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Two forms of finite integral transform are applied to the issue of vibration induced by moving load/mass. The first form is finite Fourier transform, of which the application is limited only for structures with simply supported boundary conditions. For structures with boundary conditions other than simply supported, generalized finite integral transform (GFIT) is applied. The primary difference between the two methods is different kernels of the transformation being adopted; for instance, in the finite Fourier transform, the kernel is sine or cosine function whereas for GFIT the kernel consists of the eigenfunctions of the differential operator appearing in the original partial differential equation to be solved. Tradditionally, the characteristic beam functions are expressed as the combinations of trigonometric and hyperbolic functions. However, it is difficult and tedious to express the kernel for beams in forms of trigonometric and hyperbolic functions, not to mention for plates with complicated boundary conditions. In addition, it is quite difficult to obtain explicit eigenfunctions for a structure such as the beam with rotationally restrained supports. Thus, GFIT would be not applicable for the issue of vibration induced by moving load/mass for such structures.

In this paper, with use of Stokes’ transformation, the application of the finite Fourier transform to vibration analysis associated with moving load/mass is extended to structures with general boundary conditions. The explicit eigenfunctions in the forms of Fourier series are first obtained. Then, as the eigenfuncetions are simpler than hyperbolic equations, GFIT with kernel of the eigenfunctions is employed to solve the vibration problems associated with moving load/mass. It is demonstrated that the finite Fourier transform can be directly applicable to the problems and a corresponding unified approach is presented. Numerical analyses based on the two proposed methods are carried out and results from the methods are compared. Although the vibration induced by moving load/mass for beams with rotationally restrained supports are presnted, the proposed methods are applicable for beams with other complicated boundary conditions. In addition, the methods can be extended to analysis of vibration induced by moving load/mass for plates with general boundary conditions.

The prominent features of the proposed methods are: (a) the methods readily yield solutions for vibrations induced by moving load and moving mass for beams with elastically restrained supports; (b) the proposed methods can be used to obtain general solutions of the problems for beams with other boundary conditions; (c) the convergence of the series solutions can always be achieved and the accuracy of solution can be obtained to any desired degree.