Papers by Keyword: Arbitrary Boundary Conditions

Abstract: In this investigation, an improved Fourier series method (IFSM) is employed to predict the static and dynamic characteristics of annular sector plates with arbitrary boundary conditions. Regardless of boundary supports, the displacement function is invariantly expressed as a modified two-dimensional Fourier series containing sine and cosine function. It is capable of dealing with the possible discontinuities at elastic boundary edges. The unknown Fourier coefficients are treated as generalized coordinates, and determined using Rayleigh-Ritz method. Unlike most of the existing solution techniques, the current approach can be universally applied to a variety of edge restraints including all classical cases and their combinations. The accuracy and reliability of the current method are fully illustrated through all the numerical examples.

Abstract: In order to study the rule of deformation prediction of coal mining subsidence in three-dimensional space, it is necessary to establish a three-dimensional geological model. This paper introduced the idea, construction methods and key technologies of three-dimensional geological modeling based on block method and arbitrary boundary conditions by using of VC++ and OpenGL development environment. For the method to build three-dimensional model is simple and accurate. It can be used in the study of mining subsidence prediction and displaying of deformation and failure in the three-dimensional space.

Abstract: Under the Euler-Bernoulli beam theory, the wave propagation method is used for the vibration analysis of beams with arbitrary boundary conditions. The boundary conditions end the beam could be arbitrary that all the conventional homogeneous beam boundary conditions can be included by setting the stiffnesses of the springs be infinity or zero. In this paper, the flexural displacement of the beam is expressed in the wave propagation form including wave numbers. The wavenumber could be obtained in a known form for conventional boundary conditions. So the results are obtained through the boundary conditions and the known wavenumbers and compared with the numerical results. In order to validate the correctness, results with different stiffness are compared with those obtained by previous published papers.

Abstract: Despite a large number of technical papers on vibration of composite shallow shells, all the previous papers have dealt with shallow shells with uniform curvature to avoid difficulty in the analysis. Recent composite products, however, require various surface designs of thin panels from the viewpoint of industrial design, for example, in the fender and door panel designs of commercial vehicles. The present study proposes an analytical method to deal with vibration of shallow shells with non-uniform curvature. An interpolating function is introduced to represent the required surface shape and the corresponding curvature is derived as a function of the position (x,y). The obtained curvature is substituted into the total potential energy of the shell, and the procedure is shown to derive a frequency equation in the Ritz method. Numerical examples clarifies the effects of non-
uniform curvature on the natural frequencies and mode shapes.