Flexural Waves

Flexural Waves

 

flexural deformations that are propagated in bars and plates. The length of flexural waves λ is always much greater than the thickness of the bar or plate. If the wavelength becomes comparable to the thickness of the plate, then motion in the wave becomes more complex and the wave is no longer said to be flexural. Examples of flexural waves are waves in a tuning fork, in the sounding boards of musical instruments, and in the exit cones of loudspeakers and those that arise during vibration of thin-wall mechanical structures (the frames of airplanes and motor vehicles, the roofs and walls of buildings, and other objects). Traveling flexural waves arise in very long bars and in large plates. On propagation of flexural waves each element of the bar is shifted perpendicular to the axis of the bar or to the plane of the plate. Dispersion is characteristic of flexural waves. The phase velocity of monochromatic flexural waves is proportional to the square root of the frequency. The group velocity of flexural waves is equal to twice the phase velocity. In bars and plates whose dimensions are limited in the direction of propagation of flexural waves, standing flexural waves arise as a result of reflections from the ends. Flexural waves are possible not only in flat but also in curved plates (shells).

I. A. VIKTOTOV

References in periodicals archive ?
Both the free and forced response of tires have been studied in this way, and the contributions of flexural waves, longitudinal waves, and shear waves have been identified from the modal analysis, findings which are in agreement with analytical models.
Based on a previous study [5], the flexural wave speed in the treadband is relatively slow and dispersive at low frequencies, while the fast, in-plane longitudinal wave can propagate at more than 600 m/s in the same frequency range.
Features like the fast in-plane wave along the treadband circumference with a cut-on frequency around 360 Hz and the second branch of the treadband flexural wave starting at about 400 Hz were also captured.
Doyle and Kamle [5, 6] had taken an experimental study of the reflection and transmission of flexural waves at an arbitrary T-joint.
where [c.sub.2] and [c'.sub.2] are velocities of the longitudinal and flexural waves in string 2.
Kamle, "An experimental study of the reflection and transmission of flexural waves at discontinuities," Journal of Applied Mechanics, vol.
Kamle, "An experimental study of the reflection and transmission of flexural waves at an arbitrary T-joint," Journal of Applied Mechanics, vol.
Cabrasa, "Dispersion degeneracies and standing modes in flexural waves supported by Rayleigh beam structures," International Journal of Solids and Structures, vol.
We denote the displacement of the reflected longitudinal wave by [u.sub.1], the lateral displacement produced by the flexural wave by [v.sub.1] in beam 1, the longitudinal displacement in string 2 by [u.sub.2], the lateral displacement in string 2 by [v.sub.2], the longitudinal displacement in beam 3 by [u.sub.3], and the lateral displacement in beam 3 by [v.sub.3].
Shibuya, Experimental Wavelet Analysis of Flexural Waves in Beams.
At very narrow diameters, cut-off effects act like a high pass filter, leaving only lower order modes as the means by which low frequency longitudinal, torsional and flexural waves can be transmitted.
Flexural waves that may not have been present in the original waveform can also be excited.