OVERVIEW

The course introduces the experimentation, modeling and simulation of mechanical systems characterized by dynamic behavior, i.e. represented by quantities (e.g. displacements, stresses, deformations, etc.) that vary over time. During the semester, 5 case studies are treated, designed to stimulate the understanding of relevant phenomena in the field of vibration mechanics and aeroelasticity. Each case study is treated in an experimental, analytical and numerical way.

AIMS AND CONTENT

LEARNING OUTCOMES

Qualitative understanding of dynamical phenomena relevant for mechanical engineering. Ability to model dynamics of mechanical systems. Ability to realize simple experiments in mechanics. Ability to design and select vibration reduction devices

AIMS AND LEARNING OUTCOMES

Ability to design and carry out simple experiments on mechanical systems

Ability to perform simple vibration measurements and analyze the data obtained (using Matlab)

Ability to summarize the salient aspects of an experimental observation

Ability to build mathematical models based on basic physical principles to reproduce experimental observations

Ability to numerically simulate dynamic systems (using Matlab and Simulink)

Ability to design experiments aimed at estimating model parameters

PREREQUISITES

Mathematics (differentoial equations)

Physics (Newton's laws)

TEACHING METHODS

The didactic approach is inductive, i.e. it starts from the observation of experimental evidence (experimentation), builds mathematical models on the basis of basic physical principles (modeling), uses the models obtained to reproduce the observed reality (simulation).

SYLLABUS/CONTENT

Introduction to the course. Course setting and philosophy. Teaching materials. Elements of evaluation.
1. Introduction to Matlab and simulink
1.1 Matlab installation.
1.2 Fundamentals: Matlab as a calculator; Variables (vectors, matrices); assignment; operations.
1.3 Data representation: Plot functions (lines and surfaces);
1.4 Data exchange with other environments: reading / writing files
1.5 Simulink: Environment, graphics simulation

2. Simple oscillator in free motion.
2.1 Experiment with accelerometer and vibrometer.
2.1.1 Experiment description: how the oscillator is made (and why), how the sensors work, the measurement chain
2.1.2 Experiment observation: vibration from initial condition (harmonic motion with exponential envelope), effect of mass (test with two different masses, it is noted that the period of oscillation changes)
2.2 Oscillator modeling
2.2.1 Balance of forces using Newton's equations. Undamped equation.
2.2.2 Simulink oscillator model. Description of blocks needed to build the model (integrator, gain. Model building by feedback
2.2.3 Observations: mass effect, kinetic and potential energy calculation (the model is conservative); the equation of motion could be obtained through the Lagrange equations; dynamic meaning of the parameters (natural pulsation, natural period)
2.2.4 Introduction of dissipation to reconcile the model with experimentation. Viscous model
2.2.5 Damped oscillator simulink model. I observe that the motion is extinguished with exponential envelope
2.2.6 Dissipated energy. Because the force proportional to the speed is non-conservative
2.2.7 Dynamic meaning of parameters (omega_n, zeta)
2.3 Parameter identification
2.3.1 Measurement of stiffness for the identification of omega_n
2.3.2 Measurement of logarithmic decrease by estimation zeta

3. Forced s-dof response
3.2 Model for rotating force
3.1 Experiment with eccentric rotating mass.
3.1.1 Observations: the amplitude increases when Omega is close to omega_n; the phase between rotation and response changes as it passes through the resonance
2.4 Validation of the s-dof model. Upload measured data; parameter estimation (omega_n from stastic test, zeta from dynamic test); estimate initial conditions; comparison measure and simulated
3.2.1 Analytical formulation of steady-state response with harmonic force. Frequency response function
3.3.2 Laboratory measurement of FRF. Calculation of frequency and phase force from tacho probe. FRF diagram

4. Double pendulum connected with springs
4.0.1 Experimental observations: a pendulum behaves like an oscillator; I observe beating for some initial conditions
4.1 Single pendulum model with springs
4.2 Double pendulum model (two degrees of freedom system)
4.2.1 Equations of motion
4.3 Coordinate change to decouple equations.
4.2.2 Implementation in simulink
4.3 Initial conditions effect
4.2.2 Implementation in simulink
4.4 Beating

5. Transverse vibration of a taut string
5.1 Experiment: the string has vibrations of great amplitude if excited at a certain frequency; the frequency that produces amplification changes with voltage; if Omega produces amplification, then k * Omega also produces amplification; if Omega produces a deformation with a half wave, then k * Omega produces a deformation with k half waves
5.2 Modeling: discrete model, transition to continuum, PDE.
5.2.1 Solution by separation of variables. Modes of vibration and natural frequencies. Modal representation of the displacement.
5.3 Effect of initial conditions
5.3.1 Experiments with guitar
5.3.2 Transfer of initial conditions to principal coordinates
5.3.3 Free answer simulation. Principal coordinate evolution. Spatial shape evolution

6. Vortex Induced Vibrations (VIV)
6.1 Experimentation in the wind tunnel on a circular cylinder with flexible supports
6.1.1 Description of the experiment: elastic supports, allowed modes of vibration, sources of dissipation
6.1.2 Analysis of the dynamic response: transverse harmonic motion, Strouhal's law, lock-in
6.1.3 Description of the fluid dynamics phenomenon by means of CFD animation
6.2 VIV modeling of an isolated circular cylinder. Autonomous force model, motion dependent force, wake oscillator

7. Aeroelastic instability of an airfoil
7.1 Experimentation in the wind tunnel
7.1.1 Description of the experiment: control parameters
7.1.2 Analysis of the experiment: dynamic instability (flutter)
7.2 Flutter modeling: two degrees of freedom system and self-excited forces according to the quasi-static approach
7.3 Prediction of the critical instability speed

RECOMMENDED READING/BIBLIOGRAPHY

Lecture notes available on Aulaweb

TEACHERS AND EXAM BOARD

Exam Board

LUIGI CARASSALE (President)

ABDELHAKIM BOURAS

DAVIDE IAFFALDANO

MATTEO ZOPPI

LESSONS

LESSONS START

https://corsi.unige.it/8720/p/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Project developed possibly in a group and oral discussion

ASSESSMENT METHODS

Analysis of the project

Assessment of the comprehension from the ora discussion

Exam schedule