Analytical and Reduced-Order Modeling of a Timoshenko Beam with Point Actuation

We present frequency-domain models of a controlled mechanical system consisting of a flexible beam and a rigid body. The transfer function for the beam, governed by the Timoshenko equations under the body-beam interface conditions, is derived analytically. Based on this infinite-dimensional representation, reduced-order models are constructed within the framework of Loewner matrices. A comparative analysis of the Bode plots is presented for the beam model using different choices of sensor-actuator pairs to validate the proposed frequency-domain modeling framework.