Plane waves and eigenfrequency study in a transversely isotropic magneto-thermoelastic medium under the effect of a constant angular velocity

Abd-alla, Abo-el-nour N.; Alshaikh, Fatimah; Vescovo, Dionisio Del; Spagnuolo, Mario

doi:10.1080/01495739.2017.1334528

Cited by 28 publications

(5 citation statements)

References 29 publications

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“…The damping property of a mechanical system is an essential feature in many applications. To provide a gallery of the potential important fields of application, it suffices to mention some examples of one-dimensional (1D) structures (see, for example, previous studies [25–28]), two-dimensional (2D) structures [29], robotic arms [30,31], building or granular materials [32–34], biosystems [35], viscoelastic materials [36–38], and wave propagation in generalized media where thermal effects are taken into account [39,40]. In these cases, the mechanical system has to be synthesized, focusing on the demand of producing a particular attitude to damping.…”

Section: Discussionmentioning

confidence: 99%

Approximation of dissipative systems by elastic chains: Numerical evidence

Bersani

Caressa

Dell’Isola

2022

Mathematics and Mechanics of Solids

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An old and debated problem in Mechanics concerns the capacity of finite dimensional Lagrangian systems to describe dissipation phenomena. It is true that Helmholtz conditions determine not-always verifiable conditions establishing when a system of n second-order ordinary differential equations in normal form (nODEs) be the Lagrange equations deriving from an nth dimensional Lagrangian. However, it is also true that one could conjecture that, given nODEs it is possible to find a ( n+ k)th dimensional Lagrangian such that the evolution of suitably chosen n Lagrangian parameters allows for the approximation of the solutions of the nODEs. In fact, while it is well known that the ordinary differential equations (ODEs) usually introduced for describing some dissipation phenomena do not verify Helmholtz conditions, in this paper, we give some preliminary evidence for a positive answer to the conjecture that a dissipative system having n degrees of freedom (DOFs) can be approximated, in a finite time interval and in a suitable norm, by an extended Lagrangian system, having a greater number of DOFs. The theoretical foundation necessary to formulate such a conjecture is here laid and three different examples of extended Lagrangians are shown. Finally, we give some computational results, which encourage to deepen the study of the theoretical aspects of the problem.

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Section: Discussionmentioning

confidence: 99%

Approximation of dissipative systems by elastic chains: Numerical evidence

Bersani

Caressa

Dell’Isola

2022

Mathematics and Mechanics of Solids

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“…Finally, it would be interesting to study the dynamics in pantographic structures of the same dimensions as those presented in this article. In fact, the propagation of waves in generalized continua [64][65][66] is a non-trivial problem and can lead to unexpected results. Some preliminary results in the field of pantographic structures can be found in [67,68].…”

Section: Discussionmentioning

confidence: 99%

Parametric Experimentation on Pantographic Unit Cells Reveals Local Extremum Configuration

et al. 2019

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Pantographic metamaterials are known for their ability to have large deformation while remaining in the elastic regime. We have performed a set of experiments on 3D printed pantographic unit cells to parametrically investigate their response when undergoing tensile, compression, and shear loading with the aim of i) studying the role of each parameter in the resultant mechanical behavior of the sample, and ii) providing a benchmark for the mathematical models developed to describe pantographic structures. Results show the existence of local extrema in the space of the geometrical parameters, suggesting the use of optimization techniques to find optimal geometrical parameters resulting in desired functionalities. We have also performed tensile relaxation tests on the samples, with the results indicating the complexity of the dynamic behavior and the existence of multiple relaxation characteristic times. Such results can be used to for calibrating mathematical models describing pantographic structures under dynamic loadings.

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“…For a more complicated 2D triangular lattice, higher-order material parameters associated with the third gradient elasticity, have been determined by tension, shear and vibration tests in [46]. Before studying damage and fracture in generalized material, it will be useful to perform some dynamic analyses as the one presented in [47,48]. In particular, first experimental results about dynamic behavior in pantographic metamaterials has been discussed in [49].…”

Section: Discussionmentioning

confidence: 99%

A continual model of a damaged medium used for analyzing fatigue life of polycrystalline structural alloys under thermal–mechanical loading

Volkov

Игумнов

Dell’Isola

et al. 2019

Continuum Mech. Thermodyn.

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The main physical laws of thermal-plastic deformation and fatigue damage accumulation processes in polycrystalline structural alloys under various regimes of cyclic thermal-mechanical loading are considered. Within the framework of mechanics of damaged media, a mathematical model is developed that describes thermal-plastic deformation and fatigue damage accumulation processes under low-cycle loading. The model consists of three interrelated parts: relations defining plastic behavior of the material, accounting for its dependence on the failure process; evolutionary equations describing damage accumulation kinetics; a strength criterion of the damaged material. The plasticity model based on the notion of yield surface and the principle of orthogonality of the plastic strain vector to the yield surface is used as defining relations. This version of defining equations of plasticity describes the main effects of the deformation process under monotone cyclic, proportional and nonproportional loading regimes. The version of kinetic equations of damage accumulation is based on introducing a scalar parameter of damage degree and energy principles, and account for the main effects of nucleation, growth and merging of microdefects under arbitrary regimes of low-cycle loading. The strength criterion of the damaged material is based on reaching a critical value of the damage degree. The results of numerically modeling cyclic thermal-plastic deformation and fatigue damage accumulation in heat-resistant alloys (Nimonic 80A, Haynes 188) under combined thermal-mechanical loading are presented. Special atten-Communicated by Andreas Öchsner.

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Plane waves and eigenfrequency study in a transversely isotropic magneto-thermoelastic medium under the effect of a constant angular velocity

Cited by 28 publications

References 29 publications

Approximation of dissipative systems by elastic chains: Numerical evidence

Approximation of dissipative systems by elastic chains: Numerical evidence

Parametric Experimentation on Pantographic Unit Cells Reveals Local Extremum Configuration

A continual model of a damaged medium used for analyzing fatigue life of polycrystalline structural alloys under thermal–mechanical loading

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