The vibration problems of composite sandwich plates (CSPs) are frequently observe in engineering applications. Based on this observation, this paper investigates the dynamic response and chaotic phenomena of CSPs to elucidate the dynamic effects of the complex edge and multiple parameters on CSPs. In this paper, a quadrilateral CSP with a variable edge is proposed, based on the Winkler–Pasternak elastic foundation. One edge of the CSP is defined as a variable edge according to classical curve function forms. The CSP consists of an anti-tetrachiral honeycomb core with negative Poisson’s ratio (NPR) and two face sheets. Based on the classical shell theory and von Karman nonlinear assumption, the motion differential equation of proposed system under external periodic excitation vertical to the CSP and the boundary condition of four-sided simply supported is established, and the dynamic characteristics of the system are calculated theoretically by using the Galerkin’s method. The effects of geometric parameters on the nonlinear dynamic response of the system are discussed. To validate the reliability and accuracy of theoretical results, corresponding numerical calculation via finite element method is conducted for comparison. The results show numerical calculation showed good agreement with theoretical results. The elastic foundation significantly enhances the load-carrying capacity. Compared to the case without an elastic foundation, the vibration amplitude drops to 20%, while the natural frequencies increase by 119% to 126%. With excitation load increasing, anti-tetrachiral NPR core exhibits better vibration absorption capacity than traditional honeycomb core, and mechanical properties of core are improved by increasing cell number or thickness. Through analysis of the Lyapunov exponent, it is found that the CSP becomes unstable when the excitation frequency approaches the natural frequency or the excitation load exceeds the critical load. Among edge-defined power, arc and absolute exponential function, the CSP with arc function shows the best load-bearing capacity.
AldersonAAldersonKLAttardD, et al. (2010) Elastic constants of 3-4-and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading. Composites Science and Technology70(7): 1042–1048.
2.
AraniHKShariyatM (2023) Nonlinear 2D-DQ volume-preservative global–local dynamic analysis of composite sandwich plates with soft hyperelastic cores and viscoelastic Winkler-Pasternak foundations. Structures55: 727–746.
3.
ArgatovIIGuinovart-DíazRSabinaFJ (2012) On local indentation and impact compliance of isotropic auxetic materials from the continuum mechanics viewpoint. International Journal of Engineering Science54: 42–57.
4.
BelabedZTounsiABousahlaAA, et al. (2024) Accurate free and forced vibration behavior prediction of functionally graded sandwich beams with variable cross-section: a finite element assessment. Mechanics Based Design of Structures and Machines52(11): 9144–9177.
5.
BentrarHChorfiSMBelaliaSA, et al. (2023) Effect of porosity distribution on free vibration of functionally graded sandwich plate using the P-version of the finite element method. Structural Engineering and Mechanics, An Int’l Journal88(6): 551–567.
6.
ChitourMBouhadraABouradaF, et al. (2024) Stability analysis of imperfect FG sandwich plates containing metallic foam cores under various boundary conditions. Structures61: 106021.
7.
DatNDQuanTQDucND (2022) Vibration analysis of auxetic laminated plate with magneto-electro-elastic face sheets subjected to blast loading. Composite Structures280: 114925.
8.
DucNDSeung-EockKTuanND, et al. (2017) New approach to study nonlinear dynamic response and vibration of sandwich composite cylindrical panels with auxetic honeycomb core layer. Aerospace Science and Technology70: 396–404.
9.
DzungNMTanNCHaNH, et al. (2024) Effects of edge-crack orientation and depth on non-linear dynamics of laminated nanocomposite single-variable-edge plates. Engineering Structures304: 117553.
10.
GrimaJNGattRFarrugiaPS (2008) On the properties of auxetic meta-tetrachiral structures. Physica Status Solidi (B)245(3): 511–520.
11.
HaNHLongNTNinhDG, et al. (2022) Research on vibrational characteristics of nanocomposite double-variable-edge plates immersed in liquid under the effect of explosive loads. Ocean Engineering262: 112093.
12.
HaNHTanNCNinhDG, et al. (2023) Dynamical and chaotic analyses of single-variable-edge cylindrical panels made of sandwich auxetic honeycomb core layer in thermal environment. Thin-Walled Structures183: 110300.
13.
HaNHTanNCDzungNM, et al. (2024) A new study for dynamical characteristics of double-variable-edge and variable thickness plates made of open-cell porous metal. Aerospace Science and Technology145: 108830.
14.
HajmohammadMHKolahchiRZareiMS, et al. (2019) Dynamic response of auxetic honeycomb plates integrated with agglomerated CNT-reinforced face sheets subjected to blast load based on visco-sinusoidal theory. International Journal of Mechanical Sciences153: 391–401.
15.
HuLLLuoZRZhangZY, et al. (2019) Mechanical property of re-entrant anti-trichiral honeycombs under large deformation. Composites Part B: Engineering163: 107–120.
16.
JavidFLiuJShimJ, et al. (2016) Mechanics of instability-induced pattern transformations in elastomeric porous cylinders. Journal of the Mechanics and Physics of Solids96: 1–17.
17.
JinXWangZNingJ, et al. (2016) Dynamic response of sandwich structures with graded auxetic honeycomb cores under blast loading. Composites Part B: Engineering106: 206–217.
18.
JinSKorkolisYPLiY (2019) Shear resistance of an auxetic chiral mechanical metamaterial. International Journal of Solids and Structures174: 28–37.
19.
KaddariMBalubaidMMahmoudSR, et al. (2024) Influence of porosity distribution on buckling behavior of FG sandwich plates using a quasi-3D refined plate theory. Mechanics Based Design of Structures and Machines53: 3635–3662.
KumarPKucherovLRyvkinM (2020) Fracture toughness of self-similar hierarchical material. International Journal of Solids and Structures203: 210–223.
22.
LafiDEBouhadraAMamenB, et al. (2024) Combined influence of variable distribution models and boundary conditions on the thermodynamic behavior of FG sandwich plates lying on various elastic foundations. Structural Engineering and Mechanics, An Int'l Journal89(2): 103–119.
23.
LakhdarZChorfiSMBelaliaSA, et al. (2024) Free vibration and bending analysis of porous bi-directional FGM sandwich shell using a TSDT p-version finite element method. Acta Mechanica235(6): 3657–3686.
24.
LiYLiWLiD, et al. (2025) Study on shear postbuckling and failure of perforated plates: modeling and experiments. AIAA Journal1–9. doi: 10.2514/1.J064246.
25.
LiuHLiD (2025) Study on the energy absorption effect and impact resistance of a composite sandwich panel with carbon fiber reinforced re-entrant hexagonal honeycomb core with negative Poisson's ratio. European Journal of Mechanics - A: Solids109: 105447.
26.
LvWLiD (2024) A metamaterial with enhanced effective stiffness and negative Poisson's ratio for frictional energy dissipation. European Journal of Mechanics - A: Solids107: 105390.
27.
LvWLiD (2025) A novel compression torsion coupling metamaterial with repeatable energy dissipation characteristics. Smart Materials and Structures34: 035003.
28.
LvWDongLLiD (2023) A novel metamaterial with individually adjustable and sign-switchable Poisson’s ratio. European Journal of Mechanics - A: Solids97: 104851.
29.
MaLChenYLYangJS, et al. (2018) Modal characteristics and damping enhancement of carbon fiber composite auxetic double-arrow corrugated sandwich panels. Composite Structures203: 539–550.
MamandiA (2023) Nonlocal large deflection analysis of a cantilever nanobeam on a nonlinear Winkler-Pasternak elastic foundation and under uniformly distributed lateral load. Journal of Mechanical Science and Technology37(2): 813–824.
32.
MirfatahSMTayebikhoramiSShahmohammadiMA, et al. (2023) Geometrically nonlinear analysis of sandwich panels with auxetic honeycomb core and nanocomposite enriched face-sheets under periodic and impulsive loads. Aerospace Science and Technology135: 108195.
33.
MousanezhadDHaghpanahBGhoshR, et al. (2016) Elastic properties of chiral, anti-chiral, and hierarchical honeycombs: a simple energy-based approach. Theoretical and Applied Mechanics Letters6(2): 81–96.
34.
NguyenNVNguyen-XuanHNguyenTN, et al. (2021) A comprehensive analysis of auxetic honeycomb sandwich plates with graphene nanoplatelets reinforcement. Composite Structures259: 113213.
35.
NinhDGVan VangTHaNH, et al. (2022) Effect of cracks on dynamical responses of double-variable-edge plates made of graphene nanoplatelets-reinforced porous matrix and sur-bonded by piezoelectric layers subjected to thermo-mechanical loads. European Journal of Mechanics - A: Solids96: 104742.
36.
NinhDGLongNTVan VangT, et al. (2023) A new study for aeroplane wing shapes made of boron nitride nanotubes-reinforced aluminium, Part I: review, dynamical analyses and simulation. Composite Structures303: 116239.
37.
PhamHATranHQTranMT, et al. (2022) Free vibration analysis and optimization of doubly-curved stiffened sandwich shells with functionally graded skins and auxetic honeycomb core layer. Thin-Walled Structures179: 109571.
38.
QiCYangSWangD, et al. (2013) Ballistic resistance of honeycomb sandwich panels under in-plane high-velocity impact. TheScientificWorldJOURNAL2013(1): 892781.
39.
QiCRemennikovAPeiLZ, et al. (2017) Impact and close-in blast response of auxetic honeycomb-cored sandwich panels: experimental tests and numerical simulations. Composite Structures180: 161–178.
40.
SobhaniEAvcarM (2022) Natural frequency analysis of imperfect GNPRN conical shell, cylindrical shell, and annular plate structures resting on Winkler-Pasternak Foundations under arbitrary boundary conditions. Engineering Analysis with Boundary Elements144: 145–164.
41.
SuXWZhuDMZhengC, et al. (2019) Mechanical properties of 65Mn chiral structure with three ligaments. Acta Mechanica Sinica35: 88–98.
42.
TounsiAMostefaAHBousahlaAA, et al. (2023a) Thermodynamical bending analysis of P-FG sandwich plates resting on nonlinear visco-Pasternak’s elastic foundations. Steel and Composite Structures49(3): 307–323.
43.
TounsiATahirSIAl-OstaMA, et al. (2023b) An integral quasi-3D computational model for the hygro-thermal wave propagation of imperfect FGM sandwich plates. Computers and Concrete32(1): 61–74.
44.
TounsiABousahlaAATahirSI, et al. (2024) Influences of different boundary conditions and hygro-thermal environment on the free vibration responses of FGM sandwich plates resting on viscoelastic foundation. International Journal of Structural Stability and Dynamics24(11): 2450117.
45.
TranTTPhamQHNguyen-ThoiT, et al. (2020) Dynamic analysis of sandwich auxetic honeycomb plates subjected to moving oscillator load on elastic foundation. Advances in Materials Science and Engineering2020(1): 6309130.
46.
Viet HoangVNHoangHNGia NinhD (2022) Dynamic and chaotic responses of porous nanocomposite nonrectangular plates with single-variable-edge. AIAA Journal60(2): 1116–1151.
47.
WangCLvWLiD (2024) Study on the mechanical properties of the thin-walled double circular tube filled with a novel NPR lattice core based on the concave rotating mechanism. Smart Materials and Structures34(2): 025003.
YangSQiCWangD, et al. (2013) A comparative study of ballistic resistance of sandwich panels with aluminum foam and auxetic honeycomb cores. Advances in Mechanical Engineering5: 589216.
50.
YanzuoLZhenyuLJinshuiY (2022) Vibration behavior and damping performance of carbon fiber composite doublearrow corrugated auxetic structures. Journal of Composite Materials39(08): 4117–4128.
51.
ZhangPSchiavonePQingH (2023) A unified local-nonlocal integral formulation for dynamic stability of FG porous viscoelastic Timoshenko beams resting on nonlocal Winkler-Pasternak foundation. Composite Structures322: 117416.
52.
ZhuXZhangJZhangW, et al. (2019) Vibration frequencies and energies of an auxetic honeycomb sandwich plate. Mechanics of Advanced Materials and Structures26(23): 1951–1957.
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