there is a welldefined relationship between the geometric characteristics of the MSM systems and physical properties of the modeled materials. It is also demonstrated that these models exhibit a proper convergence to a unique solution upon mesh refinement and thus can represent elastic materials with a high precision.
In this paper we show how to construct mass spring models for the representation of homogeneous isotropic elastic materials with adjustable Poisson's ratio. Classical formulation of elasticity on mass spring models leads to the result, that while materials with any value of Young's modulus can be modeled reliably, only fixed value of Poisson's ratio is possible. We show how to extend the conventional model to overcome this limitation. The technique is demonstrated on cubic lattice as well as disordered networks.
In this paper we analyse static properties of mass spring models (MSMs) with the focus of modelling non crystalline materials, and explore basic improvements, which can be made to MSMs with disordered point placement. Presented techniques address the problem of high variance of MSM properties which occur due to randomised nature of point distribution. The focus is placed on tuning spring parameters in a way which would compensate for local non-uniformity of point and spring density. We demonstrate that a simple force balancing algorithm can improve properties of the MSM on a global scale, while a more detailed stress distribution analysis is needed to achieve local scale improvements. Considered MSMs are three dimensional.
In this paper, we show how to construct mass spring models for the representation of homogeneous isotropic elastic materials with adjustable Poisson's ratio. Classical formulation of elasticity on mass spring models leads to the result, that while materials with any value of Young's modulus can be modeled reliably, only fixed value of Poisson's ratio is possible. We show how to extend the conventional model to overcome this limitation.
This paper studies the regular and irregular vibrations of two degrees of freedom autoparametrical system, when the excitation is made by an electric motor (with unbalanced mass), which works with limited power supply. The investigated system consists of a pendulum of the length l and mass m, and a body of mass M suspended on the flexible element. It was assumed that the damping force acting on the body of mass M and resistive moment acting on the pedulum are non-linear. In this case, the excitation has to be expressed as an equation describing how the energy source supplies the energy to the system. The non-ideal source of power adds one degree of freedom, and then the system has three degrees of freedom. The system has been researched for known characteristic of the energy source (DC motor). The equations of motion have been solved numerically what permit to enrich the investigations and to examine not only small and steady state oscillations but also large-amplitude oscillations in transient states. The influence of motor’s speed on the phenomenon of energy transfer has been researched. Near the internal and external resonance region, except different kind of periodic vibration, the chaotic vibration has been observed. For characterizing an irregular chaotic response bifurcation diagrams and time histories, power spectral densities, Poincare´ maps and maximal exponents of Lyapunov have been constructed.
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