Nanotechnology Engineering

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.

Knowledge of notions of mathematical analysis and physics (mechanics)

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

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

Lessons in the Classroom

Fourier series, Fourier transforms, convolution integral, signal sampling, sampling theorem, aliasing. Laplace transform. Elements of statistics and probability theory to introduce the study of random functions. Stationary and ergodic random functions. Correlation of signals, power spectral density. Dynamics of rigid body Dynamics of single degree of freedom systems. Unforced and forced problem with harmonic forcing without damping, definition of viscous damping and structural damping, unforced and forced problem with harmonic forcing with damping, unit step response, unit impulse response, deterministic generic forcing response, function of frequency response, response to random excitation: power spectral density of the response. Dynamics of systems with n degrees of freedom. Formulation of d'Alembert and Lagrange, force balance equations, natural modes and natural frequencies of vibration, forced systems and modal analysis. Viscous damping, proportional viscous damping, structural damping, matrix of frequency response functions, response of excitation systems single input single output (SISO), single input multi output (SIMO), multi input multi output (MIMO), response to excitation random and matrix of the power spectral densities of the responses, outline of the identification of modal parameters from experimental tests. Dynamics of continuous systems Study of structural dynamics problems through a modal approach (calculation of the eigenfunctions and natural frequencies of vibration): chord vibrations, longitudinal vibrations of rods, torsional vibrations of shafts, bending vibrations of beams, vibrations of membranes, bending vibrations of plates; modal analysis for the determination of the response of continuous dynamic systems excited with deterministic forcing, complex frequency response function for continuous systems, response to random excitation. Longitudinal waves, bending waves in infinite means (beams and plates), reflection of the waves around the semi-infinite means and closure of the wave train. Excitation of plates hit by acoustic waves, wave impedance, noise transmission through barriers, sound irradiation from vibrating plates. High frequency problems: solution through statistical energy techniques, Statistical Energy Analysis. Entropic approach for mechanical problems: definition of Khinchin entropy function, definition of thermodynamic temperature of mechanical systems. Vibration isolation and control Impact insulation techniques, low and high frequency insulation. Stability of dynamic systems, hints of analysis of systems in feedback, PID regulators, hints of optimal control techniques. LQR.

Knowledge of notions of mathematical analysis and physics (mechanics)

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

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

Lessons In the Classroom