Purpose
The purpose of this paper is the dynamic analysis of the coupled rotation and vibration motion of a system containing a central rigid body to which is attached a flexible beam.
Design/methodology/approach
The methodology includes the Lagrange’s formulation by using the extended Hamilton’s Principle in conjunction with the assumed modes method to describe the system of equations by ordinary differential equations. The first unconstrained mode of vibration was considered as the solution for the transversal displacement. Such mode emerges as the eigenvalue problem solution associated to the dynamics of the system. The control strategy adopted is a nonlinear analogy of the linear quadratic regulator problem as the Riccati equation is solved at every integration step during the numerical solutions. This strategy is known as state-dependent Riccati equation.
Findings
By means of computational simulations, it was found the relation between controlled motion and inertia ratio.
Research limitations/implications
This work is limited to planar case and fixed hub.
Practical implications
Practical implications of this work realize the design of lighter yet dexterous structures.
Originality/value
The contribution of this paper is the position and vibration control of a flexible beam accounting for nonlinearity effects and the fact that the structure to where it is clamped has a comparable inertia.
Explicit symplectic-precise iteration algorithms for linear quadratic regulator and matrix differential Riccati equation
