


Politecnico di Torino  
Academic Year 2015/16  
01OAIQD, 01OAINE Dynamic design of machines 

Master of sciencelevel of the Bologna process in Mechanical Engineering  Torino 





Subject fundamentals
The main aim of the subject is to provide the students with the basic knowledge needed for the structural dynamic analysis and design. Computational methods, and particularly the numerical methods more common in the design practice, are dealt with in details, without neglecting the theoretical aspects needed to obtain the deeper knowledge of the subject required to operate in the present innovative industrial environment. The last part of the course is dedicated to the study of the dynamic analysis of rotating machinery and reciprocating engines.

Expected learning outcomes
Students are required to learn the basics of the dynamics of vibration and of the analytical and numerical methods commonly used. They must learn how to apply this knowledge to the actual dynamic study of machines and their elements, using them in a design context. The ability of interpreting in a critical way the results obtained, in particular through numerical methods, is also required. Student must also learn to produce technical documentation of the work done..

Prerequisites / Assumed knowledge
A good knowledge of the basic concepts of applied mechanics and of the methods of static stress analysis is required. A basic ability in using the relevant computer codes is also required, although no previous experience with specific numerical tools is needed.

Contents
The subject is based on a total of 60 hours of lectures plus 20 hours of classroom or laboratory exercises,
Introduction to the course (2 hours) Mechanical design. Static and dynamic stress analysis. Classical and numerical approach. Automatic computation in design. Numerical simulation. Computer aided engineering (CAE). Part 1: an overview of dynamic analysis of linear systems (14 hours): Discrete linear systems: equations of motion in the configuration space; equations in Lagrange form. State space. Block diagrams. Free behavior of single and multid.o.f. systems. Modal uncoupling; modal participation factors. Forced response to harmonic excitation. Structural damping; systems with frequency dependent parameters. Forced response to non harmonic excitation; short account of random vibrations. General considerations on continuous systems, Beams and bars. EulerBernoulli beams. Modes of continuous systems. Timoshenko beams. Effect of axial forces on flexural behaviour of beams; vibrating strings. Part 2: numerical methods and discretization techniques (16 hours): Discretization methods. Assumed modes and lumped parameter methods. Transfer matrices methods: Myklestadt and Holzer Methods. Finite element method in dynamics. Static, dynamic and Guyan reduction. Time domain and frequency domain solutions, numerical simulation Part 3: Dynamics of rotating machines (14 hours): Vibrations of rotors: Campbell diagram, critical speeds and fields of instability. Undamped and damped Jeffcott rotor. Rotor with 4 degrees of freedom, gyroscopic effect. Rotors with many degrees of freedom. Nonisotropic machines. Rotors on hydrodynamic bearings. Balancing of rotors. Parte 4: Dynamics of reciprocating machines (10 hours): Vibration of reciprocating engines and compressors, classical frequency domain and numerical time domain methods, equivalent system for torsional vibration, damping of torsional and axial vibrations of crankshafts. Parte 5: An overview on nonlinear vibration (4 hours): approximated methods , Duffing equation, jump phenomenon. Numerical simulation, basic concepts on chaotic vibration. 
Delivery modes
The exercise classes will deal with a number of exercises aimed to a better understanding of the subjects dealt with during theoretical classes and in a number of projects, the students will prepare in teams of two. The technical reports on the projects will deal specific problems of dynamic structural analysis related to specific machine elements
Some of these exercises will be performed in a computer lab, using specific numerical tools, while others will be performed in the experimental lab. 
Texts, readings, handouts and other learning resources
The textbook for the subject is:
Genta G., Vibration Dynamics and Control, Springer, New York, 2009, ISBN 978 0 387 79579 9 or, alternatively, , Genta G., Vibrazioni delle strutture e delle macchine, Levrotto e Bella, Torino, 1996. Other textbooks that can be used for specific parts of the course are Genta G, Vibration of structures and machines, III ed., Springer, New York, 1998, ISBN: 0 387 98506 9 and Genta G., Dynamics of Rotating Systems, Springer, New York, 2005 ISBN: 0387209360. Additional material for exercises will be supplied through the course website. 
Assessment and grading criteria
The exam consists of a written test with multiple choice questions and a discussion and evaluation of the projects. The students can choose to have an additional oral examination.

