Dynamic and Quasi-Static Bending of Saturated Poroelastic Timoshenko Cantilever Beam

Based on the three-dmiensional Gurtin-type variational principle of the incompressible saturated porousmedia, first, a one-dimensionalm athematical model for dynamics of the saturated poroelastic Timoshenko Cantilever beam was established with a ssumptions of deformatin of the classical single phase Tmioshenko beam and the movement of pore fluid only in the axial direction of the saturated poroelasic beam. This mathematical model can be degene rated into the Euler-Bernoullim odel, Rayleigh model and Shear model of the saturated poroelastic beam, respe ctively, under some specialcases. Secondly, dynamic and quasi-static behavior of a saturated poroelastic Tmioshenko cant ilever beam with mipermeable and permeable at its fixed and free end, respectively, subjected to a step load at its free end, was analyzed by the Laplace transform. The variations of the deflections at the beam free end against the tmie were shown in figures, and the influences of the in teraction coefficient between the porefluid and solid skele to naswellas the slenderness ratio of the beam on the dynamic/quasi-static performances of the beam were examined. It is shown that the quasi-static deflections of the saturated poroela stic beam possess the creep behavior smiilar to that of viscoelastic beam. In dynamic responses, with the slenderness ratio increasing, the vibration periods and amplitudes of the deflections at the free end increase, and the tmie needed for deflections to approachits stationary values also increases. Whereas, with the interaction coefficient increasing, the vibrations of the beam deflections decay more strongly, and, eventually, the deflections of the saturated poroelastic beam converge to the static deflections of the classic single phase Tmioshenko beam.