Bending and vibration of a discontinuous beam with a curvic coupling under different axial forces
- PDF / 1,617,795 Bytes
- 13 Pages / 595.276 x 785.197 pts Page_size
- 102 Downloads / 215 Views
RESEARCH ARTICLE
Heng LIU, Jie HONG, Dayi ZHANG
Bending and vibration of a discontinuous beam with a curvic coupling under different axial forces
© The Author(s) 2020. This article is published with open access at link.springer.com and journal.hep.com.cn 2020
Abstract The transverse stiffness and vibration characteristics of discontinuous beams can significantly differ from those of continuous beams given that an abrupt change in stiffness may occur at the interface of the former. In this study, the equations for the deflection curve and vibration frequencies of a simply supported discontinuous beam under axial loads are derived analytically on the basis of boundary, continuity, and deformation compatibility conditions by using equivalent spring models. The equation for the deflection curve is solved using undetermined coefficient methods. The normal function of the transverse vibration equation is obtained by separating variables. The differential equations for the beam that consider moments of inertia, shearing effects, and gyroscopic moments are investigated using the transfer matrix method. The deflection and vibration frequencies of the discontinuous beam are studied under different axial loads and connection spring stiffness. Results show that deflection decreases and vibration frequencies increase exponentially with increasing connection spring stiffness. Moreover, both variables remain steady when connection spring stiffness reaches a considerable value. Lastly, an experimental study is conducted to investigate the vibration characteristics of a discontinuous beam with a curvic coupling, and the results exhibit a good match with the proposed model. Keywords discontinuous beam, bending stiffness, transverse vibration, axial loads, gyroscopic moments
Received October 6, 2019; accepted December 24, 2019
✉
Heng LIU, Jie HONG, Dayi ZHANG ( ) School of Energy and Power Engineering, Beihang University, Beijing 100191, China E-mail: [email protected] Heng LIU State Key Laboratory of Laser Propulsion and Application, Beijing Power Machinery Institute, Beijing 100074, China
1
Introduction
The mechanical structure of an aeroengine rotor can be simplified as a structural system that consists of multisection beams and connecting structures. The multisection beams in the rotor are typically defined as a discontinuous beam [1]. The deflection of continuous beams can be easily obtained via the classical principles of material mechanics [2]. However, given that a discontinuous beam has physical contact interfaces that cause discontinuities in mechanical properties, an abrupt change in stiffness may occur and result in complexity in predicting the bending and vibration of a discontinuous beam [3–6]. Various models have been developed to simulate the bending and vibration of continuous Euler–Bernoulli and Timoshenko beams. Han et al. [7] developed a mechanical model that considered damping to analyze a double-beam system with a viscoelastic connection layer. The governing differential equation was formulated on the basis of E
Data Loading...
