A State-Space Method for Vibration of Double-Beam Systems with Variable Cross Sections
Publication: Journal of Engineering Mechanics
Volume 150, Issue 11
Abstract
In this paper, a state-space method for double-beam systems with variable cross sections is developed, making it possible to calculate the transverse vibration of the double-beams accurately and effectively. Due to the variability in the double-beam cross sections with the viscoelastic interlayer in between, the governing equations of vibration for the systems become highly coupled partial differential equations, making the problem difficult to solve. A basic double-beam system is introduced to modify the original governing equations to two inhomogeneous differential equations. Given the separation of variables, several mode-shape coefficients and a state variable are defined to construct the state-space equations. The coupling terms and variables are transferred into the constant coefficient matrix of the state-space equations, decoupling them. Numerical procedures are presented to solve the state-space equations to obtain homogenous and inhomogeneous solutions, including the natural frequencies and mode shapes in free vibration and the dynamic responses in forced vibration, respectively. The method has substantial advantages in decoupling high-order partial differential equations and can be further extended to solve complex structural systems. Numerical results also demonstrate that the method is accurate and efficient. Finally, an engineering application with a rail-bridge with a floating slab track is discussed in detail with the method.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work was sponsored by the National Science Foundation (NSF) under Grant No. CMMI-1229405, MOE Key Laboratory of Deep Earth Science and Engineering (MOEKLDESE) under Grant No. DUSE201706, Fundamental Research Funds for the Central Universities (FRFCU), and Department of Human Resources and Social Security of Sichuan Province (DHRSSSP) under Grant No. 2021-29-32. The support is gratefully acknowledged.
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Published In
Journal of Engineering Mechanics
Volume 150 • Issue 11 • November 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Nov 29, 2023
Accepted: Jul 1, 2024
Published online: Sep 11, 2024
Published in print: Nov 1, 2024
Discussion open until: Feb 11, 2025
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