Frequency-Domain Analysis of the Euler-Bernoulli and Timoshenko Beams with Attached Masses

TL;DR

This paper develops frequency-domain models for Euler-Bernoulli and Timoshenko beams with attached masses, analyzing their dynamic behavior and control system responses.

Contribution

It derives state space equations and transfer functions for both beam models considering damping and control, enabling comparison of their frequency responses.

Findings

Transfer functions for both beam models are obtained.

Bode plots compare the dynamic responses with different damping and output configurations.

The models facilitate analysis of control and damping effects on beam vibrations.

Abstract

This work focuses on the frequency-domain modeling of a control system with a flexible beam and a rigid body. A simply supported beam is equipped with a spring-loaded control actuator and possesses local damping effect. Using Hamilton's variational principle, the equations of motion are derived in the state space form taking into account interface conditions involving lumped control and local damping. The transfer functions are obtained for the Timoshenko and Euler--Bernoulli beam models with the output measurements provided by a point sensor. Comparative Bode plots are presented for the two beam models with different choices of output signals and damping coefficients.