Development and application of approximate analytical methods (e.g., method of finite elements) for the solution of problems involving determination of dynamic and vibrational response of mechanical systems with complex geometry or nonlinear characteristics.
Course Content (Syllabus)
Dynamic analysis of two dimensional structural elements (membranes, disks, plates). Classical approximate methods in structural dynamics (Rayleigh, Rayleigh-Ritz, Galerkin method, assumed mode method). Method of finite elements (geometric discretization, derivation of mass and stiffness matrix and excitation vector for single-dimensional elements, coordinate transformation and assembly of global matrices). Nonlinear oscillations and stability of dynamical systems: free oscillation, self-excited oscillations, external, parametric and internal resonance.
Course Bibliography (Eudoxus)
• Σ. Νατσιάβας, “Ταλαντώσεις Δυναμικών Συστημάτων με μη Γραμμικά Χαρακτηριστικά,” Εκδόσεις Ζήτη, Θεσσαλονίκη, 2000.
• Α. Κανάραχος και Ι. Αντωνιάδης, “Δυναμική Μηχανών,” Εκδόσεις Παπασωτηρίου, Αθήνα.
Additional bibliography for study
1. W.C. Hurty and M.F. Rubinstein, "Dynamics of Structures," Prentice Hall, 1964.
2. R.W. Clough and J. Penzien, "Dynamics of Structures," McGraw-Hill, 1975.
3. L. Meirovitch, "Analytical Methods in Vibrations," The MacMillan Company, 1967.
4. R.R. Craig, "Structural Dynamics," J. Wiley & Sons, 1981.
5. S.S. Rao, "Mechanical Vibrations," 2nd ed., Addison Wesley, 1990.
6. A.D. Dimarogonas and S. Haddad, "Vibration for Engineers," Prentice Hall, Englewood Clifs, New Jersey, 1992.
7. K.J. Bathe, "Finite Element Procedures in Engineering Analysis," Prentice Hall, 1982.
8. A.H. Nayfeh and D.T. Mook, "Nonlinear Oscillations," J. Wiley & Sons, 1979.
9. J.J. Stoker, "Nonlinear Vibrations," Interscience Publishers, Inc. 1950.