Trapezoidal plates, such as aircraft vertical tails, are highly susceptible to structural vibrations under complex aerodynamic environments. Variable stiffness composites are often employed to improve structural performance, but the coupling effects between curvilinear fibers and boundary conditions vary significantly. This paper investigates the coupling mechanism between variable stiffness and boundary conditions in trapezoidal sandwich plates. A structural evaluation model is established based on a higher-order shear theory combined with a discrete numerical approach, balancing high computational accuracy and efficiency for irregular domains. Quantitative analysis indicates that the dynamic effectiveness of variable stiffness designs is strictly dependent on boundary conditions. Under simply supported boundaries, curvilinear fibers fully stimulate bend-twist coupling, yielding a 6.71% increment in the fundamental frequency. Conversely, under cantilevered boundaries, the strong root fixation alters this coupling effect, consequently causing a severe frequency reduction of 16.05%. This study elucidates the physical competition among geometric configuration, variable stiffness paths, and boundary conditions, thereby suggesting application adjustments for variable stiffness composites under varying boundaries. These findings provide a reference for the dynamic design of trapezoidal sandwich plates in engineering applications.
AbualnourMYouzeraHChikhA, et al. (2026) On the dynamic behavior of cylindrical shell with graphene nanoplatelets (GNPs) faces and hexagonal honeycomb core layer. Mechanics Research Communications153: 104637. https://doi.org/10.1016/j.mechrescom.2026.104637
2.
BellmanRCastiJ (1971) Differential quadrature and long-term integration. Journal of Mathematical Analysis and Applications34(2): 235–238. https://doi.org/10.1016/0022-247x(71)90110-7
3.
BousmahaKBelaliaSAChorfiSM, et al. (2026) On the dynamic behavior of plates made of porous advanced materials reinforced with carbon nanotubes using a p-version of finite element method. Mechanics Based Design of Structures and Machines54(1): 2534679. https://doi.org/10.1080/15397734.2025.2534679
4.
BurtonWSNoorAK (1995) Assessment of computational models for sandwich panels and shells. Computer Methods in Applied Mechanics and Engineering124(3): 125–151. https://doi.org/10.1016/0045-7825(94)00750-h
5.
CarreraEBrischettoS (2009) A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates. Applied Mechanics Reviews62(1): 1–17. https://doi.org/10.1115/1.3013824
6.
ChiriacRVrabieM (2016) The first order shear deformation theory for sandwich plates. Intersections/Intersecţii13(1): 37–47.
7.
CivalekÖ (2008) Free vibration analysis of symmetrically laminated composite plates with first-order shear deformation theory (FSDT) by discrete singular convolution method. Finite Elements in Analysis and Design44(12–13): 725–731. https://doi.org/10.1016/j.finel.2008.04.001
8.
CivalekOJalaeiMH (2020) Shear buckling analysis of functionally graded (FG) carbon nanotube reinforced skew plates with different boundary conditions. Aerospace Science and Technology99: 105753. https://doi.org/10.1016/j.ast.2020.105753
9.
DhotrePKSrinivasaCV (2021) On free vibration of laminated skew sandwich plates: a finite element analysis. Nonlinear Engineering10(1): 66–76. https://doi.org/10.1515/nleng-2021-0006
10.
FarsadiTAsadiDKurtaranH (2021) Fundamental frequency optimization of variable stiffness composite skew plates. Acta Mechanica232(2): 555–573, Springer Vienna. https://doi.org/10.1007/s00707-020-02871-9
11.
FarsaniSRRamianAJafari-TalookolaeiRA, et al. (2021) Free vibration analysis of rectangular sandwich plates with compressible core and various boundary conditions. Journal of Sandwich Structures and Materials23(8): 4077–4106. https://doi.org/10.1177/1099636220979276
12.
FuMYinJ (1999) Equivalent elastic parameters of the honeycomb core. Lixue Xuebao31(1): 113–118, (in Chinese).
13.
GhavidelNAlibeiglooA (2024) Free vibration analysis of cylindrical sandwich panel with electro-rheological core and FG-GPLRC facing sheets based on first order shear deformation theory referred by qatu. Journal of Vibration and Control30(3–4): 545–575. https://doi.org/10.1177/10775463221148535
14.
GibsonLJAshbyMFSchajerGS, et al. (1982) The mechanics of two dimensional cellular materials. Proceedings of the Royal Society of London, Series A382: 25–42. https://doi.org/10.1098/rspa.1982.0087
15.
GuptaAPradyumnaS (2022) Geometrically nonlinear dynamic analysis of variable stiffness composite laminated and sandwich shell panels. Thin-Walled Structures173: 109021. https://doi.org/10.1016/j.tws.2022.109021
16.
GürdalZOlmedoR (1993) In-plane response of laminates with spatially varying fiber orientations: variable stiffness concept. AIAA Journal31(4): 751–758. https://doi.org/10.2514/3.11613
17.
HachemiM (2020) Vibration analysis of variable stiffness laminated composite sandwich plates. Mechanics of Advanced Materials and Structures27(19): 1687–1700, Taylor & Francis. https://doi.org/10.1080/15376494.2018.1524951
18.
HachemiM (2022) Layer-wise solutions for variable stiffness composite laminated sandwich plate using curvilinear fibers. Mechanics of Advanced Materials and Structures29(26): 5460–5477, Taylor & Francis. https://doi.org/10.1080/15376494.2021.1956028
19.
HachemiMGuenanouACheboutR, et al. (2023) Mechanical behaviors of variable stiffness composite laminated sandwich plates using layer-wise model. Journal of the Brazilian Society of Mechanical Sciences and Engineering45(2): 1–21, Springer Berlin Heidelberg. https://doi.org/10.1007/s40430-022-03949-2
HoumatA (2020) Three-dimensional solutions for free vibration of variable stiffness laminated sandwich plates with curvilinear fibers. Journal of Sandwich Structures and Materials22(3): 896–925. https://doi.org/10.1177/1099636218778731
22.
HyerMWCharetteRF (1991) Use of curvilinear fiber format in composite structure design. AIAA Journal29(6): 1011–1015. https://doi.org/10.2514/3.10697
23.
HyerMWLeeHH (1991) The use of curvilinear fiber format to improve buckling resistance of composite plates with central circular holes. Composite Structures18(3): 239–261. https://doi.org/10.1016/0263-8223(91)90035-w
24.
LiHZhangWZhangYF (2024) Vibration analysis of graphene-reinforced porous aluminum-based variable-walled thickness sandwich joined conical-conical panel with elastic boundary conditions using differential quadrature method. Thin-Walled Structures201: 112016. https://doi.org/10.1016/j.tws.2024.112016
25.
LiewKMHuangYQReddyJN (2003) Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method. Computer Methods in Applied Mechanics and Engineering192: 2203–2222. https://doi.org/10.1016/s0045-7825(03)00238-x
26.
LiuTZhengHYZhangW, et al. (2024) Nonlinear forced vibrations of functionally graded three-phase composite cylindrical shell subjected to aerodynamic forces, external excitations and hygrothermal environment. Thin-Walled Structures195: 111511. https://doi.org/10.1016/j.tws.2023.111511
27.
MalikMBertCW (1995) Differential quadrature analysis of free vibration of symmetric cross-ply laminates with shear deformation and rotatory inertia. Shock and Vibration2(4): 321–338. https://doi.org/10.1155/1995/703928
28.
MohamedSMYYouzeraHTounsiA, et al. (2025) Free vibrations analysis of a functionally graded honeycomb (FGH) sandwich cylindrical shell using a quasi-3D theory. International Journal of Structural Stability and Dynamics 2750159. Available at: https://doi.org/10.1142/S0219455427501598.
29.
MohamedSMYYouzeraHTounsiA, et al. (2027) Free vibration and flexural loss factors of viscoelastic laminated composite truncated conical shells using harmonic differential quadrature method. International Journal of Structural Stability and Dynamics. 2750223. Available at: https://doi.org/10.1142/S0219455427502233
30.
MohantyAParidaSPDashRR (2026) Free and forced vibration response of sandwiched composite plate with functionally graded carbon and glass fiber – reinforced polymeric face sheet. Journal of Vibration and Control1–21. Available at: https://doi.org/10.1177/10775463261420027
31.
NoorAKBurtonWSBertCW (1996) Computational models for sandwich panels and shells. Applied Mechanics Reviews49(3): 155–199. https://doi.org/10.1115/1.3101923
32.
PandeySPradyumnaS (2015) A new C0 higher-order layerwise finite element formulation for the analysis of laminated and sandwich plates. Composite Structures131: 1–16. https://doi.org/10.1016/j.compstruct.2015.04.034
33.
RahmaniSSeidiHKakavandF, et al. (2024) Free vibration analysis of a cantilever trapezoidal sandwich plate with an auxetic reentrant honeycomb core and laminated nanocomposite polymer/CNT/fiber face sheets. Mechanics Based Design of Structures and Machines52(9): 7180–7210. https://doi.org/10.1080/15397734.2023.2288663
34.
RebaiaBTidjaniMLakhemissiT, et al. (2026) Investigation study of isotropic porous FG spherical shells using a refined higher-order shear deformation theory. Geomechanics and Engineering44(6): 775–795.
35.
ReddyJN (2004) Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. 2nd edition. CRC Press.
36.
RibeiroPAkhavanHTeterA, et al. (2014) A review on the mechanical behaviour of curvilinear fibre composite laminated panels. Journal of Composite Materials48(22): 2761–2777. https://doi.org/10.1177/0021998313502066
37.
SaidiARAbdollahiMBahaadiniR (2023) Flutter analysis of honeycomb sandwich trapezoidal wings reinforced with GPLs. Thin-Walled Structures183: 110353. https://doi.org/10.1016/j.tws.2022.110353
38.
SerdounSMNHamza CherifSM (2016) Free vibration analysis of composite and sandwich plates by alternative hierarchical finite element method based on Reddy’s C1 HSDT. Journal of Sandwich Structures and Materials18(4): 501–528. https://doi.org/10.1177/1099636215603033
39.
ShuC (2000) Differential Quadrature and its Application in Engineering. Springer-Verlag.
40.
TorabiKAfshariHAboutalebiFH (2019) Vibration and flutter analyses of cantilever trapezoidal honeycomb sandwich plates. Journal of Sandwich Structures and Materials21(8): 2887–2920. https://doi.org/10.1177/1099636217728746
41.
TornabeneFFantuzziNBacciocchiM (2019) Foam core composite sandwich plates and shells with variable stiffness: effect of the curvilinear fiber path on the modal response. Journal of Sandwich Structures and Materials21(1): 320–365. https://doi.org/10.1177/1099636217693623
42.
VinsonJR (1999) The Behavior of Sandwich Structures of Isotropic and Composite Materials. Technomic Publishing Company.
WangS (1997) Free vibration analysis of skew fibre-reinforced composite laminates based on first-order shear deformation plate theory. Computers and Structures63(3): 525–538. https://doi.org/10.1016/s0045-7949(96)00357-4
45.
WangCMAngKKYangL, et al. (2000) Free vibration of skew sandwich plates with laminated facings. Journal of Sound and Vibration235(2): 317–340. https://doi.org/10.1006/jsvi.2000.2918
46.
WangQWangZChenT (2025) Coupled out-of-plane bending and torsion vibration characteristics of variable stiffness circular curved beam under elastic constraints. Journal of Vibration and Control32(11-12): 1–12. https://doi.org/10.1177/10775463251332724
47.
YaoGCaoZWZhuLS (2023) Nonlinear vibration analysis of a pyramid lattice sandwich plate in subsonic airflow. Mechanics Based Design of Structures and Machines51(9): 4912–4928. https://doi.org/10.1080/15397734.2021.1982393
48.
YouzeraHMeftahSABousahlaAA, et al. (2026) Dynamic analysis of porous FGM viscoelastic sandwich beams using differential transform method (DTM). Journal of Vibration and Control, Epub ahead of print 2026. https://doi.org/10.1177/10775463261423108
49.
ZhangLWXiaoLN (2017) Mechanical behavior of laminated CNT-reinforced composite skew plates subjected to dynamic loading. Composites Part B: Engineering122: 219–230. https://doi.org/10.1016/j.compositesb.2017.03.041
50.
ZhengYBuGGuoX, et al. (2026a) Resonance responses and nonlinear dynamics of three-phase composite trapezoidal plates for stern rudders of underwater vehicles. Ocean Engineering352: 124556. https://doi.org/10.1016/j.oceaneng.2026.124556
51.
ZhengYDuanJLiuT, et al. (2026b) Free vibrations, resonant responses, and nonlinear dynamics of a supersonic axially moving functionally graded three-phase composite truncated conical shell. Communications in Nonlinear Science and Numerical Simulation157: 109655. https://doi.org/10.1016/j.cnsns.2026.109655
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
