Studies On Dynamic Interactions Of Saturated Soil And Timoshenko Beam

The dynamic interaction between saturated soil and Timoshenko beam is an issue belonging to the dynamic and static contact problems of soil and structures, it is a supplement for the research field of interaction between ground and foundation. Its study involves mathematics, mechanics and geotechnical engineering disciplines, being a very important scientific research value, while it has a wide range of important application value in the engineering community just as hydraulic engineering, construction engineering, road engineering, dynamics engineering and so on.Based on the basic equations of transversely isotropic saturated soil and the research of the dynamic interaction between the saturated porous half-plane and infinite Bernoulli beam, the dynamic interactions between saturated porous half-plane of the foundation and the Timoshenko beam as well as between saturated porous half-space of the foundation and the Timoshenko beam are studied and analyzed respectively. Finally, Bernoulli beams and Timoshenko beams in various foundations are compared and analyzed by a concrete example.As the saturated soil foundation reaction is unknown, the analysis must be conducted by considering the interaction between beam and foundation. In order to solve the deflection of beam, series solution is adopted. The deflection, internal forces, loads, subgrade reaction and the settlement of foundation surface under the beam are expanded into Fourier series, the issue of dynamic interaction between soil and Timoshenko beam is transformed into the solving problem of algebraic equations by using Fourier transformation. The undetermined coefficients are confirmed through the boundary conditions of foundation surface and the compatibility conditions of beam-foundation. Then through solving the algebraic equations, steady-state vibration of Timoshenko beam of saturated soil is systematically analyzed by using analytical method. For the saturated half-space problems, based on the transversely isotropic saturated soil basic equations and the research of the dynamic interaction between saturated porous half-space and infinite Bernoulli beam, the saturated soil dynamic issue of transversely isotropic is degenerated and basic equations of transversely isotropic saturated porous half-space problem are established. The basic differential equations are solved by adopting successive decoupling elimination method which is more simple and practical than traditional solution introducing displacement function.By the superposition method, processing measures of the external load of general surface force, couple and so on are founded. The numerical integration issue is the main problem involved when carrying out the numerical solution. As for meeting with "infinite shock points", because its integral area is infinite and the integrand function shows parameters as infinite concussion in integral domain, general methods will not be applicable and special method should be adopted to solve. In this paper, a precise and practical method is provided through dividing integral area by the zero, singular point of integrand and adopting the way of real part, imaginary part integrated respectively. The proposed solution method for the dynamic interaction problem between saturated soils and Timoshenko beam is also applicable to Bernoulli beam. Finally, concrete examples are given to make a comparative analysis of the Bernoulli beams on the different foundations.