Applied Mathematics and Mechanics >
Stiffness and natural vibration of a rotating sandwich metal porous cantilever pre-twisted plate reinforced by graphene
Received date: 2025-07-10
Revised date: 2025-10-21
Online published: 2025-12-30
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 12272056 and 11832002)
Copyright
With the continuous increase in performance requirements for power systems in the aerospace and low-altitude economy sectors, designing lightweight and high-strength blade structures with excellent dynamic characteristics has become critical. This paper puts forward a dynamic model for a rotating functionally graded graphene-reinforced (FG-GPR) sandwich metal porous cantilever pre-twisted plate (PTP), aiming to analyze its natural vibration characteristics. To this end, the mixture principle and the revised Halpin-Tsai model are used to determine the parameters of graphene and porosity distributions in the core layer. With the classical plate theory, the Rayleigh-Ritz method, and the polynomials, the dynamic equations are derived to solve for the free vibration mode shapes and frequencies of the rotating FG-GPR sandwich metal porous cantilever PTP. The comparison of natural frequencies and mode shapes with available literature results confirms the precision of the theoretical formulation and numerical computations. The bending stiffnesses are analyzed. Finally, the effects of different graphene/pore distributions, length-to-thickness/width ratios, layer thickness ratios, twist angles, and rotational speeds on the natural frequencies of the system are systematically investigated.
Chengmin NIE , Fu GUO , Yuxin HAO , Xiaojun GU . Stiffness and natural vibration of a rotating sandwich metal porous cantilever pre-twisted plate reinforced by graphene[J]. Applied Mathematics and Mechanics, 2026 , 47(1) : 135 -152 . DOI: 10.1007/s10483-026-3341-8
| [1] | CARRERA, E., FILIPPI, M., and ZAPPINO, E. Free vibration analysis of rotating composite blades via Carrera unified formulation. Composite Structures, 106, 317–325 (2013) |
| [2] | RAFIEE, M., NITZSCHE, F., and LABROSSE, M. Dynamics, vibration and control of rotating composite beams and blades: a critical review. Thin-Walled Structures, 119, 795–819 (2017) |
| [3] | ROY, P. A. and MEGUID, S. A. Analytical modeling of the coupled nonlinear free vibration response of a rotating blade in a gas turbine engine. Acta Mechanica, 229, 3355–3373 (2018) |
| [4] | SARAVIA, C. M., MACHADO, S. P., and CORTíNEZ, V. H. Free vibration and dynamic stability of rotating thin-walled composite beams. European Journal of Mechanics-A/Solids, 30(3), 432–441 (2011) |
| [5] | RAMESH, M. N. V. and RAO, N. M. Free vibration analysis of pre-twisted rotating FGM beams. International Journal of Mechanics and Materials in Design, 9, 367–383 (2013) |
| [6] | FAZELZADEH, S. A., MALEKZADEH, P., ZAHEDINEJAD, P., and HOSSEINI, M. Vibration analysis of functionally graded thin-walled rotating blades under high temperature supersonic flow using the differential quadrature method. Journal of Sound and Vibration, 306(1-2), 333–348 (2007) |
| [7] | LIBRESCU, L., OH, S. Y., and SONG, O. Spinning thin-walled beams made of functionally graded materials: modeling, vibration and instability. European Journal of Mechanics-A/Solids, 23(3), 499–515 (2004) |
| [8] | OH, S. Y., SONG, O., and LIBRESCU, L. Effects of pretwist and presetting on coupled bending vibrations of rotating thin-walled composite beams. International Journal of Solids and Structures, 40(5), 1203–1224 (2003) |
| [9] | YANG, S. M. and TSAO, S. M. Dynamics of a pretwisted blade under nonconstant rotating speed. Computers & Structures, 62(4), 643–651 (1997) |
| [10] | GULYAEV, V. I. and KHUDOLII, S. N. Vibrations of curved and twisted blades during complex rotation. International Applied Mechanics, 41, 449–454 (2005) |
| [11] | CHANDIRAMANI, N. K., SHETE, C. D., and LIBRESCU, L. I. Vibration of higher-order-shearable pretwisted rotating composite blades. International Journal of Mechanical Sciences, 45(12), 2017–2041 (2003) |
| [12] | SINHA, S. K. and TURNER, K. E. Natural frequencies of a pre-twisted blade in a centrifugal force field. Journal of Sound and Vibration, 330(11), 2655–2681 (2011) |
| [13] | GUO, X., ZENG, J., MA, H., ZHAO, C., YU, X., and WEN, B. A dynamic model for simulating rubbing between blade and flexible casing. Journal of Sound and Vibration, 466, 115036 (2020) |
| [14] | HU, X. X., SAKIYAMA, T., and ITAKURA, K. A new numerical procedure for free vibrations of pretwisted plates. Archive of Applied Mechanics, 72, 330–341 (2002) |
| [15] | LEISSA, A. W., LEE, J. K., and WANG, A. J. Vibrations of twisted rotating blades. Journal of Vibration and Acoustics, 106(2), 251–257 (1984) |
| [16] | LIU, L. T., HAO, Y. X., ZHANG, W., and CHEN, J. Free vibration analysis of rotating pretwisted functionally graded sandwich blades. International Journal of Aerospace Engineering, 2018, 2727452 (2018) |
| [17] | CAO, D., LIU, B., YAO, M., and ZHANG, W. Free vibration analysis of a pre-twisted sandwich blade with thermal barrier coatings layers. Science China Technological Sciences, 60, 1747–1761 (2017) |
| [18] | GORMAN, D. J. Accurate free vibration analysis of the orthotropic cantilever plate. Journal of Sound and Vibration, 181(4), 605–618 (1995) |
| [19] | KUMARI, E. Free vibration analysis of rotating laminated composite plate type blades with variable thickness. Materials Today: Proceedings, 43, 1762–1773 (2021) |
| [20] | GU, X. J., ZHANG, W., and ZHANG, Y. F. A novel dynamic model on nonlinear vibrations of functionally graded graphene platelet reinforced rotating pretwisted composite blade considering subsonic airflow excitation and blade-casing rubbing. Composite Structures, 315, 116936 (2023) |
| [21] | ZHANG, W., GU, X. J., and ZHANG, Y. F. New modeling on vibrations and bifurcations of FGGP reinforced pretwisted composite rotating blade under axial aerodynamic force: theoretical and numerical researches. Thin-Walled Structures, 184, 110523 (2023) |
| [22] | GU, X. J., ZHANG, Y. F., ZHANG, W, BI, Q. S., and LU, S. F. Investigation on the 1:2:3 internal resonance of high dimensional nonlinear dynamic system for FGGP reinforced rotating pre-twisted blade under the aerodynamic forces. Communications in Nonlinear Science and Numerical Simulation, 130, 107736 (2024) |
| [23] | LI, C. and CHENG, H. Free vibration analysis of a rotating varying-thickness-twisted blade with arbitrary boundary conditions. Journal of Sound and Vibration, 492, 115791 (2021) |
| [24] | HU, X. X., SAKIYAMA, T., MATSUDA, H., and MORITA, C. Fundamental vibration of rotating cantilever blades with pre-twist. Journal of Sound and Vibration, 271(1-2), 47–66 (2004) |
| [25] | ZHANG, W., NIU, Y., and BEHDINAN, K. Vibration characteristics of rotating pretwisted composite tapered blade with graphene coating layers. Aerospace Science and Technology, 98, 105644 (2020) |
| [26] | CHEN, Y., JIN, G., YE, T., and LEE, H. P. Three-dimensional vibration analysis of rotating pre-twisted cylindrical isotropic and functionally graded shell panels. Journal of Sound and Vibration, 517, 116581 (2022) |
| [27] | KEE, Y. J. and KIM, J. H. Vibration characteristics of initially twisted rotating shell type composite blades. Composite Structures, 64(2), 151–159 (2004) |
| [28] | ZHONG, S., JIN, G., and YE, T. Isogeometric vibration and material optimization of rotating in-plane functionally graded thin-shell blades with variable thickness. Thin-Walled Structures, 185, 110593 (2023) |
| [29] | GUO, H., OUYANG, X., ?UR, K. K., and WU, X. Meshless numerical approach to flutter analysis of rotating pre-twisted nanocomposite blades subjected to supersonic airflow. Engineering Analysis with Boundary Elements, 132, 1–11 (2021) |
| [30] | ZHANG, L. W., PAN, Z. Z., and CHEN, X. Vibration characteristics of matrix cracked pretwisted hybrid composite blades containing CNTRC layers. Journal of Sound and Vibration, 473, 115242 (2020) |
| [31] | YAO, M., WANG, S., NIU, Y., WU, Q., and WANG, C. Vibration characteristics of pre-twisted rotating Ti-SiC composite airfoil blade. Applied Mathematical Modelling, 128, 392–409 (2024) |
| [32] | SUN, K. C., HAO, Y. X., ZHANG, W., YANG, S. W., and CAO, Y. T. Effect of graphene reinforcement on free vibration and material properties of the FG-GPLRC porous cantilever torsional plate. International Journal of Structural Stability and Dynamics, 24(4), 2450041 (2024) |
| [33] | MENG, Y., MAO, X. Y., DING, H., and CHEN, L. Q. Nonlinear vibrations of a composite circular plate with a rigid body. Applied Mathematics and Mechanics (English Edition), 44(6), 857–876 (2023) https://doi.org/10.1007/s10483-023-3005-8 |
| [34] | HAO, Y. X., SUN, L., ZHANG, W., and LI, H. Active traveling wave vibration control of elastic supported conical shells with smart micro fiber composites based on the differential quadrature method. Applied Mathematics and Mechanics (English Edition), 46(2), 305–322 (2025) https://doi.org/10.1007/s10483-025-3216-7 |
| [35] | NGUYEN, Q. H., NGUYEN, L. B., NGUYEN, H. B., and NGUYEN-XUAN, H. A three-variable high order shear deformation theory for isogeometric free vibration, buckling and instability analysis of FG porous plates reinforced by graphene platelets. Composite Structures, 245, 112321 (2020) |
| [36] | DONG, Y. H., LI, Y. H., CHEN, D., and YANG, J. Vibration characteristics of functionally graded graphene reinforced porous nanocomposite cylindrical shells with spinning motion. Composites Part B: Engineering, 145, 1–13 (2018) |
| [37] | WANG, Y. Q., YE, C., and ZU, J. W. Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets. Aerospace Science and Technology, 85, 359–370 (2019) |
| [38] | AFFDL, J. C. H. and KARDOS, J. L. The Halpin-Tsai equations: a review. Polymer Engineering & Science, 16(5), 344–352 (1976) |
| [39] | RAFIEE, M. A., RAFIEE, J., WANG, Z., SONG, H., YU, Z. Z., and KORATKAR, N. Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano, 3(12), 3884–3890 (2009) |
| [40] | QATU, M. S. and LEISSA, A. W. Vibration studies for laminated composite twisted cantilever plates. International Journal of Mechanical Sciences, 33(11), 927–940 (1991) |
/
| 〈 |
|
〉 |
Email Alert
RSS