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Table 9 Coefficients \({a}_{i}\) for various \(N\) of Rayleigh–Ritz procedure in case (3)

From: Nonlinear analysis of Euler beams resting on a tensionless soil with arbitrary configurations

Coefficients \({a}_{i}\)

\(N=9\)

\(N=7\)

\(N=5\)

\({a}_{2}\)

\(3.693980624\times {10}^{-3}\)

\(2.982531822\times {10}^{-3}\)

\(6.741008214\times {10}^{-3}\)

\({a}_{3}\)

\(-2.171660765\times {10}^{-2}\)

\(-7.087635317\times {10}^{-3}\)

\(-5.122002053\times {10}^{-2}\)

\({a}_{4}\)

\(-3.000365755\times {10}^{-3}\)

\(-1.021538762\times {10}^{-1}\)

\(5.763218439\times {10}^{-2}\)

\({a}_{5}\)

\(-7.178569399\times {10}^{-2}\)

\(2.170854003\times {10}^{-1}\)

\(-2.676483347\times {10}^{-4}\)

\({a}_{6}\)

\(2.623333605\times {10}^{-1}\)

\(-8.320853304\times {10}^{-2}\)

\({a}_{7}\)

\(-4.084992482\times {10}^{-2}\)

\(-1.891235161\times {10}^{-2}\)

\({a}_{8}\)

\(-2.669188602\times {10}^{-1}\)

\({a}_{9}\)

\(1.479964372\times {10}^{-1}\)