Analyses of the vibrational power flow characteristics of an internally supported beam with elastic boundary conditions

Abstract

In order to effectively solve the problem of abrupt changes associated with the bending moment and shear force parameters at the supports, in this study, a model is established to analyze the vibrational power flow analysis model of an internally supported beam under elastic boundary conditions. The beam structure is divided into subbeam-I and subbeam-II coupled through an elastic joint at the supporting position. The vibration displacement of the beam is expanded by a Fourier series with a smooth boundary. In accordance with the energy principle, the Lagrangian function of the beam structure with arbitrary boundary constraints considering the internal support stiffness is established, and the system characteristic equation is obtained by solving the model with the Rayleigh-Ritz method. Then, the power flow distribution and dynamic response characteristics of the beam vibration system are calculated according to the theory of vibrational power flow. Numerical and traditional methods are used to validate the correctness and reliability of the proposed model. Based on the established model, we study the influence of parameters, including the lateral support stiffness, rotational constraint stiffness, and internal support position, on the vibration power flow, support transmission loss, and total output power flow of any elastic boundary beam structure. The present model can overcome the numerical instability of the energy flow at the abrupt transition point by the traditional method. Moreover, it does not need to reconstruct the model when there are system boundary variations. It has the advantages of high efficiency and high precision and provides an effective means for the vibrational energy flow characteristic analysis of internally supported beam structures under elastic boundary conditions.