Under the assumptions of Euler beam and plane stress, this study formulates the governing equations of flexural vibrations for the porous beam and plate using Biot’s poroelastic theory. Then, the stiffness matrices of the porous beam, plate and medium elements are derived in Laplace domain. Thereafter, using the impulsive loading and the elastic boundary conditions, the finite element frequency domain analyses are performed to study the dynamic behaviors of porous beams, plates, and mediums. In order to match the application condition, the dynamic behaviors of stiffened porous plates (porous beam coupled with porous plate) and porous beam coupled with porous medium are also evaluated.
The porous beam, plate, and medium present a typical dissipation effect due to the interaction between the saturated fluid and the solid skeleton. Upon examining the reduction of modal amplitudes of the saturated porous beam and plate, the dissipation effect is found growing with the increase of the fluid’s viscosity, and the bulk modulus of the fluid has major effect on their modal frequencies. Therefore, by changing of the saturated fluid, the modal frequency and amplitude of the porous beam and plate can be adjusted. From the modal frequency fluctuations of the stiffened porous plate, the increase of both dissipation coefficient and modal frequency are clearly observed with the raise of porosity. Hence, the dynamic behavior of the stiffened porous plate can be precisely adjusted by the changes of the porosity and the saturated fluid. In addition, the analysis results of the coupling of a porous beam with an acoustic field show that the coupled modal frequencies of the porous beam and the acoustic field can be simultaneously observed, as well as the remarkable changes on the modal frequencies and amplitudes.