Wave Propagation in Elastic Solids

Institution:
IUSS Pavia
Specialization:
ES - Engineering Seismology
Term:
Spring 2011
Teacher(s):
CARLO G. LAI, ROBERTO PAOLUCCI
Credits:
6
Date (from - to):
04/04/2011 – 06/05/2011

The course aims at illustrating the classical theories of wave propagation in elastic solids and their application to the solution of relevant engineering problems. After some mathematical preliminaries which include fundamentals of complex variable theory, Fourier-Bessel and Laplace integral transforms, the basic theorems of linear elastodynamics are introduced. The course will then focus on the study of free and forced vibrations of one and two dimensional solids such as rings, membranes and plates. Next, a selected number of 2D and 3D wave propagation problems in elastic continua will be studied together with their interaction with boundaries and surfaces of discontinuities. Topics include the generation of Stoneley-Scholte waves and the study of wave motion with cylindrical and spherical symmetry. The course will then illustrate the application of the concepts of elastodynamics to the solution of challenging engineering problems. Among them the study of the vibrational impact induced by moving loads at the free-surface of an elastic half-space under subsonic, transonic and supersonic regimes. The final part of the course is an introduction to advanced numerical techniques, such as boundary and spectral element methods, to the solution of wave propagation problems in elastic continua.

The course consists of lectures aimed to illustrate the theory and practicing sessions devoted to the solution of theoretical and practical problems.

Suggested readings:

  • Achenbach, J.D. (1999). "Wave Propagation in Elastic Solid", North-Holland (main reference textbook).
  • Eringen, A.G. and Suhubi, E.S. (1975) "Elastodynamics", Vol. II, Academic Press.
  • Graff, K.F. (1991). "Wave Motion in Elastic Solids", Dover Publications.
  • Kausel, E. (2006). "Fundamental Solutions in Elastodynamics" Cambridge Press.
  • Scientific articles and other material will be provided by the instructors.

Notes:

Assignments will be periodically assigned throughout the course. The final examination will consist of a two hours, written test. The test format is closed-book however an equation-sheet will be provided to the students. Grading: 40% Assignments - 60% Final Exam.