Checking date: 19/03/2024

Course: 2024/2025

Mechanical vibrations fundamentals
Bachelor in Mechanical Engineering (Plan: 446 - Estudio: 221)

Coordinating teacher: CALVO RAMOS, JOSE ANTONIO

Department assigned to the subject: Mechanical Engineering Department

Type: Compulsory
ECTS Credits: 3.0 ECTS


Requirements (Subjects that are assumed to be known)
Functions Derivation Basic derivation theorems. Multivariable functions Introduction to differential equations. Particle and Rigid Bodies Kinematics. Particle and Rigid Bodies Dynamics.
By the end of this subject, students will be able to have: 1. Knowledge and understanding of linear differential equations which are applicable in mechanical vibration problems 2. Knowledge and understanding of key aspects of mechanical vibrations fundamentals; 3. The ability to apply their knowledge and understanding to identify, formulate and solve problems of mechanical vibrations using established methods; 4. The ability to combine theory and practice to solve problems of mechanical vibrations; 5. An understanding of applicable techniques and methods in mechanical vibrations, and of their limitations;
Skills and learning outcomes
Description of contents: programme
1.- Introduction to differential calculus 1.1.- Functions of a Variable 1.2.- Mathematical Models 1.3.- Classification of Differential Equations 1.4.- Linear Ordinary Differential Equations 1.5.- Solution of Differential Equations 1.6.- Solution of Homogeneous First Order Diff Eq. 1.7.- Solution of Non homogeneous Linear First Order Diff Eq. 1.8.- Solution of Second Order Diff. Eq. 1.9.- Integration methods 2.- Numerical methods for solving differential equations 2.1.- Introduction 2.2.- Euler's method 2.3.- Taylor's method 2.4.- Runge-Kutta methods 3.- Introduction to MATLAB 3.1.- Introduction 3.2.- General Rules 3.3.- Basic Operations 3.4.- Output formats 3.5.- Matrices and Vectors 3.6.- Graphics in MATLAB 3.7.- Programming in MATLAB 3.8.- SIMULINK 4.- Solution of Differential Equations using MATLAB 4.1.- Introduction 4.2.- ODE function 4.3.- Solution of a first order Differential Equations 4.4.- Solution of second order Differential Equations 4.5.- Solution of Differential Equations by SIMULINK 5.- Introduction to mechanical vibrations: 5.1.- Introduction 5.2.- Classification of vibrations 5.3.- Components of an oscillatory system 5.4.- Simple Harmonic Motion (SHM) 5.5.- Energy of a Simple Harmonic Movement 5.6.- Nonlinear vibrations 6.- Damped mechanical vibrations and forced vibrations 6.1.- Damped harmonic oscillator 6.2.- Differential equation of Damped Movement 6.3.- Damping coefficient 6.4.- Solution to the Differential Equation of Damped Motion 6.5.- Logarithmic Decrease 6.6.- Forced vibrations 6.7.- Transmissibility coefficient 6.8.- Resonance 7.- Systems of 2 Degrees of Freedom and N Degrees of Freedom 7.1.- Introduction 7.2.- Undamped free vibrations for 2 DOF 7.3.- Forced undamped vibrations for 2 DOF 7.4.- Damped forced vibrations for 2 DOF 7.5.- N DOF Vibrations systems
Learning activities and methodology
Master class Classroom exercises Laboratories exercices Personal work. Team Work
Assessment System
  • % end-of-term-examination 40
  • % of continuous assessment (assigments, laboratory, practicals...) 60

Calendar of Continuous assessment

Extraordinary call: regulations
Basic Bibliography
  • R. Kent Nagle; E.B Saff Arthur and David Snider. Fundamentals of differential equations. Pearson. 2012
  • Alonso de Mena, Ana Isabel; Álvarez López, Jorge. ; Calzada Delgado, Juan Antonio.. Ecuaciones diferenciales ordinarias. Delta Publicaciones . 2010
  • Felipe Lafita Babio, Hilario Mata Corte¿s. Vibraciones meca¿nicas en ingenieri¿a. INTA. 1964
  • Jose¿ Carlos Bellido Guerrero Alberto Donoso Bello¿n Sebastia¿n Lajara Lo¿pez. Ecuaciones diferenciales ordinarias. Paraninfo . 2014
  • SS Rao and Fook Yap Fah. Mechanical vibrations. Singapore : Pearson Education South Asia. 2011
  • William T. Thomson. Teoría de Vibraciones. Prentice / Hall. 1981
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