Dynamic Response of Non-prismatic Bernoulli Euler Beam with Exponentially Varying Thickness Resting on Variable Elastic Foundation

Abstract

In this paper, the motion of a non-prismatic Bernoulli-Euler beam with exponentially varying thickness resting on variable elastic foundation and under the loads moving with constant velocity is analyzed. The governing equation is a fourth order partial differential equation. The solution technique is based on the method of Galerkin with series representation of Heaviside function and Struble’s asymptotic method. The results shows that, for the same natural frequency, the critical speed for the system traversed by moving force is greater than that under the influence of a moving mass. Also, increase in the values of the structural parameters such as foundation stiffness, foundation modulus, length of the beam and exponential factor reduces the responseamplitude of the beam for both moving force and moving mass problems. Furthermore, it is found that the moving force solution is not always an upper bound for the accurate solution for the non-prismatic Bernoulli-Euler beam.