Applying Method of Line on cantilever beam under varying loads - Iyad F., Al-Najjar; Jálics, Károly (Design of Machines and Structures, 2025)
The Method of Lines (MoL) is a powerful numerical technique for solving partial differential equations (PDEs) by discretising the spatial domain while keeping time as a continuous variable. In this study, we employ MoL to solve the fourth-order beam equation, which governs the dynamics of an Euler-Bernoulli cantilever beam. The primary objective is to develop a simplified computational model for a wind turbine blade, treated as a cantilever beam subjected to dynamic loading. The spatial discretisation is performed using finite difference approximations, transforming the governing PDE into a system of second-order ordinary differential equations (ODEs). The resulting ODE system is then integrated over time using Runge-Kutta.