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In this research, the free vibrations of beams made of saturated proelastic materials under different boundary conditions have been investigated. The equation governing the transverse movement of the beam is derived based on the Euler-Bernoulli theory of beams and using the relations governing the stress-strain of proelastic materials using Hamilton's principle. Different models of porosity distribution along the longitudinal length of the beam have been considered. The governing equation in different boundary conditions of double-ended, double-ended, and single-ended single-ended boundary conditions is determined by the differential quadratic method for three different types of uniform, linear, and quadratic porosity distribution along the length of the hollow beam. The natural frequencies of free vibration of the longitudinal porous beam have been obtained. The effect of porous material parameters on the change of natural frequencies in different boundary conditions has been concluded. The results obtained have been compared and validated with the results presented by other researchers.
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