Session: VIB-14-01: Vibration of Continuous Systems

Paper Number: 94648

94648 - Sympathetic Resonance 

This presentation describes arguably the most important feature of mechanical vibration: resonance, in the form of a useful teaching tool, ideal for demonstration purposes within the classroom or lab setting. It is based on the simple dynamic response of flexible cantilevers, and evolves naturally from the underlying principles of a vibrating reed tachometer. Utilizing a 3D-printer, these ideas conveniently encompass the phenomenon of resonance in which all the cantilevers of a similar length respond in harmony when just one of their number is plucked.

The tuning fork is routinely used as an acoustic resonator. It provides a convenient means of producing a sound of a certain pitch, and thus presents calibration opportunities, not only in musical instruments. The concept of resonance is exploited in a variety of disparate contexts in scientific applications, including AFM, MRI, electrical circuits, lasers and optics, and nanotechnology. As a fundamental physical phenomenon it plays a key role in the teaching of vibration. Here, we describe using a 3D printer to facilitate an effective demonstration of resonance. The device is self-contained and need not involve any measurement, since the demonstration can be based on a purely visual appreciation. Many conventional demonstrations of resonance involve the use of a (non-trivial) variable-frequency driving device or signal, but the system described in this paper involves just very simple ideas and direct observation (and a 3D-printer).

The flexural stiffness of any thin structural element depends on a variety of material and geometric properties, but especially the length of the member since natural frequency tends to scale with the inverse of the length squared. A continuous elastic system possesses an infinite number of frequencies and mode shapes, but here we shall focus on the lowest frequency in bending vibration of prismatic cantilevers, that is, members in which the cross-sectional properties are constant throughout the length. The length range of interest means that frequencies associated with higher modes (of the longest cantilever) do not interfere with the fundamental bending mode (of the shortest), and damping, which is generally low, tends to reduce the influence of higher modes in any case.

A key issue will be exploited: since all the dimensions of the various cantilevers can be printed to a high degree of precision, and using the same material, then it is relatively easy to isolate a single parameter for change - length. Thus, the effect of imperfect parameter identification is obviated, since each cantilever is printed within one single contiguous piece, and use is made of direct comparison.

Presenting Author: Lawrence Virgin Duke Univ

Presenting Author Biography: The author is a professor of Mechanical Engineering at Duke University in North Carolina, which he joined in 1988. He has research interests in buckling, nonlinear vibrations and 3D-printing. He has authored two books: Introduction to Experimental Nonlinear Dynamics (2000) and Vibration of Axially-Loaded Structures (2007), both by Cambridge University Press.

Authors:

Lawrence Virgin Duke Univ