2. Reference solution#
2.1. Calculation method used for the reference solution#
The reference solution is written for the degrees of freedom for node \(\mathit{N1}\):
\(\left(-{\omega }^{2}\left[\begin{array}{cccccc}10& \text{}& \text{}& \text{}& \text{}& \text{}\\ \text{}& 10& \text{}& \text{}& \text{}& \text{}\\ \text{}& \text{}& 10& \text{}& \text{}& \text{}\\ \text{}& \text{}& \text{}& 10& \text{}& \text{}\\ \text{}& \text{}& \text{}& \text{}& 10& \text{}\\ \text{}& \text{}& \text{}& \text{}& \text{}& 10\end{array}\right]+\left[\begin{array}{cccccc}160& \text{}& \text{}& \text{}& \text{}& \text{}\\ \text{}& 180& \text{}& \text{}& \text{}& \text{}\\ \text{}& \text{}& 1280& \text{}& \text{}& \text{}\\ \text{}& \text{}& \text{}& 180& \text{}& \text{}\\ \text{}& \text{}& \text{}& \text{}& 1280& \text{}\\ \text{}& \text{}& \text{}& \text{}& \text{}& 1960\end{array}\right]\right)x=0\)
2.2. Benchmark results#
We get the following six pulses squared \({\omega }_{i}^{2}\) in \({\text{rd.s}}^{-2}\): \(16\), \(18\), \(18\), \(128\), \(128\), \(196\) in.
Hence the following frequencies: \({f}_{i}=\frac{{\omega }_{i}}{2\pi }\)
Mode |
Frequency (\(\mathit{Hz}\)) |
1 |
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2 |
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3 |
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4 |
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5 |
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6 |
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2.3. Uncertainty about the solution#
Analytical solution.