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J. Compos. Sci.
Volume 9
Issue 5
10.3390/jcs9050215
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Article

Free Vibration Characteristics of Functionally Graded Material (FGM) Beams on Three-Parameter Viscoelastic Foundation

by
Shuming Jia
1,
Guojiang Yang
2,
Yu Pu
1,
Pengfei Ma
1,* and
Kan Li
1
1
College of Civil Engineering, Lanzhou Institute of Technology, Lanzhou 730050, China
2
Gansu Civil Engineering Science Research Institute Co., Ltd., Lanzhou 730010, China
*
Author to whom correspondence should be addressed.
J. Compos. Sci. 2025, 9(5), 215; https://doi.org/10.3390/jcs9050215
Submission received: 2 April 2025 / Revised: 27 April 2025 / Accepted: 27 April 2025 / Published: 28 April 2025
(This article belongs to the Special Issue Editorial Board Members’ Collection Series: Modeling and Simulation of Composite Materials)
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Abstract

This study numerically investigated free vibration characteristics of functionally graded material (FGM) beams on Winkler–Pasternak three-parameter elastic foundations using the modified generalized differential quadrature (MGDQ) method. To compare the effects of different beam theories on the predicted frequency responses, an nth order generalized beam theory was employed to establish the governing equations of the system’s dynamic model within the Hamilton framework. As a pioneering effort, a MATLAB (version 2021a) computational program implementing the MGDQ method was developed to obtain the free vibration responses of foundation-supported FGM beams. Parametric analyses were conducted through numerical simulations to systematically examine the influences of various factors, including beam theories, damping coefficients, foundation stiffness parameters, boundary conditions, gradient indices, and span-to-thickness ratios, on the natural frequencies and damping ratios of FGM beams. The findings provide an essential theoretical foundation for dynamic characteristic analysis and functional design of foundation-supported FGM beam structures.
Keywords: functionally graded material beams; viscoelastic foundation; n-th order generalized beam theory; eigen frequency; critical damping; damping ratio functionally graded material beams; viscoelastic foundation; n-th order generalized beam theory; eigen frequency; critical damping; damping ratio

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MDPI and ACS Style

Jia, S.; Yang, G.; Pu, Y.; Ma, P.; Li, K. Free Vibration Characteristics of Functionally Graded Material (FGM) Beams on Three-Parameter Viscoelastic Foundation. J. Compos. Sci. 2025, 9, 215. https://doi.org/10.3390/jcs9050215

AMA Style

Jia S, Yang G, Pu Y, Ma P, Li K. Free Vibration Characteristics of Functionally Graded Material (FGM) Beams on Three-Parameter Viscoelastic Foundation. Journal of Composites Science. 2025; 9(5):215. https://doi.org/10.3390/jcs9050215

Chicago/Turabian Style

Jia, Shuming, Guojiang Yang, Yu Pu, Pengfei Ma, and Kan Li. 2025. "Free Vibration Characteristics of Functionally Graded Material (FGM) Beams on Three-Parameter Viscoelastic Foundation" Journal of Composites Science 9, no. 5: 215. https://doi.org/10.3390/jcs9050215

APA Style

Jia, S., Yang, G., Pu, Y., Ma, P., & Li, K. (2025). Free Vibration Characteristics of Functionally Graded Material (FGM) Beams on Three-Parameter Viscoelastic Foundation. Journal of Composites Science, 9(5), 215. https://doi.org/10.3390/jcs9050215

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