If you are looking to get into the for modal analysis, or perhaps simulation examples using Python , I can provide those.
: Covers the mathematical foundations of variable mass and fluid movement.
Changes in engine gimbal angles exert concentrated forces and moments at the actuator attachment points. This directly excites high-frequency structural bending modes. 6. Computational Frameworks and Simulation dynamics and simulation of flexible rockets pdf
: A classic NASA report that examines the mathematical modeling of elastic bodies under longitudinal acceleration while accounting for rapid mass depletion NASA (.gov)
The modeling and simulation of flexible rockets is a critical field in aerospace engineering, moving beyond classical rigid-body assumptions to account for the elastic behavior of modern, slender launch vehicles. This discipline ensures that a rocket's structural flexibility, when coupled with liquid fuel slosh and moving engine nozzles, does not lead to instability or structural failure during flight. Core Dynamics of Flexible Rockets If you are looking to get into the
Includes shear deformation and rotational inertia; essential for thicker, multi-payload fairing configurations. B. Finite Element Method (FEM) and Modal Reduction
2021 edition covering advanced modeling techniques. essential for thicker
The dynamics of a flexible rocket are typically formulated using the Euler-Bernoulli or Timoshenko beam theories, augmented to account for axial thrust and aerodynamic forces. For bending vibration in a single plane, the governing equation is:
Using Lagrange’s equations or the principle of virtual work, the fully coupled non-linear equations of motion are expressed in matrix form: