The course is an advanced module on vibrations of mechanical systems, with emphasis on distributed parameter systems. Techniques for the discretisation of distributed parameter systems, with special reference to the finite element method, are also covered by the course. The course also contains a short introduction to rotordynamics.
Dynamics and vibration of discrete systems with more than one degree of freedom (dof)
Methods for writing the equations of motion of multi-dof systems. Equations of motion using the set of principal coordinates and representation of system motion in terms of modal superposition. Techniques for the identification of modal parameters from measurements of the system’s dynamic behaviour. Introduction to the spatial dynamics of rigid bodies.
Dynamics of mono-dimensional continuous systems - Analytical solutions. Axial and torsional vibrations of beams: propagative and standing wave solutions, natural frequencies and modes of vibration for different boundary conditions. Transversal vibrations of stretched strings. Bending vibrations of slender beams (Euler-Bernoulli formulation): standing wave solution, natural frequencies and modes of vibration for different boundary conditions. Free vibration of systems of beams, analytical solutions. Forced vibration for systems of beams: the modal superposition principle. Orthogonality of the modes of vibration for mono-dimensional continua.
Dynamics of mono-dimensional continuous systems - The finite element method. Discretisation methods for continuous systems. The finite element method. Beam type finite elements: shape functions, local and global coordinates, stiffness and damping matrices, effect of static axial tension. Expression of the nodal forces corresponding to typical concentrated and distributed loads. Assembling finite elements into a model, boundary conditions. Structural damping model. Calculations of the natural frequencies and modes of vibration, calculation of frequency response function and of the response to arbitrary loads. Outline of the application of the Finite Element method with 2D and 3D discretisation.
Rotordynamics. Dynamic problems in rotating machines. Rotor schematisation. Numerical model of the fluid lubricated journal bearing and linearisation: equivalent stiffness and damping matrices. Instability produced by oil film forces. Bending critical speeds and methods for rotor balancing.
 Diana G., Cheli F.: Dinamica e Vibrazioni dei Sistemi meccanici, Polipress, 2008.
 Meirovitch L.: Fundamentals of Vibrations, Mc Graw-Hill International Edition.
 Handouts available on the course site