Abstract
Pre-stresses or axial loadings induced by deformations of adjacent structures, edge constraints or mounting inaccuracies and elastic supporting components attached to one side of the sandwich structures may affect the aerothermoelastic stability, which is an important subject in the design of supersonic aircraft. Therefore, the nonlinear flutter and thermal buckling behavior of composite lattice sandwich beams with translational springs under axial loading in supersonic airflow is investigated in this paper. In the structural modeling, the von Kármán large-deflection theory is applied to establish the stain–displacement relations. The aerodynamic pressure is evaluated by the supersonic piston theory. The differential equations of motion are obtained by Hamilton’s principle and the assumed mode method. The highlight of this study is that a new approach for limit cycle oscillation (LCO) suppression and thermal buckling elimination without changing the stiffness of the lattice sandwich structure is proposed by utilizing the axial loading and translational springs. The structural natural frequencies are obtained and compared with reference results in the literature. The influences of the axial loading and the translational springs on the nonlinear supersonic flutter and thermal buckling properties of the sandwich beams are analyzed. Numerical results indicate that the present method is effective for nonlinear flutter suppression, and the thermal buckling effect can be completely eliminated by adjusting the axial loading of the sandwich beams.
Similar content being viewed by others
References
Liu, T., Deng, Z.C., Lu, T.J.: Analytical modeling and finite element simulation of the plastic collapse of sandwich beams with pin-reinforced foam cores. Int. J. Solids Struct. 45, 5127–5151 (2008)
Zhang, J., Ye, Y., Qin, Q.: Large deflections of multilayer sandwich beams with metal foam cores under transverse loading. Acta Mech. 229(9), 3585–3599 (2018)
Xu, G.D., Wang, Z.H., Zeng, T., Cheng, S., Fang, D.N.: Mechanical response of carbon/epoxy composite sandwich structures with three-dimensional corrugated cores. Compos. Sci. Technol. 156, 296–304 (2018)
Yang, J.S., Ma, L., Chaves-Vargas, M., Huang, T.X., Schröder, K.U., Schmidt, R., Wu, L.Z.: Influence of manufacturing defects on modal properties of composite pyramidal truss-like core sandwich cylindrical panels. Compos. Sci. Technol. 147, 89–99 (2017)
Thamburaj, P., Sun, J.Q.: Effect of material and geometry on the sound and vibration transmission across a sandwich beam. J. Vib. Acoust. 123(2), 205–212 (2001)
Chandra, N., Gopal, K.V.N., Raja, S.: Vibro-acoustic response of sandwich plates with functionally graded core. Acta Mech. 228(8), 2775–2789 (2017)
Yuan, W., Song, H.W., Wang, X., Huang, C.G.: Experimental investigation on thermal buckling behavior of truss-core sandwich panels. AIAA J. 53(4), 948–957 (2014)
Chai, Y., Du, S., Li, F., Zhang, C.: Vibration characteristics of simply supported pyramidal lattice sandwich plates on elastic foundation: Theory and experiments. Thin-Walled Struct. 166, 108116 (2021)
Shiau, L.C., Kuo, S.Y.: Free vibration of thermally buckled composite sandwich plates. J. Vib. Acoust. 128(1), 1–7 (2006)
Bhangale, R.K., Ganesan, N.: Thermoelastic buckling and vibration behavior of a functionally graded sandwich beam with constrained viscoelastic core. J. Sound Vib. 295, 294–316 (2006)
Kiani, Y.: Thermal postbuckling of temperature-dependent sandwich beams with carbon nanotube-reinforced face sheets. J. Therm. Stresses 39(9), 1098–1110 (2016)
Li, C., Shen, H.S., Wang, H.: Thermal post-buckling of sandwich beams with functionally graded negative Poisson’s ratio honeycomb core. Int. J. Mech. Sci. 152, 289–297 (2019)
Iurlaro, L., Ascione, A., Gherlone, M., Mattone, M., Sciuva, M.D.: Free vibration analysis of sandwich beams using the Refined Zigzag Theory: An experimental assessment. Meccanica 50(10), 2525–2535 (2015)
Yao, G., Li, F.M.: Nonlinear primary resonances of lattice sandwich beams with pyramidal truss core and viscoelastic surfaces. Acta Mech. 229(10), 4091–4100 (2018)
Chen, D., Kitipornchai, S., Yang, J.: Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core. Thin-Walled Structures 107, 39–48 (2016)
Alambeigi, K., Mohammadimehr, M., Bamdad, M., Rabczuk, T.: Free and forced vibration analysis of a sandwich beam considering porous core and SMA hybrid composite face layers on Vlasov’s foundation. Acta Mech. 231, 3199–3218 (2020)
Farsadi, T., Asadi, D., Kurtaran, H.: Nonlinear flutter response of a composite plate applying curvilinear fiber paths. Acta Mech. 231(2), 715–731 (2020)
Zappino, E., Carrera, E., Cinefra, M.: Aeroelastic analysis of composite pinched panels using higher-order shell elements. J. Spacecr. Rocket. 52(3), 999–1003 (2015)
Li, F.M., Song, Z.G., Sun, C.C.: Aeroelastic properties of sandwich beam with pyramidal lattice core considering geometric nonlinearity in the supersonic airflow. Acta Mech. Solida Sin. 28(6), 639–646 (2015)
Khorshidi, K., Karimi, M., Amabili, M.: Aeroelastic analysis of rectangular plates coupled to sloshing fluid. Acta Mech. 231, 3183–3198 (2020)
Amabili, M., Pellicano, F.: Multimode approach to nonlinear supersonic flutter of imperfect circular cylindrical shells. J. Appl. Mech. 69(2), 117–129 (2002)
Amabili, M., Pellicano, F.: Nonlinear supersonic flutter of circular cylindrical shells. AIAA J. 39(4), 564–573 (2001)
Mousavi, S.B., Yazdi, A.A.: Flutter of delaminated three-phase nano-composite beam-plates. Mech. Adv. Mater. Struct. 27(7), 561–568 (2020)
Yang, X.D., Yu, T.J., Zhang, W., Qian, Y.J., Yao, M.H.: Damping effect on supersonic panel flutter of composite plate with viscoelastic mid-layer. Compos. Struct. 137, 105–113 (2016)
Chai, Y., Li, F., Song, Z., Zhang, C.: Influence of the boundary relaxation on the flutter and thermal buckling of composite laminated panels. Aerospace Sci. Technol. 104, 106000 (2020)
Asadi, H., Beheshti, A.R.: On the nonlinear dynamic responses of FG-CNTRC beams exposed to aerothermal loads using third-order piston theory. Acta Mech. 229(6), 2413–2430 (2018)
Chai, Y.Y., Li, F.M., Song, Z.G.: Nonlinear flutter suppression and thermal buckling elimination for composite lattice sandwich panels. AIAA J. 57(11), 4863–4872 (2019)
Zhou, K., Huang, X.C., Zhang, Z.G., Hua, H.X.: Aero-thermo-elastic flutter analysis of coupled plate structures in supersonic flow with general boundary conditions. J. Sound Vib. 430, 36–58 (2018)
Zhou, K., Su, J.P., Hua, H.X.: Aero-thermo-elastic flutter analysis of supersonic moderately thick orthotropic plates with general boundary conditions. Int. J. Mech. Sci. 141, 46–57 (2018)
Chai, Y.Y., Song, Z.G., Li, F.M.: Investigations on the influences of elastic foundations on the aerothermoelastic flutter and thermal buckling properties of lattice sandwich panels in supersonic airflow. Acta Astronaut. 140, 176–189 (2017)
Chai, Y.Y., Song, Z.G., Li, F.M.: Investigations on the aerothermoelastic properties of composite laminated cylindrical shells with elastic boundaries in supersonic airflow based on the Rayleigh-Ritz method. Aerosp. Sci. Technol. 82, 534–544 (2018)
Young, T.H., Lee, C.W., Chen, F.Y.: Dynamic stability of skew plates subjected to aerodynamic and random in–plane forces. J. Sound Vib. 250(3), 401–414 (2002)
Epureanu, B.I., Tang, L.S., Paidoussis, M.P.: Coherent structures and their influence on the dynamics of aeroelastic panels. Int. J. Non-Linear Mech. 39(6), 977–991 (2004)
Kariappa, Somashekar B.R., Shah, C.G.: Discrete element approach to flutter of skew panels with in-plane forces under yawed supersonic flow. AIAA J. 8(11), 2017–2022 (1970)
Shiau, L.C., Chen, Y.S.: Effects of in-plane load on flutter of homogeneous laminated beam plates with delamination. J. Vib. Acoust. 123(1), 61–66 (2001)
Asadi, H., Wang, Q.: An investigation on the aeroelastic flutter characteristics of FG-CNTRC beams in the supersonic flow. Compos. B Eng. 116, 486–499 (2017)
Yang, X.D., Zhang, W., Wang, H.B., Yao, M.H.: The nonlinear dynamical analysis of a sandwich plate with in-plane loading in supersonic flow. Int. J. Bifurc. Chaos 26(09), 1650144 (2016)
Asgari, M., Kouchakzadeh, M.A.: Aeroelastic characteristics of magneto-rheological fluid sandwich beams in supersonic airflow. Compos. Struct. 143, 93–102 (2016)
Barzegari, M.M., Dardel, M., Fathi, A., Ghadimi, M.: Aeroelastic characteristics of cantilever wing with embedded shape memory alloys. Acta Astronaut. 79, 189–202 (2012)
Guo, X., Lee, Y.Y., Mei, C.: Supersonic nonlinear panel flutter suppression using shape memory alloys. J. Aircr. 44(4), 1139–1149 (2007)
Zhang, Y.W., Zhang, H., Hou, S., Xu, K.F., Chen, L.Q.: Vibration suppression of composite laminated plate with nonlinear energy sink. Acta Astronaut. 123, 109–115 (2016)
Song, Z.G., Li, F.M.: Active aeroelastic flutter analysis and vibration control of supersonic beams using the piezoelectric actuator/sensor pairs. Smart Mater. Struct. 20(5), 055013 (2011)
Chai, Y.Y., Song, Z.G., Li, F.M.: Active aerothermoelastic flutter suppression of composite laminated panels with time-dependent boundaries. Compos. Struct. 179, 61–76 (2017)
Farhadi, S., Hosseini-Hashemi, S.: Flutter stabilization of cantilevered plates using a bonded patch. Acta Mech. 219(3), 241–254 (2011)
Hasheminejad, S.M., Motaaleghi, M.A.: Aeroelastic analysis and active flutter suppression of an electro-rheological sandwich cylindrical panel under yawed supersonic flow. Aerosp. Sci. Technol. 42, 118–127 (2015)
Pacheco, D.R.Q., Marques, F.D., Ferreira, A.J.M.: Panel flutter suppression with nonlinear energy sinks: Numerical modeling and analysis. Int. J. Non-Linear Mech. 106, 108–114 (2018)
Li, Q.Q., Mei, C., Huang, J.K.: Suppression of thermal postbuckling and nonlinear panel flutter motions using piezoelectric actuators. AIAA J. 45(8), 1861–1873 (2007)
Chai, Y.Y., Li, F.M., Song, Z.G., Zhang, C.Z.: Aerothermoelastic flutter analysis and active vibration suppression of nonlinear composite laminated panels with time-dependent boundary conditions in supersonic airflow. J. Intell. Mater. Syst. Struct. 29(4), 653–668 (2018)
Samadpour, M., Asadi, H., Wang, Q.: Nonlinear aero-thermal flutter postponement of supersonic laminated composite beams with shape memory alloys. Eur. J. Mech. A/Solids 57, 18–28 (2016)
Song, Z.G., Li, F.M.: Aeroelastic analysis and active flutter control of nonlinear lattice sandwich beams. Nonlinear Dyn. 76(1), 57–68 (2014)
Chopra, I.: Flutter of a panel supported on an elastic foundation. AIAA J. 13(5), 687–688 (1975)
Goldman, B.D., Dowell, E.H.: Nonlinear oscillations of a fluttering plate resting on a unidirectional elastic foundation. AIAA J. 52(10), 2364–2368 (2014)
Emam, S., Eltaher, M.A.: Buckling and postbuckling of composite beams in hygrothermal environments. Compos. Struct. 152, 665–675 (2016)
Shen, H.S., Lin, F., Xiang, Y.: Nonlinear vibration of functionally graded graphene-reinforced composite laminated beams resting on elastic foundations in thermal environments. Nonlinear Dyn. 90(2), 899–914 (2017)
Aydogdu, M.: Thermal buckling analysis of cross-ply laminated composite beams with general boundary conditions. Compos. Sci. Technol. 67(6), 1096–1104 (2007)
Zhang, D.B., Tang, Y.Q., Ding, H., Chen, L.Q.: Parametric and internal resonance of a transporting plate with a varying tension. Nonlinear Dyn. 98(4), 2491–2508 (2019)
Zhang, L.W.: On the study of the effect of in-plane forces on the frequency parameters of CNT-reinforced composite skew plates. Compos. Struct. 160, 824–837 (2017)
Ahmed, K.M.: Free vibration of curved sandwich beams by the method of finite elements. J. Sound Vib. 18(1), 61–74 (1971)
Hwu, C., Chang, W.C., Gai, H.S.: Vibration suppression of composite sandwich beams. J. Sound Vib. 272, 1–20 (2004)
Lou, J., Ma, L., Wu, L.Z.: Free vibration analysis of simply supported sandwich beams with lattice truss core. Mater. Sci. Eng., B 177(19), 1712–1716 (2012)
Acknowledgements
This research was supported by the National Natural Science Foundation of China (Project Nos. 12072083, 11761131006, 11802069) and the German Research Foundation (DFG, Project No. ZH 15/30-1).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Chai, Y., Li, F. & Zhang, C. A new method for suppressing nonlinear flutter and thermal buckling of composite lattice sandwich beams. Acta Mech 233, 121–136 (2022). https://doi.org/10.1007/s00707-021-03107-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-021-03107-0