Abstract
Based on the nonlocal theory and the theory of saturated porous media, the mathematical and physical model and governing equations of the steady-state response of the incompressible nonlocal saturated poroelastic beam under vertical harmonic loading are established with assumption of the movement of the liquid-phase fluid only in the axial direction of the beam and considering the nonlocal effects such as particle size, pore size, and pore dynamic stress. The dynamic response of a saturated poroelastic cantilever beam with permeability at both ends under a vertical harmonic concentrated force at the free end is studied. In the frequency domain, the analytical expressions of deflection amplification factor and equivalent couple amplification factor of liquid fluid pressure are given. The effects of nonlocal coefficient τ, mechanical parameter α, and geometric parameter β on the deflection amplification factor and equivalent couple amplification factor at the midpoint of the nonlocal saturated poroelastic cantilever beam are studied. The results show that the steady-state vibration of the incompressible nonlocal saturated poroelastic cantilever beam has resonance. When the nonlocal effect is considered, the deflection amplification factor and the equivalent couple amplification factor are larger, so the influence of the nonlocal effect on the steady-state response of the beam should not be ignored. The geometric parameter β has significant effect on the peak positions of the curves of the deflection amplification factor and the equivalent couple amplification factor varying with frequency.
Highlights
Saturated porous structures are widely used in civil engineering, aviation, transportation, and other engineering fields because of their good sound absorption and energy consumption. e research on the mechanical behavior of saturated porous structures has significant engineering application value and academic value. erefore, since Biot put forward the theory of saturated porous media [1, 2], the research on vibration and wave propagation in saturated porous media has attracted the attention of many scholars [3,4,5,6,7,8,9]
Since Biot theory assumes that the wave length of saturated porous media is larger than the pore size, the influence of pore size effect on wave propagation is not considered and the influence of pore size is very significant at high frequency [10]
Considering the harmony of the problem, the parameters meet wS w Seiωt, Mp M peiωt, and MSxE M SxEeiωt, where w S, M p, and MSxE are the amplitudes of wS, Mp, and MSxE, respectively. e following equations can be obtained by substituting wS, Mp, and MSxE into vertical dynamic control equations (25) and (26) of the incompressible nonlocal saturated poroelastic beam: We introduce the dimensionless variables and parameters as follows: x x/L, ω ω/T ωL/v, τ e0a/L, T v/L, v ES/ρS, w wS/L, MP LMp/ESI, q L 2Q/ESI, α (1 − 2υ)κL2T /ESnF2 (1 − 2υ)κL/
Summary
Based on the nonlocal theory and the theory of saturated porous media, the mathematical and physical model and governing equations of the steady-state response of the incompressible nonlocal saturated poroelastic beam under vertical harmonic loading are established with assumption of the movement of the liquid-phase fluid only in the axial direction of the beam and considering the nonlocal effects such as particle size, pore size, and pore dynamic stress. E dynamic response of a saturated poroelastic cantilever beam with permeability at both ends under a vertical harmonic concentrated force at the free end is studied. E effects of nonlocal coefficient τ, mechanical parameter α, and geometric parameter β on the deflection amplification factor and equivalent couple amplification factor at the midpoint of the nonlocal saturated poroelastic cantilever beam are studied.
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