Horizontal Vibrations of Embedded Foundation in Multi-Layered Poroelastic Soils

In this paper, the dynamic response of rigid foundations of arbitrary shape embedded in multi-layered poroelastic soils subjected to time-harmonic horizontal loading is presented. The soil-structure interaction problem is investigated by employing a discretization technique and flexibility equations based on the influence functions obtained from an exact stiffness matrix scheme. The present solution scheme is verified with relevant existing solutions of rigid foundations on homogeneous elastic and poroelastic media. A selected set of numerical results are illustrated to portray the influence of various parameters, namely, frequency of excitation, poroelastic material parameters, foundation shapes, embedded depth, and the supporting soil systems, on non-dimensional horizontal compliances of rigid foundations

Influence of Surface Stresses on the Deflection of Circular Nanoplate with Two-Parameter Elastic Substrate

This paper presents the influence of surface energy effects on the deflection of circular nanoplate with two-parameter elastic substrate. The governing equation for axisymmetric bending of the nanoplate, based on the Gurtin-Murdoch surface elasticity theory, resting on a Winkler-Pasternak elastic foundation is derived from a variational approach based on the concept of minimum total potential energy. The analytical general solution to the governing equation is then obtained in terms of the modified Bessel functions. Finally, closed-form solutions for deflections, bending moment and transverse shear in the nanoplate subjected to normally distributed loading are presented explicitly for the boundary conditions of simple, clamped, and free edges.  A set of numerical solutions are selected to demonstrate the influence of surface material parameters and the substrate moduli on the deflection and bending moment profiles of a silicon nanoplate on Winkler-Pasternak foundation. It is found that the nanoplate clearly shows size-dependent behaviors, and becomes stiffer with the existence of surface stresses

Dynamic interaction between elastic plate and transversely isotropic poroelastic medium

In this paper, dynamic response of an elastic circular plate, under axisymmetric time-harmonic vertical loading, resting on a transversely isotropic poroelastic half-space is investigated. The plate-half-space contact surface is assumed to be smooth and fully permeable. The discretization techniques are employed to solve the unknown normal traction at the contact surface based on the solution of flexibility equations. The vertical displacement of the plate is represented by an admissible function containing a set of generalized coordinates. Solutions for generalized coordinates are obtained by establishing the equation of motion of the plate through the application of Lagrange’s equations of motion. Selected numerical results corresponding to the deflections of a circular plate, with different degrees of flexibility, resting on a transversely isotropic poroelastic half-space are presented

Influence of Surface Energy Effects on Elastic Fields of a Layered Elastic Medium under Surface Loading

This paper presents the analysis of a layered elastic half space under the action of axisymmetric surface loading and the influence of the surface energy effects. The boundary value problems for the bulk and the surface are formulated based on classical linear elasticity and a complete Gurtin-Murdoch constitutive relation. An analytical technique using Love’s representation and the Hankel integral transform is employed to derive an integral-form solution for both displacement and stress fields. An efficient numerical quadrature is then applied to accurately evaluate all involved integrals. Selected numerical results are presented to portray the influence of various parameters on elastic fields. Numerical results indicate that the surface stress displays a significant influence on both displacement and stress fields. It is also found that the layered half space becomes stiffer with the presence of surface stresses. In addition, unlike the classical elasticity solution, size-dependent behavior of elastic fields is noted. The present analytical solutions provide fundamental understanding of the influence of surface energy on layered elastic materials. It can also be used as a benchmark solution for the development of numerical techniques such as FEM and BEM, for analysis of more complex problems involving a layered medium under the influence of surface energy effects

Dynamic impedances of multiple strips on multi-layered transversely isotropic poroelastic soils

Geo-materials naturally display a certain degree of anisotropy due to various effects such as deposition. Besides, they are often two-phase materials with a solid skeleton and voids filled with water, and commonly known as poroelastic materials. In the past, despite numerous studies investigating the vibrations of strip foundations, dynamic impedance functions for multiple strip footings bonded to the surface of a multi-layered transversely isotropic poroelastic half-plane have never been reported in the literature. They are first presented in this paper. All strip foundations are assumed to be rigid, fully permeable, and subjected to three types of time-harmonic loadings. The dynamic interaction problem is investigated by using an exact stiffness matrix method and a discretization technique. The flexibility equations are established by enforcing the appropriate rigid body displacement boundary conditions at each footing-layered soil interface. Numerical results for dynamic impedance functions of two-strip system are presented to illustrate the influence of various effects on dynamic responses of multiple rigid strip foundations