Dynamic Responses of Beam Deflection Model Using γ-Splines Functions and Fourier Transform Discretization Solvers

Throughout this paper, we use Fourier Transform Discretization (FTD) to solve the dynamic deflection of the beam deformation model. The considered problem is a Partial Differential Equation with non-homogeneous boundary conditions, which expresses the displacement of beam under the effect of an arbitrary moving source force. Our method is usually carried out in two steps. Firstly, the equations and boundary conditions are changed into other equivalent equations and mixed boundary conditions for the frequency parameters. The approximate solution of this last problem is computed using a weak variational analysis technique based on the higher-order Normalized Uniform Polynomial Splines solver. Secondly, several quadrature techniques are employed to calculate the Inverse Fourier Transform of the solution, and then we give a comparison report between the numerous numerical computations of this integral. Careful numerical experiments are presented to indicate the success and well-precious resolution properties for all kinds of smooth and discontinuous solutions and plots of field of displacements of the beam. Similarly, as an application, the FTD and splines finite element methods are employed to solve the coupled Timoshenko transverse vibrating equations with non-homogeneous boundary conditions.