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The lower bound for the frequency coefficient is obtained by means of an extension of Dunkerley's method.
Since the eigenvalue is a function of the optimization parameter γ, by minimizing it with respect to γ one finds an optimized value of the fundamental frequency coefficient.
For the case of a rigidly clamped plate results are presented of numerical experiments on minimizing the calculated value of the fundamental frequency coefficient by using Schmidt's approach.
An unknown parameter γ is included in the polynomials and this allows for optimization of the frequency coefficient by minimizing it with respect to γ.
Since the calculated eigenvalue constitutes an upper bound, by minimizing it with respect to the undetermined exponent, one is able to improve the value of the frequency coefficient.
Lord Rayleigh's optimization concept when solving integral equations by means of the Ritz method is used to determine the fundamental frequency coefficient of several vibrating systems.
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The DCT is performed on an N x N square matrix of pixel values, and it yields an N x N square matrix of frequency coefficients.
Good agreement is obtained with frequency coefficients determined two decades ago by means of a variational method.
Fundamental frequency coefficients are determined for several combinations of length to width ratios and flexibility coefficients.
The numerical results indicate that the inclusion of frequency coefficients definitely affects the accuracy of the predictions.
Frequency coefficients corresponding to the lower symmetric and antisymmetric modes of transverse vibration are tabulated.
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