Vibrational Energy Flow Model for a High Damping Beam with Constant Axial Force

Xiaoyan Teng,Nan Liu,Jiang Xudong

doi:10.1155/2020/3584048

Abstract

The energy flow analysis (EFA) method is developed to predict the energy density of a high damping beam with constant axial force in the high-frequency range. The energy density and intensity of the beam are associated with high structural damping loss factor and axial force and introduced to derive the energy transmission equation. For high damping situation, the energy loss equation is derived by considering the relationship between potential energy and total energy. Then, the energy density governing equation is obtained. Finally, the feasibility of the EFA approach is validated by comparing the EFA results with the modal solutions for various frequencies and structural damping loss factors. The effects of structural damping loss factor and axial force on the energy density distribution are also discussed in detail.

Highlights

With the development of high-speed aircrafts and transportation vehicles, high-frequency vibration of components is of great concern for both academic and industrial communities in recent years
We extend the energy flow analysis (EFA) model developed by Zhang et al [23] to high damping beams with axial force. is paper is organized as follows
To validate the proposed EFA formulation and investigate the effects of structural damping loss factor and axial force, various energy flow analyses are performed for a pinnedpinned beam at both ends shown in Figure 1. e results from analytical solutions of EFA governing equation are compared with exact modal solutions (Appendix A and Appendix B), which are defined as time averaged energy density obtained from the displacement solutions

Summary

Introduction

With the development of high-speed aircrafts and transportation vehicles, high-frequency vibration of components is of great concern for both academic and industrial communities in recent years. The energy density governing equation is derived from the energy transmission equation and the energy loss equation for a high damping beam with axial force. 2. Energy Density Governing Equation of a High Damping Beam with Constant Axial Force. In a vibrating beam with constant axial force, the time averaged potential energy density can be expressed as [27]. Substituting equations (13) and (17) into equation (18), the energy density governing equation for the high damping beam with axial force can be derived as d2〈e〉 dx. E energy transition equation represents the relationship between time and space averaged energy density and intensity without group velocity because the damping effect is not neglected. On account of high structural damping, the potential energy density is not the same as the kinetic energy density of the structure. us, the energy loss equation is derived according to the relationship between potential energy and total energy

Solution of Energy Density Governing Equation

Verification and Discussion

Application to Beams with Different Boundary

Conclusion

Mode Shapes for High Damping Beams with Axial Force