Lecture

Dissipative Free Regime in Vibratory Mechanics

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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 subcritical, supercritical, and critical cases in the dissipative free regime of vibratory mechanics, exploring the energy approach, types of relative damping, and solutions for different damping scenarios. The instructor explains the roots of characteristic equations, proper pulsation of damped oscillators, and integration constants for various damping conditions.

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 (29)

Harmonic oscillator

In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x: where k is a positive constant. If F is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude).

Damping

Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples include viscous drag (a liquid's viscosity can hinder an oscillatory system, causing it to slow down; see viscous damping) in mechanical systems, resistance in electronic oscillators, and absorption and scattering of light in optical oscillators.

Critical speed

In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating object, such as a shaft, propeller, leadscrew, or gear. As the speed of rotation approaches the object's natural frequency, the object begins to resonate, which dramatically increases system vibration. The resulting resonance occurs regardless of orientation. When the rotational speed is equal to the numerical value of the natural vibration, then that speed is referred to as critical speed.

Vibration

Vibration () is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The oscillations may be periodic, such as the motion of a pendulum, or random, such as the movement of a tire on a gravel road. Vibration can be desirable: for example, the motion of a tuning fork, the reed in a woodwind instrument or harmonica, a mobile phone, or the cone of a loudspeaker. In many cases, however, vibration is undesirable, wasting energy and creating unwanted sound.

Oscillation

Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such as those between atoms.

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