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

• Autores: Damián Aranda Iglesias
• Directores de la Tesis: Jose Antonio Rodriguez Martinez (dir. tes.), Guadalupe Vadillo Martín (codir. tes.)
• Lectura: En la Universidad Carlos III de Madrid ( España ) en 2017
• Idioma: español
• Tribunal Calificador de la Tesis: Ignacio Romero Olleros (presid.), Massimo Ruzzene (secret.), Antonino Morassi (voc.)
• Programa de doctorado: Programa de Doctorado en Ingeniería Mecánica y de Organización Industrial por la Universidad Carlos III de Madrid
• Materias:
  • Física
    • Mecánica
      • Mecánica de medios continuos
• Enlaces
  • Tesis en acceso abierto en: e-Archivo
• Resumen

  • The objective of this dissertation is to develop a comprehensive theoretical approach on the role of the constitutive model on the dynamic radial deformations of nonlinear elastic thick-walled structures. Using 1D and 2D models, cylindrical and spherical thick-walled shells are considered, in their capacity as canonical configurations 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, arteries... are examples of nonlinear elastic structures with spherical and cylindrical geometries which are constantly subjected to all kinds of vibratory 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 thick-walled shells. We investigate free and forced vibrations using different initial and boundary conditions: (1) ab initio elastic stored and kinetic energies, (2) constant radial pressure, (3) linearly time dependent radial pressure and (4) periodic time dependent radial pressure. 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, for which 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 behaviour of the thick-walled shells plays a fundamental role in the dynamic response of the structure. In particular, we have demonstrated the influence of the constitutive model on: (1) the loss of oscillatory behaviour of the structure, (2) the transition from periodic motion to quasi-periodic and chaotic, (3) the nonlinear resonances diagrams of the shells, (4) the propagation of shock waves within the structure and (5) the onset and development of cavitation instabilities.