Sentence examples for approximate formulae from inspiring English sources

The three approximate formulae considered in this study are based on: (a) the Weingarten Soedel approximation of the Donnell Mushtari Vlasov equations, (b) the Calladine Koga improved classical-beam-on-Winkler-foundation model, and (c) the Timoshenko-beam-on-Pasternak-foundation analogy of the shell.

The results are compared to approximate formulae, for resonance conditions.

Finally, approximate formulae for the estimation of residual stress are given.

Some approximate formulae are presented for the reflection coefficients of flanged and unflanged pipes.

Approximate formulae are proposed for estimating natural frequencies of isotropic and specially orthotropic skew plates with clamped sides.

The approximate formulae, however, give reasonable estimates, if one excludes bimodal spectra with very light modal damping.

Thus, the closed-form approximate formulas provided in this paper are approximately similar to the accurate formulas, and system performance can be evaluated by using such formulas.

Feb 2007 update: thanks to a Curious reader for pointing out that this is an approximate formula.

To predict them it is necessary to make certain assumptions and to use certain approximate formulas not described here.

The proof is given for the previous named "approximate formulas" (labeled as Formula II).

Approximate formulas in the literature do not include the effect of wind.