Course Content (Syllabus)
Analytical dynamics (generalized coordinates, motion constraints, principle of virtual work, d’ Alembert’s principle, Lagrange’s equations, Hamilton’s principle). Free vibration and forced response of multiple degree of freedom linear oscillators (natural frequencies and mode shapes, orthogonality conditions, modal analysis, resonance). Classical (Rayleigh, Caughey) damping. Linear rotordynamics (analytical methods, bi-orthogonality, finite element method). Numerical solution of kinematical equations and equations of motion of linear and nonlinear mechanical systems, structures and mechanisms (solution of systems of algebraic equations, eigenproblems and differential equations). Direct determination of constant and periodic steady-state motions. Continuation techniques. Rotordynamics. Applications (selected examples from rigid body dynamics, vibration isolation, vibration absorption, selection of flywheels and mass balancing in turbomachinery).
Additional bibliography for study
• Greenwood, D.T., Principles of Dynamics, Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1988.
• Meirovitch, L., Methods of Analytical Dynamics, McGraw-Hill Inc., New York, 1970.
• Craig, Jr., R.R., Structural Dynamics - An Introduction to Computer Methods, J. Wiley & Sons, New York, 1981.
• Childs, D.W., Turbomacinery Rotordynamics: Phenomena, Modeling & Analysis, J. Wiley & Sons, New York, 1993.
• Muszynska A, Rotor dynamics, CRC Press, 2005.
• Adams ML Jr, Rotating Machinery Vibration: From Analysis to Troubleshooting, CRC Press, 2009.