Structural dynamics

Objectives
The aim of this course is to acquire the concepts and methods required to study the dynamics of simple oscillating systems.
Skills acquired

Be able to equate linear mechanical oscillators using the fundamental principle of dynamics: translational and rotational systems
Be able to solve free-running, damped systems with one degree of freedom
Be able to solve forced-running, damped systems with one degree of freedom by spectral analysis via the frequency transfer function
Be able to analyze modal and solve free-running, 2-degree-of-freedom systems
Be able to grasp the concepts of frequencies, natural pulsations, resonances and natural modes, transient and steady state.

Skills in progress

Mobilize a broad field of fundamental and technical sciences related to aeronautical and space mechanical systems, and have the associated capacity for analysis and synthesis
Choose and implement the relevant analysis and characterization methods for mechanical systems
Design, dimension, implement and test a metallic or composite repair/modification
Have a global systems approach to mechanical systems Reason in a context of international regulatory constraints
Integrate into a professional environment in France or abroad Communicate orally and in writing in English
Evaluate one's own skills and steer one's career path

AP5SIMAI
AP6SACON

Contents

Introduction to oscillating systems, concepts of frequency, natural pulsations, resonances and natural modes, transient and steady state
PFD in translation
Reminders on undeformable solids
PFD in rotation
Viscous damping
Methods of solving in the free state with initial conditions
Methods of solving in the forced state with any force
Methods of solving in the forced state with a harmonic force in the steady state
Definition and use of the FRF and link with the notion of transfer function in automatic control,
Free-running resolution methods with initial conditions
Modal analysis.
TP1: 1-degree-of-freedom free-running oscillating system: mass-spring system, single-wire and 2-wire pendulum.
TP2: Free-running 2-degree-of-freedom oscillating system: Simplified numerical modeling of helicopter landing (translation/rotation coupling)

Teaching method

Teaching associated with online resources in Moodle
Integrated lecture/DD approach with in-class demonstrations
Strong connection between TDs and TPs.

Specialization: Aeronautical structures