Table 14 Coefficients \({a}_{i}\) for various N of Rayleigh–Ritz procedures in case (5)
From: Nonlinear analysis of Euler beams resting on a tensionless soil with arbitrary configurations
Coefficients \({a}_{i}\) | \(N=15\) | \(N=13\) | \(N=11\) |
|---|---|---|---|
\({a}_{1}\) | \(-9.621729056\) | \(1.26509266\) | \(-0.1934752187\) |
\({a}_{2}\) | \(18.39089276\) | \(-2.402425146\) | \(0.3641356857\) |
\({a}_{3}\) | \(-16.04410765\) | \(2.054943739\) | \(-0.3028682506\) |
\({a}_{4}\) | \(12.75497774\) | \(-1.579207895\) | \(0.2216699238\) |
\({a}_{5}\) | \(-9.213226612\) | \(1.085004054\) | \(-0.1418129818\) |
\({a}_{6}\) | \(6.01949861\) | \(-0.6617807486\) | \(0.0781559243\) |
\({a}_{7}\) | \(-3.534956678\) | \(0.3545439777\) | \(0.03633997966\) |
\({a}_{8}\) | \(1.849693568\) | \(-0.1642435165\) | \(0.01380962478\) |
\({a}_{9}\) | \(-0.8520413131\) | \(0.06429408045\) | \(-0.004043946098\) |
\({a}_{10}\) | \(0.3396967581\) | \(-0.020516978\times {10}^{-2}\) | \(8.075018814\times {10}^{-4}\) |
\({a}_{11}\) | \(-0.1143678132\) | \(0.005015763\times {10}^{-3}\) | \(-8.115198537\times {10}^{-5}\) |
\({a}_{12}\) | \(0.03131058729\) | \(-8.326536226\times {10}^{-4}\) | – |
\({a}_{13}\) | \(-0.006544519907\) | \(6.9774709\times {10}^{-5}\) | – |
\({a}_{14}\) | \(9.271890423\times {10}^{-3}\) | – | – |
\({a}_{15}\) | \(-6.647133278\times {10}^{-5}\) | – | – |