Mechanical Engineering

ANTONIO CULLA
SILVIA MILANA

Aim of the course is the study of electromechanical systems of dimensions close to that of the micrometer by means of physical -mathematical models with lumped and distributed parameters. Particular attention is also paid to the study of control techniques for the design of complex micro-mechatronic systems with the function of actuators and sensors. The application areas range from the control of mechanical vibrations and noise to micro robotics.

Knowledge and Understanding:
Understand the principles of the dynamics of discrete and continuous systems and the fundamentals of modal analysis. K1
Know FEM methodologies for dynamic simulation. K2

Ability to Apply Knowledge and Understanding:
Use MATLAB for the simulation of mechanical and vibrational systems. S1
Perform modal and harmonic analyses using FEM models. S2
Configure a microcontroller, read sensors, and drive actuators. S3

Independent Judgment:
Evaluate modeling choices and control strategies. J1

Communication Skills:
Describe results and simulations using appropriate technical language. C1

Learning Ability:
Integrate theory, simulation, and experimentation in complex mechatronic contexts. L1

Knowledge of notions of mathematical analysis and physics (mechanics)

Module 1 – Kinematics and Dynamics of the Rigid Body (4 hours)

Kinematics and dynamics of the rigid body. Equations of motion written in body coordinates.
MATLAB exercises: numerical simulations of constrained and free motions.

Module 2 – Dynamics of Single Degree of Freedom Systems (8 hours)

Free and forced vibration problems, with and without damping.
Viscous and structural damping.
Responses to step, impulse, and harmonic excitations.
Frequency response function.
MATLAB exercises: implementation of motion equations and comparison with theoretical solutions.

Module 3 – Dynamics of Multi Degree of Freedom Systems (10 hours)

Formulation according to d’Alembert and Lagrange.
Mass, damping, and stiffness matrices.
Natural modes and natural frequencies of vibration.
Forced systems and modal analysis.
Viscous, proportional, and structural damping.
Matrix of frequency response functions.
SISO, SIMO, and MIMO responses; response to random excitation and power spectral density matrices of the responses.
Introduction to modal parameter identification.
MATLAB and FEM exercises: computation of natural modes and modal analysis of discrete systems.

Module 4 – Dynamics of Continuous Systems (10 hours)

Vibrations of strings, rods, shafts, beams, membranes, and plates.
Eigenfunctions and natural frequencies of vibration.
Modal analysis and complex frequency response function.
Response to random excitation.
High-frequency problems and Statistical Energy Analysis (SEA).
FEM exercises: modal analysis of beams and plates.

Module 5 – Vibration Isolation and Control (8 hours)

Impact isolation techniques, low- and high-frequency isolation.
Stability of dynamic systems.
Feedback system analysis and PID controllers.
MATLAB exercises: simulation of isolated systems and PID control.

Module 6 – Signal Analysis (8 hours)

Fourier series and Fourier transform, discrete transform and FFT.
Convolution, signal sampling, Nyquist–Shannon sampling theorem and aliasing.
Introduction to statistics and probability theory for random signals.
Stationary and ergodic random functions, correlation, and power spectral density.
MATLAB exercises: frequency analysis of signals and the sampling theorem.

Module 7 – Microcontrollers and Applied Mechatronics (12 hours)

Introduction to the microcontroller and development tools for mechatronics.
Architecture (CPU, memory, PWM).
Basic sensors: digital and analog readings (buttons with pull-up/pull-down resistors, potentiometer on ADC), HC-SR04.
Advanced sensors: IMU, libraries, datasheets, and basic calibration.
Actuators and PWM: LED dimming, buzzer, servo, DC motor; frequency, duty cycle, electrical safety, and separate power supplies.
Control of DC motor speed using PWM and sensor feedback.
Control of a simple system: simplified system modeling (input → sensor, output → actuator), on/off control with hysteresis and simplified PID control.
Objectives: set up the environment, compile, upload, and test simple programs; interface sensors and actuators; design a basic control in a mechatronic context.

Shin, Hammond, Fundamentals of Signal Processing for Sound and Vibration Engineers, Wiley
Cannon, Dynamics of physical systems, Dover
Khinchin, Mathematical foundation of statistical mechanics, Dover
Salsa, Equazioni a derivate parziali, Springer
Giua, Seatzu, Analisi dei sistemi dinamici, Springer
Bolzern, Scattolini, Schiavoni, Fondamenti di controlli automatici, Mc Graw-Hill

Lessons in the Classroom

Attendance is reccommended

Students will present a developed project choosing the topics of the course program and take an oral test on the course program

Students will present a developed project choosing the topics of the course program and take an oral test on the course program

• Module 1 – Kinematics and Dynamics of the Rigid Body (4
  hours)
  
   
  • Books: Meirovitch – Elements of Vibration Analysis; Goldstein –
    
    Classical Mechanics; Shames – Engineering Mechanics: Dynamics.


• Module 2 – Dynamics of Single Degree of
  Freedom Systems (8 hours)
  • Books: Rao – Mechanical Vibrations; Meirovitch – Elements of
    
    Vibration Analysis; Inman – Engineering Vibration


• Module 3 – Dynamics of Multi Degree of Freedom Systems (10
  hours)
  • Books: Meirovitch – Fundamentals of Vibrations; Craig &
    
    Kurdila – Fundamentals of Structural Dynamics.
    
    
    
     


• Module 4 – Dynamics of Continuous
  Systems (10 hours)
  • Books: Meirovitch – Analytical Methods in
    
    Vibrations; Leissa – Vibration of Plates; Lyon & DeJong – Statistical
    
    Energy Analysis.


• Module 5 – Vibration Isolation and Control (8 hours)
  • Books: Den
    
    Hartog – Mechanical Vibrations; Inman – Vibration with Control; Ogata – Modern
    
    Control Engineering


• Module 6 – Signal Analysis (8 hours)
  
   
  • Books: Oppenheim & Schafer – Discrete-Time
    
    Signal Processing; Bendat & Piersol – Random Data; Papoulis – Probability,
    
    Random Variables, and Stochastic Processes.


• Module 7 – Microcontrollers and Applied Mechatronics (12
  hours)
  • Books: Barrett – Arduino Microcontroller; Monk – Programming
    
    Arduino; Baldi & Marinoni – Sistemi Meccatronici; Official datasheets
    
    (Arduino, STM32, HC-SR04, MPU6050, NTC).