Dynamic radial deformations of nonlinear elastic structures. On the influence of constitutive modeling

Mención Internacional en el título de doctorThe objective of this dissertation is to develop a comprehensive theoretical approach to the role of the constitutive model on the dynamic radial deformations of nonlinear elastic structures. Using 1D and 2D models, cylindrical and spherical thick-walled shells are considered. These geometries are representative of man-made and natural structures that can be found in a wide variety of engineering applications and biological systems. Lead-rubber bearings, vibration isolators, peristaltic pumps, rubber bushings, saccular aneurysms or arteries are examples of nonlinear elastic structures with spherical and cylindrical geometries that are constantly subjected to all kinds of vibrational and dynamic loads. The research, which starts by considering isotropic, incompressible and rate independent constitutive models, is based on the systematic incorporation of compressibility, viscosity and anisotropy in the description of the mechanical response of the material. We investigate free and forced vibrations using different initial and boundary conditions: (1) ab initio elastic stored and kinetic energies, (2) constant radial pressures, (3) linearly time dependent radial pressures and (4) harmonic time dependent radial pressures. While the isotropic and incompressible 1D elastic structures subjected to constant pressure admit an analytical closed-form solution, all the other cases need to be solved numerically. To this end, we have developed in this work a number of specific numerical schemes. The overall outcome of this dissertation is to make it plain that the constitutive model used to describe the mechanical behavior of thick-walled shells plays a fundamental role in the nonlinear dynamics of such structures. In particular, we have demonstrated the influence of the constitutive model on: (1) the loss of oscillatory behavior of the structure, (2) the transition from periodic motions to quasi-periodic and chaotic motions, (3) the nonlinear resonances of the shells, (4) the propagation of shock waves within the structure and (5) the onset and development of cavitation instabilities.Programa Oficial de Doctorado en Ingeniería Mecánica y de Organización IndustrialPresidente: Ignacio Romero Olleros.- Secretario: Massimo Ruzzene.- Vocal: Antonio Morass

A closed-form solution for asymmetric free vibration analysis of composite cylindrical shells with metamaterial honeycomb core layer based on shear deformation theory

Asymmetric free vibration analysis of composite cylindrical shells with a honeycomb core layer and adjustable Poisson’s ratio is performed analytically in this study. The equations of motion which are a system of coupled partial differential equations are extracted using Hamilton’s principle by employing the first-order shear deformation theory and they are solved analytically. To study the sensitivity of the results to the different parameters of the honeycomb structure, geometrical parameters, and boundary conditions, a parametric study is presented. It is concluded that for the auxetic composite shell with a negative Poisson’s ratio, by decreasing the Poisson ratio, the frequency decreases. Also, it is shown that by employing the composite shells the weight decreases significantly, while the asymmetric frequency will not change remarkably. By adjusting the Poisson ratio, the frequency variations are studied for a composite shell with a honeycomb core layer. The results are compared with the finite element method and some other references

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”

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 [...]