An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories

<table>Nonlinear frequency versus nondimensional amplitude for different beam slenderness ratios  (- - -) <svg height="13.55" id="M143" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 42.962502 13.55" width="42.962502" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝜂</tspan>
<tspan style="font-size: 12.50px; " x="9.7148314" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.75522" y="0">3</tspan>
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<tspan style="font-size: 12.50px; " x="0" y="0">𝜂</tspan>
<tspan style="font-size: 12.50px; " x="9.7148314" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.75522" y="0">5</tspan>
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Journal of Applied Mathematics

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Figure 5

Figure 5: An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories 

Figure 5 | An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories 