MECHANICAL VIBRATIONS
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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- GIORGIO DALPIAZ
- Credits
- 6
- Didactic period
- Secondo Semestre
- SSD
- ING-IND/13
Training objectives
- The course provides the basic knowledge and methods in order to solve technical problems concerning the dynamic and vibration behaviour of machinery and mechanical systems.
The main acquired knowledge will be:
- Classification of signals and frequency analysis;
- Lumped parameter modeling;
- Vibrations of single degree of freedom systems;
- Vibrations of systems with two and many degrees of freedom;
- Vibration measurements;
- Dynamics of the rotors.
The main skills acquired (i.e. the ability to apply acquired knowledge) will be:
- developing lumped-parameter models, calculating their parameters;
- carrying out modal analysis of lumped parameter models by analytical and numerical methods;
- numerically evaluating the vibrational response;
- carrying out vibration measurements and experimental modal analysis;
- carrying out balancing of rotors by subcritical machines. Prerequisites
- Courses of Mathematics, Physics, Theoretical Mechanics and Mechanics of Machines.
Course programme
- The course lasts 60 hours, including lessons and exercises.
The course topics are the following.
INTRODUCTION TO VIBRATIONS AND MODELING OF MECHANICAL SYSTEMS.
CLASSIFICATION OF SIGNALS AND FREQUENCY ANALYSIS: Series and Fourier Transform. Sampling of signals.
LUMPED PARAMETER MODELING.
VIBRATIONS OF ONE DEGREE OF FREEDOM SYSTEMS: Free vibrations. Energy methods; Rayleigh method and applications. Forced vibrations. Frequency Response Function. Response to periodic and aperiodic generic excitation; impulse response function; integral of convolution. Excitation proportional to the square of the frequency. Vibration isolation: mass excitation, base excitation, transmissibility, suspension effectiveness.
VIBRATIONS OF TWO AND MANY DEGREES OF FREEDOM SYSTEMS: Free vibrations of two and many degrees of freedom undamped systems. Systems with rigid modes. Method of influence coefficients. Compliance method. Orthogonality of the eigenvectors. Normalization of the eigenvectors. Energy aspects; Rayleigh quotient; structural modifications. Modal matrix and decoupling of equations. Vibration free of two- and multi-degree-of-freedom systems with proportional viscous damping. Forced vibrations of systems with two and many degrees of freedom (modal method). Frequency Response Functions and their properties.
VIBRATION MEASUREMENTS: Vibration transducers. The piezoelectric accelerometer. Shaker and instrumented hammer. Experimental modal analysis; FRF evaluation (H1 and H2 estimates); extraction of modal parameters; experimental demonstration.
ROTOR DYNAMICS: Static and dynamic imbalance. Balancing of rigid rotors. Subcritical balancing machine; experimental exercise. Balancing under operating conditions (in situ); experimental exercise. Didactic methods
- Theoretical and applicative numerical lessons, practical experimental exercises in the laboratory.
Learning assessment procedures
- Written/oral examination on the topics of the course and exercises. It consists in three questions: two questions are theoretical and methodological, mainly aimed at assessing the knowledge; one question is a numerical exercise, mainly aimed at checking skills in the procedures for vibration analysis. The questions are carried out in writing and are immediately corrected and discussed orally. The rating assigned to each question refers to both written and oral performances. The final grade is the average of the votes on the three questions. To pass the exam you must achieve a minimum final grade of 18/30.
To take the exam it is necessary to present the exercises to be carried out in writing, which will be checked and discussed.
Passing the examination is proof of having acquired the knowledge and skills specified in the training objectives. Reference texts
- Reference book:
•Meneghetti, Maggiore, Funaioli, Lezioni di meccanica applicata alle macchine. Vol. 3: Dinamica e vibrazioni delle macchine, Pàtron, 2010.
•E. Funaioli, A. Maggiore, U. Meneghetti, Lezioni di meccanica applicata alle macchine. Vol. 1: Fondamenti di Meccanica delle Macchine, Pàtron, 2005.
Other books recommended for consultation:
•Rao, Mechanical Vibrations, 3rd ed., New York, Addison-Wesley, 1995.
•Thomson W., Theory of Vibration with Applications, 4th edition, New York, Chapman & Hall, 1993.
