Longtime Dynamics of a Semilinear Lamé System

This paper is concerned with longtime dynamics of semilinear Lamé systems ∂2 t u − μ u − (λ + μ)∇divu + α∂tu + f (u) = b, defined in bounded domains ofR3 with Dirichlet boundary condition. Firstly,we establish the existence of finite dimensional global attractors subjected to a critical forcing f (u).Writing λ + μ as a positive parameter ε, we discuss some physical aspects of the limit case ε → 0. Then, we show the upper-semicontinuity of attractors with respect to the parameter when ε → 0. To our best knowledge, the analysis of attractors for dynamics of Lamé systems has not been studied before

Faceted wrinkling by contracting a curved boundary

Single-mode deformations of two-dimensional materials, such as the Miura-ori fold, are important to the design of deployable structures because of their robustness, but usually require careful pre-patterning of the material. Here, we show that inward contraction of a curved boundary produces a novel single-mode deformation without any pre-patterning. Using finite-element simulations of the contraction of a thin circular annular sheet, we show that these sheets wrinkle into a structure with negligible stretching energy, in which the contracted boundary forms spontaneous facets. We construct a strictly isometric wrinkled surface formed of triangles and cones that matches geometric and energy features closely, suggesting that this class of partly-faceted wrinkled deformations is isometric. Isometry favours the restriction of such deformations to a robust low-bending energy channel that avoids stretching. This class of buckling also offers a novel way to manipulate sheet morphology via boundary forces. Finally, it serves as a minimal model for illustrating the strong constraints imposed by geometry in elastic pattern formation.Comment: V3. Double column. 6 pages, 5 figures + S

On a system of nonlinear wave equations with the Kirchhoff-Carrier and Balakrishnan-Taylor terms

summary:We study a system of nonlinear wave equations of the Kirchhoff-Carrier type containing a variant of the Balakrishnan-Taylor damping in nonlinear terms. By the linearization method together with the Faedo-Galerkin method, we prove the local existence and uniqueness of a weak solution. On the other hand, by constructing a suitable Lyapunov functional, a sufficient condition is also established to obtain the exponential decay of weak solutions

Non-Classical Memory Kernels in Linear Viscoelasticity

In linear viscoelasticity, a large variety of regular kernels have been classically employed, depending on the mechanical properties of the materials to be modeled. Nevertheless, new viscoelastic materials, such as viscoelastic gels, have been recently discovered and their mechanical behavior requires convolution integral with singular kernels to be described. On the other hand, when the natural/artificial aging of the viscoelastic material has to be taken into account, time-dependent kernels are needed. The aim of this chapter is to present a collection of nonstandard viscoelastic kernels, with special emphasis on singular and time-dependent kernels, and discuss their ability to reproduce experimental behavior when applied to real materials. As an application, we study some magneto-rheological elastomers, where viscoelastic and magnetic effects are coupled

Mathematical and Numerical Aspects of Dynamical System Analysis

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Moore-Gibson-Thompson thermoelasticity with two temperatures

In this note we propose the Moore-Gibson-Thompson heat conduction equation with two temperatures and prove the well posedness and the exponential decay of the solutions under suitable conditions on the constitutive parameters. Later we consider the extension to the Moore-Gibson-Thompson thermoelasticity with two temperatures and prove that we cannot expect for the exponential stability even in the one-dimensional case. This last result contrasts with the one obtained for the Moore-Gibson-Thompson thermoelasticity where the exponential decay was obtained. However we prove the polynomial decay of the solutions. The paper concludes by giving the main ideas to extend the theory for inhomogeneous and anisotropic materials.Peer ReviewedPostprint (published version

14th Conference on Dynamical Systems Theory and Applications DSTA 2017 ABSTRACTS

From Preface: This is the fourteen time when the conference “Dynamical Systems – Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and the Ministry of Science and Higher Education. It is a great pleasure that our invitation has been accepted by so many people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcome nearly 250 persons from 38 countries all over the world. They decided to share the results of their research and many years experiences in the discipline of dynamical systems by submitting many very interesting papers. This booklet contains a collection of 375 abstracts, which have gained the acceptance of referees and have been qualified for publication in the conference proceedings [...]

Frequency-dependent impedance of a strip foundation group and its representation in time domain

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Experimental testing and nonlinear viscoelastic modeling of filled rubber

Owing to its unique physical properties, rubber plays a keyrole in countless industrial applications. Tires, vibration absorbers and shoe soles are only but a few of the myriad uses of natural and synthetic rubber in an industry which in 2009 had an estimated market value of 2 billion euro. Despite a peculiar internal structure, the macroscopic behavior of filled-rubber is reminiscent of several biological soft tissues. While rubber is internally constituted by flexible long chain molecules that intertwine with each other, a similar role is played, in soft-tissues, by collagen fiber bundles. As a consequence, both classes of materials are able to sustain large strains and exhibit the characteristics of a viscous fluid and an elastic solid. In industry, the requirement to model complex geometrical structures made of materials exhibiting a nonlinear constitutive behavior is a compelling reason to use Finite Element Analysis (FEA) software. The predictive capabilities of these numerical tools strongly rely upon the capabilities of the underlying model to describe the material’s rheological properties. The possibility of simulating accurately the material behavior over the entire working range avoids the use of excessive number of prototypes, thereby reducing the need for expensive and difficult experimental tests; consequently, development costs can be drastically reduced. The theory of viscoelasticity is crucial in describing materials, such as filled rubber, which exhibit time dependent stress-strain behavior. In many engineering applications, such as the estimate of the rolling resistance of tires and hysteretic losses in soft biological tissues, the energy dissipation is a primary feature to be predicted. In addition, in the usual operative range, tires, shock absorbers and other rubber components bear finite dynamic deformations. Therefore, a reliable constitutive equation must be assessed within the theory of nonlinear viscoelasticity. A review of the literature revealed significantly more well-established studies dealing with hyperelastic constitutive models, than those dealing with finite viscoelasticity. Over the years, many hyperelastic models able to describe all the relevant aspects of the quasi-static response have been introduced. Furthermore, the American norms (ASTM D412, ASTM D575, ASTM D945, ASTM D6147, ASTM D1456) establish all the experimental techniques to identify the material constitutive parameters. In this context, many authors have recently addressed the problem of finite amplitude wave propagation or focused their interest upon particular boundary value problems. On the other hand, there is a lack of well-established nonlinear viscoelastic models capable of describing all the relevant effects in the material response. Moreover, a standardization similar to that concerning the static norms is yet to be achieved. The usual methodology provides for small harmonic deformations superimposed on a large static displacement. However, such a prescription does not allow the capture of many of the relevant nonlinear phenomena. In the literature, experimental evidence concerning finite dynamic deformations is rarely reported

Modeling and Simulation in Engineering

The Special Issue Modeling and Simulation in Engineering, belonging to the section Engineering Mathematics of the Journal Mathematics, publishes original research papers dealing with advanced simulation and modeling techniques. The present book, “Modeling and Simulation in Engineering I, 2022”, contains 14 papers accepted after peer review by recognized specialists in the field. The papers address different topics occurring in engineering, such as ferrofluid transport in magnetic fields, non-fractal signal analysis, fractional derivatives, applications of swarm algorithms and evolutionary algorithms (genetic algorithms), inverse methods for inverse problems, numerical analysis of heat and mass transfer, numerical solutions for fractional differential equations, Kriging modelling, theory of the modelling methodology, and artificial neural networks for fault diagnosis in electric circuits. It is hoped that the papers selected for this issue will attract a significant audience in the scientific community and will further stimulate research involving modelling and simulation in mathematical physics and in engineering