Cantilevered Beams

Abstract

In many distributed parameter mechanical systems, the flexible element can be modeled as a beam-type structure (e.g., space structures, flexible link robots, helicopter rotor/blades, turbine blades, etc.). The most commonly used beam model is based on the classical Euler-Bernoulli theory, which provides a good description of the beam’s dynamic behavior when the beam’scross-sectional dimensions are small in comparison to its length (i.e., this model neglects the rotary inertia of the beam). A more accurate beam model is provided by the Timoshenko theory, which takes into account not only the rotary inertial energy but also the beam’s deformation owing to shear. As discussed in [15], the Timoshenko beam model has been shown to have a broader applicability than the Euler-Bernoulli model. In [1], Aldraihem et al. compared the accuracy and validity of these two beam models by simulating a cantilevered beam under distributed piezoelectric sensoring/actuation. The results provided in [1] indicated that the Timoshenko model is superior to the Euler-Bernoulli model in predicting the beam’s response. While the Timoshenko model may be more accurate at predicting the beam’s response in comparison to the Euler-Bernoulli model, the Timoshenko model is more difficult to utilize for control design purposes owing its higher order. For this reason, the design of boundary controllers for flexible-beam-type structures has been based mainly on the Euler-Bernoulli model.