Abstract:a b s t r a c tThe characteristic frequencies o of the vibrations of an elastic solid subject to boundary conditions of either zero displacement or zero traction are given by the Rayleigh quotient expressed in terms of the corresponding exact eigenfunctions. In problems that can be analytically expanded in a small parameter e, it is shown that when an approximate eigenfunction is known with an error Oðe N Þ, the Rayleigh quotient gives the frequency with an error Oðe 2N Þ, a gain of N orders. This result gener… Show more
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