Vibration Modelling and Response Characteristics Analysis of Functionally Graded Cylindrical Shells under Stationary Random Excitations

DU Zhao; ZUO Peng; SHI Xianjie

doi:10.7643/ issn.1672-9242.2026.02.013

PDF(1992 KB)

Equipment Environmental Engineering ›› 2026, Vol. 23 ›› Issue (2) : 114-122. DOI: 10.7643/ issn.1672-9242.2026.02.013

Vibration Modelling and Response Characteristics Analysis of Functionally Graded Cylindrical Shells under Stationary Random Excitations

DU Zhao¹, ZUO Peng^1,*, SHI Xianjie²

Author information +

History +

Abstract

The work aims to propose a dynamic model that can quickly and effectively predict the random vibration responses of functionally graded (FG) cylindrical shells under stationary random load, while investigating the influence of key parameters on the random vibration characteristics of the corresponding structures. The artificial spring technology was used to simulate arbitrary boundary constraints of FG cylindrical shells. The displacement admissible functions of cylindrical shells were characterized using the SGM which consisted of concise trigonometric function. Within the framework of the first order shear deformation theory, the PEM was applied to establish the energy functional of FG cylindrical shells under random load. Further, an stationary random response analysis model for FG cylindrical shells was obtained with the Rayleigh-Ritz method. Through several numerical examples analysis, the power spectral density (PSD) response results of cylindrical shells under different boundary conditions calculated by the model constructed in the article were basically consistent with the finite element results. Moreover, the deviation of natural frequencies and RMS values was within 0.5% and 1%, respectively. On this basis, the effect of some parameters, such as gradient exponent p, length-radius ratio L/R and thickness-radius ratio h/R, on the random vibration behavior of FG cylindrical shells was discussed in detail. In conclusion, the model established in the paper can analyze the free vibration and steady random vibration response characteristics of cylindrical shells with high precision and efficiency. Besides, an increase in p and L/R can weaken the stiffness of FG cylindrical shells and improve the vibration amplitude of cylindrical shells; on the contrary, the increasing h/R will enhance the structural stiffness and reduce the vibration amplitude of cylindrical shells. This research may provide theoretical reference for the dynamical design of corresponding structures in practical engineering.

Key words

functionally graded material / cylindrical shells / spectro-geometric method (SGM) / arbitrary boundary conditions / random vibration / power spectral density (PSD)

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

DU Zhao, ZUO Peng, SHI Xianjie. Vibration Modelling and Response Characteristics Analysis of Functionally Graded Cylindrical Shells under Stationary Random Excitations[J]. Equipment Environmental Engineering. 2026, 23(2): 114-122 https://doi.org/10.7643/ issn.1672-9242.2026.02.013

References

[1] THANG P T, KIM C, KIM J.Free Vibration Analysis of Bi-Directional Functionally Graded Cylindrical Shells with Varying Thickness[J]. Aerospace Science and Technology, 2023, 137: 108271.
[2] 杨萌, 李戎, 梁斌. 基于Flügge理论的功能梯度圆柱壳自由振动响应均匀化转换计算方法[J]. 振动与冲击, 2020, 39(24): 63-68.
YANG M, LI R, LIANG B.A Homogenization Transformation Method for Free Vibration Response of Functionally Graded Cylindrical Shells Based on the Flügge Theory[J]. Journal of Vibration and Shock, 2020, 39(24): 63-68.
[3] 肖笛, 王忠民. 基于辛方法的功能梯度圆柱壳振动特性分析[J]. 应用力学学报, 2019, 36(3): 704-710.
XIAO D, WANG Z M.Analysis of Vibration Characteristics of Functionally Graded Cylindrical Shells Based on Symplectic Method[J]. Chinese Journal of Applied Mechanics, 2019, 36(3): 704-710.
[4] 李文达, 杜敬涛, 杨铁军, 等. 基于改进傅里叶级数方法的旋转功能梯度圆柱壳振动特性分析[J]. 哈尔滨工程大学学报, 2016, 37(3): 388-393.
LI W D, DU J T, YANG T J, et al.Vibration Characteristics Analysis of the Rotating Functionally Graded Cylindrical Shell Structure Using an Improved Fourier Series Method[J]. Journal of Harbin Engineering University, 2016, 37(3): 388-393.
[5] SU Z, JIN G Y, YE T G.Three-Dimensional Vibration Analysis of Thick Functionally Graded Conical, Cylindrical Shell and Annular Plate Structures with Arbitrary Elastic Restraints[J]. Composite Structures, 2014, 118: 432-447.
[6] LI H C, PANG F Z, CHEN H L, et al.Vibration Analysis of Functionally Graded Porous Cylindrical Shell with Arbitrary Boundary Restraints by Using a Semi Analytical Method[J]. Composites Part B: Engineering, 2019, 164: 249-264.
[7] 唐冲, 王宇, 李学辉, 等. 任意边界条件下功能梯度阶梯圆柱壳的振动特性研究[J]. 固体力学学报, 2024, 45(4): 520-532.
TANG C, WANG Y, LI X H, et al.Research on Vibration Characteristics of Functionally Graded Stepped Cylindrical Shells with Arbitrary Boundary Conditions[J]. Chinese Journal of Solid Mechanics, 2024, 45(4): 520-532.
[8] TORABI J, ANSARI R.A Higher-Order Isoparametric Superelement for Free Vibration Analysis of Functionally Graded Shells of Revolution[J]. Thin-Walled Structures, 2018, 133: 169-179.
[9] TRAN M T, NGUYEN V L, PHAM S D, et al.Free Vibration of Stiffened Functionally Graded Circular Cylindrical Shell Resting on Winkler-Pasternak Foundation with Different Boundary Conditions under Thermal Environment[J]. Acta Mechanica, 2020, 231(6): 2545-2564.
[10] TORNABENE F.Free Vibration Analysis of Functionally Graded Conical, Cylindrical Shell and Annular Plate Structures with a Four-Parameter Power-Law Distribution[J]. Computer Methods in Applied Mechanics and Engineering, 2009, 198(37/38/39/40): 2911-2935.
[11] 刘超, 刘文光, 吕志鹏. 内环向加筋对功能梯度圆柱壳模态频率的影响[J]. 振动与冲击, 2021, 40(24): 255-262.
LIU C, LIU W G, LYU Z P.Effects of Inner Ring-Stiffener on Modal Frequencies of a Functionally Graded Cylindrical Shell[J]. Journal of Vibration and Shock, 2021, 40(24): 255-262.
[12] 胡大伟, 张志浩, 杨文龙, 等. 功能梯度圆柱夹层壳结构振动特性分析[J]. 舰船科学技术, 2022, 44(24): 11-15.
HU D W, ZHANG Z H, YANG W L, et al.Vibration Characteristics of Functionally Graded Cylindrical Sandwich Shells[J]. Ship Science and Technology, 2022, 44(24): 11-15.
[13] TORNABENE F, VIOLA E, INMAN D J.2-D Differential Quadrature Solution for Vibration Analysis of Functionally Graded Conical, Cylindrical Shell and Annular Plate Structures[J]. Journal of Sound and Vibration, 2009, 328(3): 259-290.
[14] XUE Y Q, JIN G Y, ZHANG C Y, et al.Free Vibration Analysis of Functionally Graded Porous Cylindrical Panels and Shells with Porosity Distributions along the Thickness and Length Directions[J]. Thin-Walled Structures, 2023, 184: 110448.
[15] CHEN Z X, WANG A L, QIN B, et al.Investigation on Vibration of the Functionally Graded Material-Stepped Cylindrical Shell Coupled with Annular Plate in Thermal Environment[J]. Journal of Low Frequency Noise, Vibration and Active Control, 2022, 41(1): 85-111.
[16] 高先松, 钟锐, 王青山, 等. 压电智能功能梯度材料圆柱壳自由振动的谱-切比雪夫解法[J]. 哈尔滨工程大学学报, 2025, 46(4): 787-796.
GAO X S, ZHONG R, WANG Q S, et al.Spectral- Tchebychev Method for Free Vibration Analysis of the Cylindrical Shell of Smart Piezoelectric Functionally Gradient Materials[J]. Journal of Harbin Engineering University, 2025, 46(4): 787-796.
[17] XU J W, GAO C, LI H C, et al.Jacobi-Ritz Method for Dynamic Analysis of Functionally Graded Cylindrical Shell with General Boundary Conditions Based on FSDT[J]. Computers & Structures, 2024, 305: 107552.
[18] CHEN G H, HUO H, ZHAN S X, et al.Analytical Stochastic Responses of Thin Cylindrical Shells under Various Stationary Excitations[J]. International Journal of Mechanical Sciences, 2021, 190: 106048.
[19] HUO H, ZHOU Z, CHEN G H, et al.Exact Benchmark Solutions of Random Vibration Responses for Thin- Walled Orthotropic Cylindrical Shells[J]. International Journal of Mechanical Sciences, 2021, 207: 106644.
[20] LI Y Y, ZHANG Y H, KENNEDY D.Random Vibration Analysis of Axially Compressed Cylindrical Shells under Turbulent Boundary Layer in a Symplectic System[J]. Journal of Sound and Vibration, 2017, 406: 161-180.
[21] NI B, XI L F.Stochastic Vibration Responses of Functionally Graded Three-Stage Conical-Cylindrical Combined Shell Structure Subjected to Various Stationary Stochastic Excitations[J]. International Journal of Structural Stability and Dynamics, 2025, 25(20): 2550211.
[22] LI Z, WANG Q S, YANG Q, et al.Stochastic Vibration Behaviors of Functionally Graded Graphene Platelets Reinforced Composite Joined Conical-Cylindrical-Conical Shell with Variable Taper under Moving Random Loads[J]. Composite Structures, 2025, 358: 118970.
[23] 石先杰. 复杂边界条件下旋转结构统一动力学模型的构建与研究[D]. 哈尔滨: 哈尔滨工程大学, 2014.
SHI X J.Construction and Research on Unified Dynamic Model of Rotating Structure under Complex Boundary Conditions[D]. Harbin: Harbin Engineering University, 2014.
[24] 左朋. 热环境下纤维增强飞行器舱体结构动力学建模与振动特性研究[D]. 合肥: 中国科学技术大学, 2023.
ZUO P.Research on Dynamic Modeling and Vibration Characteristics of Fiber-Reinforced Air Vehicle Cabin Structure in Thermal Environment[D]. Hefei: University of Science and Technology of China, 2023.
[25] LIN J H, ZHAO Y, ZHANG Y H.Accurate and Highly Efficient Algorithms for Structural Stationary/Non-Stationary Random Responses[J]. Computer Methods in Applied Mechanics and Engineering, 2001, 191(1/2): 103-111.
[26] PRAKASH T, GANAPATHI M.Supersonic Flutter Characteristics of Functionally Graded Flat Panels Including Thermal Effects[J]. Composite Structures, 2006, 72(1): 10-18.
[27] SHI X J, ZUO P, ZHONG R, et al.Vibration Analysis of Combined Functionally Graded Cylindrical-Conical Shells Coupled with Annular Plates in Thermal Environment[J]. Composite Structures, 2022, 294: 115738.
[28] WIJKER J.Random Vibrations in Spacecraft Structures Design[M]. Dordrecht: Springer Netherlands, 2009.

Funding

National Natural Science Foundation of China (52375136); Youth Elite Scientists Sponsorship Program of Norinco Group Testing and Research Institute (QTKT-4-19)