Applying Method of Line on cantilever beam under varying loads
DOI:
https://doi.org/10.32972/dms.2025.005Keywords:
Method of Lines, cantilever beam, varying loads, Euler-Bernoulli beam theory, simplified wind turbine bladeAbstract
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.
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