Forced Vibration Analysis of Euler-Bernoulli Double-Beam Systems by Means of Green’s Functions

ZHAO Xiang; MENG Shiyao

doi:10.21656/1000-0887.430298

Volume 44 Issue 2

Feb. 2023

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ZHAO Xiang, MENG Shiyao. Forced Vibration Analysis of Euler-Bernoulli Double-Beam Systems by Means of Green’s Functions[J]. Applied Mathematics and Mechanics, 2023, 44(2): 168-177. doi: 10.21656/1000-0887.430298

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Forced Vibration Analysis of Euler-Bernoulli Double-Beam Systems by Means of Green’s Functions

doi: 10.21656/1000-0887.430298

ZHAO Xiang,
MENG Shiyao^,

School of Civil Engineering and Geomatics, Southwest Petroleum University, Chengdu 610500, P.R.China

Received Date: 2022-09-28
Rev Recd Date: 2022-12-09

Available Online: 2023-02-01

Publish Date: 2023-02-15

Abstract

Abstract

Double-curved-beam (DCB) systems are usually seen in many engineering fields. Compared to straight double-beam systems, DCB systems are more efficient in noise and vibration control problems. To obtain closed-form solutions of steady-state forced vibrations of DCB systems, the classical Euler-Bernoulli curved beam (ECB) model was employed to model vibration equations for the DCB systems. Green’s functions and the Laplace transform methods were used to get the closed-form solutions to the vibration equations for the DCB systems. These solutions apply to arbitrary boundary conditions. Numerical tests were conducted to verify the present solutions with related results from previous literatures. Effects of some important geometric and physical parameters on vibration responses and the interaction between the elastic layer stiffness and the DCB system, were discussed. The results show that, the DCB system will degenerate to a straight double-beam system when the 2 radii approach infinity, moreover, the DCB system can be simplified as one comprising a straight beam and a curved beam.
- Green’s function,
- Euler-Bernoulli beam model,
- double-curved-beam system,
- Winkler elastic layer,
- Laplace transform

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References(18)

References

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