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Vibration mode of a clamped square plate. The vibration of plates is a special case of the more general problem of mechanical vibrations.The equations governing the motion of plates are simpler than those for general three-dimensional objects because one of the dimensions of a plate is much smaller than the other two.
For flat circular plates, p is roughly 2, but Chladni's law can also be used to describe the vibrations of cymbals, handbells, and church bells in which case p can vary from 1.4 to 2.4. [2] In fact, p can even vary for a single object, depending on which family of modes is being examined.
When resonating, a plate or membrane is divided into regions that vibrate in opposite directions, bounded by lines where no vibration occurs (nodal lines). Chladni repeated the pioneering experiments of Robert Hooke who, on 8 July, 1680, had observed the nodal patterns associated with the vibrations of glass plates.
Jenny spread powders, pastes, and liquids on a metal plate connected to an oscillator which could produce a broad spectrum of frequencies. The substances were organized into different structures characterized by geometric shapes typical of the frequency of the vibration emitted by the oscillator.
Vibration mode of a clamped square plate In continuum mechanics , plate theories are mathematical descriptions of the mechanics of flat plates that draw on the theory of beams . Plates are defined as plane structural elements with a small thickness compared to the planar dimensions. [ 1 ]
Each higher-order mode is “born” at a resonant frequency of the plate, and exists only above that frequency. For example, in a 3 ⁄ 4 inch (19mm) thick steel plate at a frequency of 200 kHz, the first four Lamb wave modes are present, and at 300 kHz, the first six. The first few higher-order modes can be distinctly observed under favorable ...
The example shows how the Rayleigh's quotient is capable of getting an accurate estimation of the lowest natural frequency. The practice of using the static displacement vector as a trial vector is valid as the static displacement vector tends to resemble the lowest vibration mode.
Vibrations of a string under a moving inertial force (v=0.5c); c is the wave speed. The discontinuity of the mass trajectory is also well visible in the Timoshenko beam. [ citation needed ] High shear stiffness emphasizes the phenomenon.