International Journal of Composite Materials and Matrices
Analysis of Non-Uniform Damped Rayleigh BeamResting on Pasternak Foundation Subjected toDistributed Load with Variable Axial Force
1Research Scholar, Department of Mathematics and Statistics, Conference University of Science and Technology, Osara, Kogi State, Nigeria
2Research Scholar, Centre for Energy Research and Development, Obafemi Awolowo University, Ile-Ife, Osun State, Nigeria
3Research Scholar, Department of Biochemistry, Chemistry, and Physics, College of Science and Mathematics, Georgia Southern University, 1332 Southern Drive Statesboro, GA, USA
4Research Scholar, Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria
5Research Scholar, Department of Building, Obafemi Awolowo University, Ile-Ife, Nigeria
6Research Scholar, Department of Mechanical Engineering (Marine Domain), Centurion University of Technology and Management, Bhubaneswar, Odisha, India
Abstract
In this paper, damped non-uniform Rayleigh beam resting on Pasternak foundation and subjected to distributed load with variable axial force has been investigated. The solution techniques to the governing equation describing the dynamical system are based on Galerkin’s method, Laplace integral transformation in conjunction with convolution theorem. Galerkin’s method is explored to reduce the fourth order non-homogeneous partial differential equation to a second order ordinary differential equation. The resulting equation is then solved using Laplace transformation while the inverse Laplace transformed is obtained with the application of convolution theorem. The transverse displacement is calculated for various values of the axial force (No), Shear modulus (Fo), Foundation Stiffness (Ko), Damping Coefficient (Δc), and Rotatory Inertia (Ro). The results are shown graphically, and it reveals that the response amplitude of the beam under distributed load reduces with increase in axial force, shear modulus, foundation modulus, damping coefficient, and rotatory inertia. Also, as the length of the beam reduces the response amplitude of the beam decreases and this implies that there is direct relationship between the beam’s response amplitude and the length of the beam. Finally, axial force and rotatory inertia have more noticeable effects on the beam subjected to the distributed compared with other structural parameters.
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