Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Vibratory Mechanics: 2 Degrees of Freedom

In course

ME-332: Mechanical vibrations

Dans ce cours on étudie la dynamique modale des structures mécaniques. Conceptes clés comme Mode Normale, Mass et Raideur effective, et Fréquences Propres sont appris pendant ce cours. ...

Description

This lecture covers the equations of motion for 2 degrees of freedom systems in the conservative free regime, focusing on symmetrical systems, viscous and elastic properties, and the canonical form of the oscillator. It also discusses the Newton equations, characteristic equations, eigenmodes, and modal vectors in the context of vibratory mechanics.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructor

Luis Guillermo Villanueva Torrijo

Guillermo Villanueva is a Tenure Track Assistant Professor at the Ecole Polytechnique Federale de Lausane (EPFL), Switzerland, in the Mechanical Engineering Institute (IGM). Before joining EPFL he was a Marie Curie post-doctoral scholar at DTU (Denmark) and Caltech (California, US); and before a post-doc at EPFL-LMIS1. He received his M.Sc. in Physics in Zaragoza (Spain) and his PhD from the UAB in Barcelona (Spain). Since the start of his PhD (2002), Prof. Villanueva has been active in the fields of NEMS/MEMS for sensing, having expertise from the design and fabrication to the characterization and applicability. He has co-authored more than 75 papers in peer-reviewed journals (h-index of 24 WoK, 32 GoS) and more than 100 contributions to international conferences. He is serving, or has served, on the program committees of IEEE-NEMS, IEEE-Sensors, MNE, IEEE-FCS and Transducers. He is editor of Microelectronic Engineering. He has co-organized MNE2014 and SNC2015; and he is currently co-organizing the short courses at Transducers 2019 and the 16th International Workshop on Nanomechanical Sensors (NMC2019).

Official source

Related concepts (31)

Equations of motion

In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system.

Euler equations (fluid dynamics)

In fluid dynamics, the Euler equations are a set of quasilinear partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular, they correspond to the Navier–Stokes equations with zero viscosity and zero thermal conductivity. The Euler equations can be applied to incompressible or compressible flow. The incompressible Euler equations consist of Cauchy equations for conservation of mass and balance of momentum, together with the incompressibility condition that the flow velocity is a solenoidal field.

Linear differential equation

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).

Normal mode

A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions.

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

Related lectures (30)

Circular Motion and Harmonic Oscillator

Explores circular motion, harmonic oscillators, and double springs, elucidating the physics principles behind them.

Canonical Transformations: Existence and Equations

Explores canonical transformations, focusing on existence, equations, simplicity, and differential equations' theory.

Canonical Transformations: Hamilton-Jacobi Equation

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

Canonical Equations: Solutions and Impulses

Explores canonical equations for isolated systems, finding solutions and analyzing impulses.

Ordinary Differential Equations: Second Order Linear Inhomogeneous