• Derived an explicit finite difference scheme (7-points stencil) with second order accuracy by discretizing the equation governing Euler-Bernoulli beam transverse vibrations.
• Implemented Python script for computation of natural frequencies of vibration, mode shapes, and vibration response of the elastic beam for different boundary conditions, viz. fixed-fixed, fixed-pinned, pinned-pinned, and fixed-free.
• von Neumann analysis was done to establish stability requirements of the solution, explicit FD scheme was found to be conditionally stable and convergent; compared the results with analytical solution to validate the approach.
Project Report: Transverse Vibration Analysis of Euler-Bernoulli Beam