1,721,065 research outputs found
Compatibilita' termodinamica della legge costitutiva anisotropa per materiali policristallini e incompressibili
No full textInstability of pre-stressed solid-fluid mixture
No full textA solid-fluid mixture is generally modelled assuming that the state of stress in the reference configuration is identically equal to zero. However, such an assumption is not always appropriate to take into account some instability phenomena occurring in Nature. In this contribution, the continuum mechanics point of view is used and the reference configuration of the solid-fluid mixture has a state of stress, i.e. the pre-stress is different from zero. The instability of the mixture with respect to the perturbation fields given by a general plane wave is then studied
Dinamica di una mensola con impatti soffici: confronto del modello infinito-dimensionale con quello equivalente ad un grado di libertà (sdof).
No full textNon-smooth dynamics of a cantilever beam subjected to a transverse harmonic force and impacting onto a soft obstacle will be presented in the talk. Upon formulating the equations of motion of the beam, proper attention will be paid to identifying the mechanical properties of
an equivalent single-degree-of-freedom (SDOF) piecewise linear impacting model. A multidegree-of-freedom (MDOF) model of the impacting beam will also be derived via standard finite elements. An “optimal” identification curve of the obstacle spring rigidities in the two models will be obtained by comparing the relevant pseudo-resonance frequencies. The identification will then be exploited in the nonlinear dynamic regime to get hints on some main,
mostly regular, features of nonlinear dynamic response of the impacting beam by the actual investigation of the behavior of the sole equivalent SDOF model, with a definitely lower computational effort. Sample regular and non-regular responses of the MDOF model will also be
presented where the identification does not work. Overall, useful points will be made as regards the possibility and the limitations of referring to a SDOF impacting model to investigate the nonlinear response of the underlying infinite-dimensional system
Experimental and numerical investigations of the responses of a cantilever beam possibly contacting a deformable and dissipative obstacle under harmonic excitation
No full textIn this paper, the dynamics of a cantilever beam subjected to harmonic excitations and to the contact of an obstacle is studied with the help of experimental and numerical investigations. The steel flexible structure is excited close to the free end with a shaker and may come into contact with a deformable and dissipative obstacle. A technique for modeling contact phenomena using piece-wise linear dynamics is applied. A finite-dimensional modal model is developed through a Galerkin projection. Concentrated masses, dampers and forces are considered in the equations of motion in such a way that the boundary conditions are those of a cantilever beam. Numerical studies are conducted by assuming finite-time contact duration to investigate the frequency response of the impacted beam for different driving frequencies. Experimental results have been extrapolated through a displacement laser sensor and a load cell. The comparison between numerical and experimental results show many qualitative and quantitative similarities.
The novelty of this paper can be synthetized in a) the development of experimental results that are in good agreement with the numerical implementation of the introduced model; b) the development of a comprehensive contact model of the beam with an unilateral, deformable and dissipative obstacle located close to the tip; c) the possibility of accounting for higher modes for the cantilever beam problem, and hence of analyzing how the response varies when moving the excitation (and/or the obstacle) along the beam, and of investigating the effect of the linearly elastic deformability of the built‐in end of the beam; d) an easy and intuitive solution to the problem of accounting for spatially singular masses, dampers, springs and forces in the motion equations; e) the possibility of accounting for finite gap and duration of the contact between beam and obstacle
Identification of two-dimensional pantographic structure via a linear D4 orthotropic second gradient elastic model
Full text linkA linear elastic second gradient orthotropic two-dimensional solid that is invariant under (Formula presented.) rotation and for mirror transformation is considered. Such anisotropy is the most general for pantographic structures that are composed of two identical orthogonal families of fibers. It is well known in the literature that the corresponding strain energy depends on nine constitutive parameters: three parameters related to the first gradient part of the strain energy and six parameters related to the second gradient part of the strain energy. In this paper, analytical solutions for simple problems, which are here referred to the heavy sheet, to the nonconventional bending, and to the trapezoidal cases, are developed and presented. On the basis of such analytical solutions, gedanken experiments were developed in such a way that the whole set of the nine constitutive parameters is completely characterized in terms of the materials that the fibers are made of (i.e., of the Young’s modulus of the fiber materials), of their cross sections (i.e., of the area and of the moment of inertia of the fiber cross sections), and of the distance between the nearest pivots. On the basis of these considerations, a remarkable form of the strain energy is derived in terms of the displacement fields that closely resembles the strain energy of simple Euler beams. Numerical simulations confirm the validity of the presented results. Classic bone-shaped deformations are derived in standard bias numerical tests and the presence of a floppy mode is also made numerically evident in the present continuum model. Finally, we also show that the largeness of the boundary layer depends on the moment of inertia of the fibers
A damaged non-homogeneous Timoshenko beam model for a dam subjected to aging effects
No full textA hemi-variational formulation for a damaged non-homogeneous Timoshenko beam is proposed here for the purpose of fast simulation of the properties of a dam. The dam is therefore modeled as a damaged non-homogeneous Timoshenko beam embedded in 2D space. The damage evolution and the mechanics of the beam are governed both by the hemi- variational principle and by the assumption on the form of the deformation energy functional, that comprehends the dissipative part owing to damage-aging effects. In the formulation, the Karush–Kuhn–Tucker (KKT) condition is derived and the damage, which locally decreases the stiffness (i.e., axial, bending, and shear stiffness) of the beam, becomes rele- vant once a measure of the elastic energy, called the normalized undamaged elastic energy, reaches a certain threshold that is constitutively prescribed ab initio. The aging effect is assumed by reducing such a threshold in the neighborhood of the bottom of the beam, where the concentration of the chemical and physical attacks is higher. As a result, we show a method for the calculation of the mechanical failure condition. In addition, we observe that, even though this threshold is assumed to decrease in a large region far from the bottom of the dam, the damage is confined at the bottom of it. Thus, we have proved that the trapezoidal shape that is used in the dam design is useful not only to decrease the state of stress in the elastic regime, but also to confine the effects of damage evolution owing to the aging effects
Identification of two-dimensional pantographic structures with a linear d4 orthotropic second gradient elastic model accounting for external bulk double forces
No full textFrequency band gaps in dielectric granular metamaterials modulated by electric field
No full textWave propagation in granular materials is known to be dispersive. Micromorphic continuum model based upon granular micromechanics (Misra, A. and P. Poorsolhjouy, Continuum Mech. Thermodyn, 2016. 28(1-2): p. 215-234.) has the ability to describe this dispersion behavior. In this pa- per we show that the dispersive behavior can be modulated by using electric field when the grains have dielectric properties. To this end, we apply the recently enhanced model that incorporates electro-elastic coupling by connecting microstrain to electric dipole and quadrupole densities due to bound charges in dielectric grains (Romeo, M., Mech. Res. Commun., 2018. 91: p. 33-38.). We particularly investigate the effect of induced polarization that arises due to an imposed electric field. Two cases of dielectric one dimensional infinite rods with the same micromorphic properties have been studied, where case 1 and 2 are in null and nonzero external electric fields, respectively. Parametric studies are performed to under- stand the contribution of the polarizability (dipole effect), intrinsic quadrupole density, and external elec- tric field on the dispersive behavior of granular media. Results predict an acoustic and an optical branch in the dispersive curve. Polarizability and external electric field are mainly affecting small wavenum- ber behavior of the wave branches, while quadrupole density alters the behavior of the material at large wavenumbers. A possibility of altering the optical branch to an acoustic branch is also observed, for which instability or attenuation occurs depending upon the direction of the imposed electric field with respect to the wave propagation direction. We find that the location and the width of the frequency band gaps can be altered using external electric field. The possibility of creating or removing frequency band gaps is also shown to exist. The extended theory accounting for electro-elasticity can therefore be utilized as a tool to analyze existing granular media, or to design granular metamaterials, as it systematizes the design process and eliminates ad-hoc manners leading to large data libraries
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