Flat Cantilever Research Articles

A Fiber-Optic Laser-Doppler Probe for Vibration Analysis of Rotating Machines

The problem of obtaining vibratory information from remote, rotating, components within a machine has been overcome by means of a laser-Doppler fiber-optic probe. Laser light is transmitted down the fiber-optic and scattered light is returned for analysis in the same way. The Twyman-Green mode of operation of the laser-Doppler system has been shown to have serious shortcomings for this type of work and a new mode has been produced, and used successfully, in conjunction with Bragg cells for frequency shifting. The use of a single set of Bragg cells to compensate for the average velocity of a rotating system, limits the allowable speed of rotation to about 1000 rpm. However, other techniques for frequency shifting are available. An experimental investigation is reported in which a rotating system, consisting of a disk carrying flat cantilever blades, was rotated at about 1000 rpm while one of the blades was excited at 163 Hz. The measured frequency of the vibrating blade was 162.8 Hz and similar accuracy was obtained for the amplitude measurements.

Investigation of the natural vibrations of plates made of composite materials with the help of the finite-element method

The modes and frequencies of small natural vibrations in a cavity of thin plates are investigated on the basis of the method of finite elements in displacements. The effect of the rigidity characteristics of a material on the natural frequencies and modes of vibrations of flat cantilever vanes whose tapered edge is restrained is studied. An example is given of the use of the finite-element method to determine the natural vibrations of an orthotropic plate in the shape of an airplane wing. Quadrangular and modified triangular bending finite elements are used to simulate a continuous system. A mass-element matrix is constructed on the basis of a four-term ("contracted") polynomial determining the deflection that permits a significant reduction of the order of the solving system.

Natural Frequencies of Uniform and Non-Uniform Rectangular Cantilever Plates

Various methods of calculating the natural frequencies of flat rectangular cantilever plates are discussed, and it is shown both analytically and experimentally that relatively simple expressions based on technical beam theory give good results even for high order modes. Experimental results indicate that the mode shapes of plates of non-uniform thickness have modes so complex that a great many terms should be used in any vibration analysis, whether finite difference or Rayleigh-Ritz.