Analysis of three-dimensional dynamic behavior in rigid frame structures

Analytical estimation of dynamic motion allows us to perform measures in advance to address the noise and vibration issues in machinery systems. In this study, we introduce a simplified formulation to analyze the three-dimensional dynamic behaviors of a rigid frame structure. Based on the Euler-Bernoulli and Timoshenko-Ehrenfest beam theories, analytic solutions of six degree -of-freedom motions are defined using the boundary conditions at the end of each beam compo-nent and coupling constraints at the structural joint of the system. All equations are combined as a linearly united matrix equation that increases the scalability of the rigid frame model, and the motions are defined by the computed coefficient vector and external force vector. This linear algebraic expression was verified with the results of modal testing. The spectral responses of the rigid frame model were obtained by experimental modal analysis and derived analytically using both beam theories. A comparison between the results showed that the accuracy of the analytic estimation was ensured with a low error rate, and the accuracy of the Timoshenko-Ehrenfest beam theory was superior to that of the Euler-Bernoulli theory. Consequently, we verified that the proposed formulation is effective and applicable for predicting the three-dimensional dynamic behavior of a rigid frame structure.