Moving mass over a viscoelastic system: asymptotic behaviours and insights into nonlinear dynamics

Moving masses are of interest in many applications of structural dynamics, soliciting in the last decades a vast debate in the scientific literature. However, despite the attention devoted to the subject, to the best of the authors’ knowledge, there is a lack of analysis about the fate of a movable mass when it rolls or slips with friction on a structure. With the aim of elucidating the dynamics of the simplest paradigm of this system and to investigate its asymptotic response, we make reference to a two-degree-of-freedom model made of an elastically vibrating carriage surmounted by a spherical mass, facing the problem both theoretically and experimentally. In case of linear systems, the analytical solutions and the laboratory tests performed on ad hoc constructed prototypes highlighted a counterintuitive asymptotic dynamics, here called binary: in the absence of friction at the interface of the bodies’ system, the mass holds its initial position or, if nonzero damping acts, at the end of the motion it is in a position that exactly recovers the initial relative distance carriage–sphere. While the first result might be somewhat obvious, the second appears rather surprising. Such a binary behaviour is also confirmed for a Duffing-like system, equipped with cubic springs, while it can be lost when non-smooth friction phenomena occur, as well as in the case of elastic springs restraining the motion of the sphere. The obtained analytical results and the numerical findings, also confirmed by experimental evidences, contribute to the basic understanding of the role played by the damping parameters governing the systems’ dynamics with respect to its asymptotic behaviour and could pave the way for designing active or passive vibration controllers of interest in engineering

Numerical experiments in 2D variational fracture

In the present work we present some results of numerical experiments obtained with a variationalmodel for quasi-static Griffith-type brittle fracture. Essentially the analysis is based on a recent formulation byFrancfort and Marigo the main difference being the fact that we rely on local rather than on globalminimization. Propagation of fracture is obtained by minimizing, in a step by step process, a form of energythat is the sum of bulk and interface terms. To solve the problem numerically we adopt discontinuous finiteelements based on variable meshes and search for the minima of the energy through descent methods. We use asort of mesh dependent relaxation of the interface energy to get out of small energy wells. The relaxationconsists in the adoption of a carefully tailored cohesive type interface energy, tending to the Griffith limit as themesh size tends to zero

Mechanical response of tensegrity-origami solar modules

This work studies the mechanics of novel origami solar modules with tensegrity architecture for integration in the dynamic solar facades of energy-efficient buildings. The analyzed modules are deployed by adjusting the rest lengths of cables attached to given nodes, so as to form a tensegrity origami. Their stiffness is tuned by adjusting the pretension of the actuation cables, when the deployment motion is locked. The insertion of solar thermal or photovoltaic panels into the rigid elements of the module makes it possible to form positive energy solar systems. The work studies the kinematics and the mechanics of the investigated structures through analytic and numerical methods. Two folding motions are examined: to open and close the modules and to track sun rays. The rapid prototyping of a physical mock-up permits an experimental validation of the force- displacement response in a given configuration of the sun-tracking motion. A procedure for the computation of the fundamental vibration modes and vibration frequencies of a quadrangular solar module is also given, and the expected response of the system under wind loading is outlined

Numerical experiments in 2D variational fracture

In the present work we present some results of numerical experiments obtained with a variationalmodel for quasi-static Griffith-type brittle fracture. Essentially the analysis is based on a recent formulation byFrancfort and Marigo the main difference being the fact that we rely on local rather than on globalminimization. Propagation of fracture is obtained by minimizing, in a step by step process, a form of energythat is the sum of bulk and interface terms. To solve the problem numerically we adopt discontinuous finiteelements based on variable meshes and search for the minima of the energy through descent methods. We use asort of mesh dependent relaxation of the interface energy to get out of small energy wells. The relaxationconsists in the adoption of a carefully tailored cohesive type interface energy, tending to the Griffith limit as themesh size tends to zero

Computational Modeling of The Mechanics of Energy Harvesters Based On Tensegrity Solar Façades

This work is focused on the computational design of tensegrity shading systems of energy efficient buildings which mitigate air conditioning consumption and optimize the energy performance of the building. It is concerned with the design of active solar façade screens based on lightweight tensegrity units, which are easily integrated with energy harvesting piezoelectric cables. The unit cells of the analyzed screens are controlled by tensioning and releasing selected cables of the structure. A numerical procedure simulates the dynamics of the analyzed tensegrity façades, by considering the opening and closure motions of the screens, and the vibrations produced by the action of dynamic wind forces. The energy harvesting ability of the proposed façade is numerically estimated

Folded states of thin walled tubes as energy minimizers

Buckling deformations of hollow cylinders whose buckled configurations consist of inextensional deformations (folding) of their middle surface can be described as minimal states in a free gradient discontinuity problem. In the contribution this general idea is applied to a far simpler context namely the case in which the shape of the folding pattern is somehow known, that is depends on a small number of discrete or continuous parameters. The example we consider is the axial compression of a tube of rectangular hollow section. If the tube is short and thin, in a sense that can be made precise in terms of the ratio between the yield stress and the Young modulus of the material, it exhibits local buckling in the form of a rather typical pattern controlled by at most three parameters. Such parameters are identified by minimizing the total potential energy and the results are compared with test results for aluminum alloy specimens