A New Approach on the Response of Non-Uniform Prestressed Timoshenko Beams on Elastic Foundation Subjected to Harmonic Loads

The dynamic response of the Timoshenko beam resting on an elastic foundation subjected to harmonic moving load using modal analysis (MA) was investigated. The method of MA was employed to obtain a closed form solution to this class of dynamical systems. In order to use MA, accurate information is needed on the natural frequencies, mode shapes and orthogonality of the mode shapes. A thorough literature survey reveals that the method has not been reported in existing literature to solve non-prestressed Timoshenko beams. Thus, we present complete information on how to use MA to derive the forced vibration responses of a simply thick beam subjected to harmonic moving loads. The effects of axial force and foundation parameters on the dynamic characteristics of the beams are studied and described in detail. In order to validate the accuracy of this method, we compare the frequency parameter with the existing literature which appears to compare favorably.

Analysis of beams on elastic foundations using Green's functions

Beams on elastic foundation are basic elements within structural analysis, which are used to model foundation beams, foundation piles, retaining walls, and more complex structures that include some of these elements. For their analysis, the finite element method is usually used [1], which produces an approximate solution of the problem; and the Green's function stiffness method [2], which produces an exact solution. This article presents a methodology 100% based on the use of Green function's (response to a unit point force), to obtain the exact response of beams on elastic foundation. The main advantage of this formulation is its computational low cost compared to the aforementioned alternatives, and even for a large number of problems, it can be expressed only by means of sums and integrals, which can be easily performed numerically. Also, a great variety of Green function's for finite and infinite beams on elastic foundations with different boundary conditions are also presented, as well as some examples with the implementation of the proposed methodology.

Seismic Analysis of Simply Supported Damped Rayleigh Beams on Elastic Foundation

In this paper, the flexural analysis of a simply supported damped Rayleigh beam subjected to distributed loads and with damping due to resistance to the transverse displacement resting on elastic foundation is obtained. The characteristics of the beam are assumed uniform over the beam length while the foundation is considered of Winkler type. In order to evaluate the vibration characteristics of the dynamical system, the Fourier sine integral transformation in conjunction with the asymptotic method of Struble is used to solve the governing equations for the transversal vibrations in the beam structure induced by moving load. The effect of prestress and other structural parameters were considered. Numerical results show that the structural parameters have significant influence on the behaviour of the dynamical system.

Engineering design of selecting particle size of gangue under solid backfill mining for protecting water resources

In view of the ecological environment damages caused by the loss of water resources and the gangue accumulation during coal mining, this paper proposed a solid backfill mining method to recover the coal seam under the water body, which could fundamentally reduce the sinking space of the overlying strata, and better prevent water-flowing fractures expanding. Consequently, according to the deformation characteristics of the overlying strata of the solid backfill mining, a mechanical model was established for superimposed beams on elastic foundation with simu?lating the expansion water-flowing fractures under solid backfill mining. A method of calculating the height of the water-flowing fractured zone was provided, and the mechanical mechanism of the development of water-flowing fractures in the overlying strata under solid backfill mining was expressed. Meanwhile, the backfill rate of the experimental working face was designed as 80% to avoid the ecological environment damages caused by gangue accumulation. The stress-strain characteristics of gangue samples under different grading size schemes were further studied.