Mathematical Modelling of a Rotating Nonlinear Flexible Beam-Like Wing

Abstract

The mathematical modelling of rotating nonlinear flexible beam-like wing with rectangular cross section is investigated here. The structure is mathematically modeled considering linear curvature and clamped-free boundary conditions. The flexible wing has an angle of attack which is considered constant. Nonlinearities resulting from the coupling between the angular velocity of the rotating axis and the transversal vibration of the beam are considered. A drag force and a lift force acting along the beam length are also included in the mathematical model. The drag force is modelled as a turbulent drag effect. The lift force is modeled as a generalized force, using the strip theory. These forces are velocity dependent nonlinear excitations acting on the bean-like wing.

Nonlinear modeling of slewing flexible structures: ideal and non ideal approaches

“…In applying the extended Hamilton Principle we obtain the governing equations of motion for the variables h(t), and v(x, t) respectively, as given by [4] 2 2 where F h and f v are given by…”

“…We follow the approach developed in [4], which is shown here for the sake of clarity. The governing equations of motion are obtained through the energy method [5][6][7][8][9].…”

“…The drag and lift forces, as considered in [4], are functions of the velocities Qሶ (x, t) and ߠ ሶ (t). The lift is also a function of the vertical velocity ݄ ሶ ሶ ሶ ሶ (t).…”

Nonlinear modeling of slewing flexible structures: ideal and non ideal approaches

“…In applying the extended Hamilton Principle we obtain the governing equations of motion for the variables h(t), and v(x, t) respectively, as given by [4] where F h and f v are given by…”

Revisiting the Nonlinear Dynamics Behavior,Control Designs and Insights on Fluid Interactions of a Flexible Slewing Spatial Structures and their Applications to Engineering Science

“…We remrked that little effort has been focused on DC motor -structure interaction which affects the dynamic properties of the slewing system,obviuosly.DC motors used in these applications are popular actuators not only because they can generate a wide range of torques and angular velocities, but also because they are quiet, clean and efficient.In the study with these kind of rotating structures, the interaction between the angular displacement also called slewing angle, and the flexible structure deflection variable can be very important in some cases, as in high angular speed maneuvers [5,6,7,8,9,10].…”