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 (- - -) Bernoulli-Euler’s, <svg height="13.45" id="M139" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 27.612499 13.45" width="27.612499" xmlns="http://www.w3.org/2000/svg">
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</svg> Rayleigh’s, (– - –) shear, and (—) Timoshenko’s Beam Models.</table>

Journal of Applied Mathematics

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Figure 3

Figure 3: An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories 

Figure 3 | An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories 