Vibration analysis of an eccentrically loaded rigid rectangular plate bonded to layered transversely isotropic poroelastic media

• The SSI problem for an eccentrically loaded rigid plate and porous media is analyzed. • The mixed boundaries for the SSI problem are described as dual integral equations. • Dual integral equations are handled with Jacobian polynomials and Bessel series. • Effects of the soil stratification, load eccentricity and frequency are explored. This paper presents a semi-analytical method for addressing the dynamic response of a rigid rectangular plate on layered transversely isotropic poroelastic media under vertical eccentric loading. The challenge lies in the biaxial mixed boundary conditions of rectangular plates and the broken spatial symmetry caused by vertical eccentric loading. Based on the steady-state response of the poroelastic media, a solution framework is established by transforming the resulting dual integral equations satisfying the mixed boundary conditions into a solvable linear system via Bessel function expansion. Following successful two-stage validation, parametric studies are conducted to quantify the influence of load eccentricity, dimensionless frequency, and soil stratification. The analysis reveals that increased load eccentricity leads to higher magnitudes and more pronounced oscillations of stress and displacement within the media. The sensitivity of the rocking compliance to the analyzed load frequency is weaker in the real part than in the imaginary part. In addition, the characteristics of the surface soil appreciably affect the dynamic response of the plate on the media.