# Modelling and simulation of mechanical systems

**Academic Year 2023/2024**- Teacher:

**Gabriele FICHERA**

## Expected Learning Outcomes

The main aim is bringing students to create numerical models suitable to simulate dynamics of complex mechanical systems, both in time and frequency domain, thus studying stability to applied force fields. Fundamental techniques of discretization of mechanical systems will be provided and specific numerical codes (Matlab ®) will be used to solve equations of motion.

## Course Structure

Taught class, Matlab lessons, vibration Lab.

*Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.*

## Required Prerequisites

## Attendance of Lessons

## Detailed Course Content

*Modeling of n-degrees of freedom mechanical systems with lumped parameters: motion equations, basic principles of multibody method, non-linear static equilibrium calculation, linear analysis (eigensolution and frequency response), modal decomposition, linear systems with non-linear forces and time integration. Examples in Matlab ® (suspension units, ride-comfort of a passenger car).*

*Vibration in continuous systems: cables and beams, frequencies and modes calculation, modal decomposition, structural and hysteretical damping.*

*Finite Element Method: shape functions for 1-D elements (cables and beams), calculation examples, frequency response function, Matlab examples.*

*Mechanical systems with 1 or 2 dofs subjected to force fields: analysis of stability and practical examples (airfoils, bearings, Matlab exercises).*

*Vehicle dynamics: tire-to-road interaction, basic models for longitudinal and lateral dynamics in pure-slip, stability in turns, quarter-car model.*

*Basic principles of experimental modal analysis with practical examples at laboratory and measurements of vibration.*

## Textbook Information

1) G. Diana, F. Cheli, “Advanced Dynamics of Mechanical Systems”, Springer

2) G. Genta, L.Morello, "The automotive chassis", Volume 2: system design, Springer

Author | Title | Publisher | Year | ISBN |
---|---|---|---|---|

Giorgio Diana, Federico Cheli | Dinamica dei sistemi meccanici vol.1&2 | Polipress | 2010 | 8873980651 |

Giorgio Diana, Federico Cheli | Advanced Dynamics of Mechanical Systems | Springer | 2015 | 978-3-319-18200-1 |

Giancarlo Genta | Meccanica dell'autoveicolo | Levrotto & Bella | 2000 | 8882180425 |

Giancarlo Genta, Lorenzo Morello | The Automotive Chassis: System Design: Volume 2: System Design | Springer | 2009 | 978-1-4020-8675-5 |

## Course Planning

Subjects | Text References | |
---|---|---|

1 | recap of 1-dof systems: free and forced response | “Advanced Dynamics of Mechanical Systems”: pages 125-155. |

2 | damping identification methods and hysteretic damping | “Advanced Dynamics of Mechanical Systems”: pages 158-162. Lecture notes: Bushings_rev2022.pdf |

3 | equations of motion of linear n dof systems | “Advanced Dynamics of Mechanical Systems” - pages 83-125. |

4 | eigenvalues and mode shapes of n-dofs systems | “Advanced Dynamics of Mechanical Systems” - pages 198-204. |

5 | forced vibration response of n dofs systems | “Advanced Dynamics of Mechanical Systems” - pages 205-211. |

6 | rubber and hydraulic mounts for vibration isolation | Lecture notes: Bushings_rev2022.pdf |

7 | suspension systems 1 and 2 dofs | “Advanced Dynamics of Mechanical Systems”: pages 155-158. Lecture notes. |

8 | modal analysis | “Advanced Dynamics of Mechanical Systems” - pages 211-239. |

9 | equations of motion of non linear n dof systems | “Advanced Dynamics of Mechanical Systems” - pages 1-6, 11-23. |

10 | Matlab models for ride comfort evaluation of a ground vehicle | "The automotive chassis". Lecture notes. |

11 | mode shapes and eigenvalues of continuous systems: cables | “Advanced Dynamics of Mechanical Systems” - pages 241-252. |

12 | mode shapes and eigenvalues of continuous systems: beams without or with axial load | “Advanced Dynamics of Mechanical Systems” - pages 252-270. |

13 | mode shapes and eigenvalues of continuous systems: axial and torsional vibrations of beams | “Advanced Dynamics of Mechanical Systems” - pages 270-274. |

14 | basic principles of finite element method, shape functions for 1-D elements: string and beam | “Advanced Dynamics of Mechanical Systems” - pages 310-322. |

15 | example of assembling matrices for an overhead vibrating line | “Advanced Dynamics of Mechanical Systems” - pages 322-341. |

16 | study of stability in 1 and 2 dofs vibrating systems | “Advanced Dynamics of Mechanical Systems” - pages 413-422. |

17 | stability of 1 dof airfoils | “Advanced Dynamics of Mechanical Systems” - pages 422-439. |

18 | stability of a 2 dofs system in a position-dependent force field | “Advanced Dynamics of Mechanical Systems” - pages 439-458. |

19 | stability of 2 dof airfoils | “Advanced Dynamics of Mechanical Systems” - pages 461-469. |

20 | Matlab examples for airfoils stability | Lecture notes. |

21 | stability of journal bearings | “Advanced Dynamics of Mechanical Systems” - pages 469-479. |

22 | basic principles and applications for signal analysis and vibration measurement | dispense del docente - lecture notes: vibration_measurement.pdfFrequency_Analysis.pdf |

23 | Matlab examples on FFT | G. Genta, ''meccanica dell'autoveicolo''G. Genta, L.Morello, "The automotive chassis", Volume 2: system design, Springer |

24 | forces applied to ground vehicles | "The automotive chassis", Volume 2: system design. Lecture notes. |

25 | tire to road interaction | "The automotive chassis", Volume 2: system design. Lecture notes. |

26 | vehicle longitudinal dynamics | "The automotive chassis", Volume 2: system design. Lecture notes. |

27 | steady state cornering, single track model, under/oversteer | "The automotive chassis", Volume 2: system design. Lecture notes. |

## Learning Assessment

### Learning Assessment Procedures

*Learning assessment may also be carried out on line, should the conditions require it.*

### Examples of frequently asked questions and / or exercises

available on:

http://studium.unict.it