The Wave Method for Solving Flexural Vibration Problems

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Abstract
In this paper the use of normal mode and wave methods in problems of dynamic loading on beams is discussed, and the methods are applied to simple problems of uniform beams under a suddenly applied load. For these problems, mathematically exact results have been obtained, enabling a comparison to be made between the two types of solution. Experimental results for these problems also have been obtained, using an apparatus which releases the beam from a deflected position, and displays a record of the resultant response on an oscillograph screen, using a time base synchronized with the release of the beam. Good agreement is obtained between the experimental and theoretical results, and it is shown that the wave solution is useful for determining the initial response of the beam, while the subsequent response can be better obtained from the normal-mode solution.

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