{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,15]],"date-time":"2025-01-15T05:34:13Z","timestamp":1736919253558,"version":"3.33.0"},"reference-count":45,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,3]],"date-time":"2022-07-03T00:00:00Z","timestamp":1656806400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Laboratory of Icing and Anti\/De-icing of CARDC","award":["IADL20210201"]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12002225"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"This paper is concerned with free vibration characteristics of a spinning composite laminated truncated conical shell subjected to hygrothermal environment. Hygrothermal strains are introduced into the constitutive law of single-layer material, and fiber orientation lies symmetrically with respect to the midplane of the composite shell. Considering the spin-induced Coriolis and centrifugal forces, as well as initial hoop tension, the governing equations of free vibration of the composite conical shell with hygrothermal effects are derived on the basis of Love\u2019s thin-shell theory and Hamilton\u2019s principle. The solution of the equations is derived using the Galerkin approach. Then, a detailed parametric study on natural frequencies and critical spinning speeds is numerically performed. Results indicate that the Coriolis force induces an asymmetric influence on natural frequencies of forward and backward traveling waves, while the centrifugal force enhances the frequencies of both traveling waves symmetrically. Initial hoop tension plays a major role in the increase of critical spinning angular speed. Temperature, moisture concentration, and design parameters show the significant influence on the free vibration characteristics of the conical shell, and thermal expansion deformation is nonnegligible in the free vibration analysis.<\/jats:p>","DOI":"10.3390\/sym14071369","type":"journal-article","created":{"date-parts":[[2022,7,5]],"date-time":"2022-07-05T03:38:55Z","timestamp":1656992335000},"page":"1369","source":"Crossref","is-referenced-by-count":5,"title":["Free Vibration Analysis of a Spinning Composite Laminated Truncated Conical Shell under Hygrothermal Environment"],"prefix":"10.3390","volume":"14","author":[{"given":"Xiao","family":"Li","sequence":"first","affiliation":[{"name":"Department of Mechanics and Engineering, Sichuan University, Chengdu 610065, China"},{"name":"Key Laboratory of Icing and Anti\/De-Icing, China Aerodynamics Research and Development Center, Mianyang 621000, China"}]},{"given":"Xuanling","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Chongqing Jiaotong University, Chongqing 400074, China"}]},{"given":"Zhihong","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Mechanics and Engineering, Sichuan University, Chengdu 610065, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.jsv.2018.05.042","article-title":"Nonlinear travelling wave vibrations of a rotating thin cylindrical shell","volume":"431","author":"Sun","year":"2018","journal-title":"J. Sound Vib."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2793","DOI":"10.1016\/j.compstruct.2010.05.003","article-title":"A review of recent research on mechanics of multifunctional composite materials and structures","volume":"92","author":"Gibson","year":"2010","journal-title":"Compos. Struct."},{"key":"ref_3","first-page":"101","article-title":"On the beats in the vibrations of a revolving cylinder or bell","volume":"7","author":"Bryan","year":"1890","journal-title":"Proc. Camb. Philos. Soc."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1229","DOI":"10.1115\/1.3428067","article-title":"Traveling waves in rotating cylindrical shells","volume":"93","author":"Srinivasan","year":"1971","journal-title":"J. Eng. Ind."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/S0263-8223(00)00080-5","article-title":"Frequency characteristics of a rotating truncated circular layered conical shell","volume":"50","author":"Li","year":"2000","journal-title":"Compos. Struct."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1006\/jsvi.1998.1432","article-title":"Influence of boundary conditions on the frequency characteristics of a rotating truncated circular conical shell","volume":"223","author":"Lam","year":"1999","journal-title":"J. Sound Vib."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1016\/S0020-7403(03)00042-0","article-title":"Generalized differential quadrature for free vibration of rotating composite laminated conical shell with various boundary conditions","volume":"45","author":"Ng","year":"2003","journal-title":"Int. J. Mech. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1016\/j.ijmecsci.2018.10.024","article-title":"Vibration characteristics of a rotating composite laminated cylindrical shell in subsonic air flow and hygrothermal environment","volume":"150","author":"Li","year":"2019","journal-title":"Int. J. Mech. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s00419-009-0311-4","article-title":"Free vibrations of rotating composite conical shells with stringer and ring stiffeners","volume":"80","author":"Talebitooti","year":"2009","journal-title":"Arch. Appl. Mech."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1016\/j.jsv.2004.01.005","article-title":"Free vibration analysis of conical shells via the element-free kp-Ritz method","volume":"281","author":"Liew","year":"2005","journal-title":"J. Sound Vib."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1006\/jsvi.1995.0436","article-title":"Vibration analysis of pre-stressed rotating thick circular conical shell","volume":"186","author":"Sivadas","year":"1995","journal-title":"J. Sound Vib."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/j.cnsns.2007.06.007","article-title":"Nonlinear vibration and stability of a rotary truncated conical shell with intercoupling of high and low order modals","volume":"14","author":"Chen","year":"2009","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3001","DOI":"10.1016\/S0020-7683(02)00234-2","article-title":"Thermally induced dynamic instability of laminated composite conical shells","volume":"39","author":"Wu","year":"2002","journal-title":"Int. J. Solids Struct."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1007\/s11071-019-05297-8","article-title":"Harmonic resonances of graphene-reinforced nonlinear cylindrical shells: Effects of spinning motion and thermal environment","volume":"99","author":"Dong","year":"2020","journal-title":"Nonlinear Dyn."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.ijmecsci.2013.01.013","article-title":"Vibration studies of rotating cylindrical shells with arbitrary edges using characteristic orthogonal polynomials in the Rayleigh\u2013Ritz method","volume":"68","author":"Sun","year":"2013","journal-title":"Int. J. Mech. Sci."},{"key":"ref_16","first-page":"1105","article-title":"Parametric Instability of a Rotating Axially Loaded FG Cylindrical Thin Shell Under Both Axial Disturbances and Thermal Effects","volume":"73","author":"Li","year":"2018","journal-title":"Z. Nat. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/j.apm.2018.01.048","article-title":"Parametric resonance of a FG cylindrical thin shell with periodic rotating angular speeds in thermal environment","volume":"59","author":"Li","year":"2018","journal-title":"Appl. Math. Model."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"105644","DOI":"10.1016\/j.ast.2019.105644","article-title":"Vibration characteristics of rotating pretwisted composite tapered blade with graphene coating layers","volume":"98","author":"Zhang","year":"2020","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.ast.2017.03.003","article-title":"Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory","volume":"66","author":"Wang","year":"2017","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.compstruct.2015.08.025","article-title":"Vibration of thin-walled laminated composite beams having open and closed sections","volume":"134","author":"Sheikh","year":"2015","journal-title":"Compos. Struct."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1016\/j.apm.2020.12.033","article-title":"Nonlinear forced vibration of in-plane bi-directional functionally graded materials rectangular plate with global and localized geometrical imperfections","volume":"93","author":"Chen","year":"2021","journal-title":"Appl. Math. Model."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"413726","DOI":"10.1016\/j.physb.2022.413726","article-title":"Nonlocal strain gradient IGA numerical solution for static bending, free vibration and buckling of sigmoid FG sandwich nanoplate","volume":"631","author":"Nguyen","year":"2022","journal-title":"Phys. B Condens. Matter"},{"key":"ref_23","first-page":"065703","article-title":"A 3D nano scale IGA for free vibration and buckling analyses of multi-directional FGM nanoshells","volume":"33","author":"Nguyen","year":"2021","journal-title":"Nanotechnology"},{"key":"ref_24","first-page":"769","article-title":"Nonlinear forced vibration of rotating composite laminated cylindrical shells under hygrothermal environment","volume":"76","author":"Li","year":"2021","journal-title":"Z. Nat. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1016\/j.compositesb.2019.01.007","article-title":"Free vibration analysis of functionally graded rotating conical shells in thermal environment","volume":"163","author":"Shakouri","year":"2019","journal-title":"Compos. Part B Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.compstruct.2016.10.031","article-title":"Discrete singular convolution method for the free vibration analysis of rotating shells with different material properties","volume":"160","author":"Civalek","year":"2017","journal-title":"Compos. Struct."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.compstruct.2014.06.023","article-title":"Free vibration analysis of rotating functionally graded carbon nanotube-reinforced composite truncated conical shells","volume":"117","author":"Heydarpour","year":"2014","journal-title":"Compos. Struct."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"113963","DOI":"10.1016\/j.engstruct.2022.113963","article-title":"Dynamic stability of graded graphene reinforced truncated conical shells under both periodic spinning speeds and axial loads considering thermal effects","volume":"256","author":"Li","year":"2022","journal-title":"Eng. Struct."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/s11012-013-9791-y","article-title":"Free vibration of functionally graded truncated conical shells under internal pressure","volume":"49","author":"Heydarpour","year":"2013","journal-title":"Meccanica"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1550053","DOI":"10.1142\/S1758825115500532","article-title":"Vibration and Acoustic Responses of an Orthotropic Composite Conical Shell in a Hygroscopic Environment","volume":"7","author":"Zhao","year":"2015","journal-title":"Int. J. Appl. Mech."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s11012-019-00945-0","article-title":"Thermal buckling and postbuckling behavior of FG-GRC laminated cylindrical shells with temperature-dependent material properties","volume":"54","author":"Shen","year":"2019","journal-title":"Meccanica"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/S0263-8223(01)00182-9","article-title":"Hygrothermal effects on the structural behaviour of thick composite laminates using higher-order theory","volume":"56","author":"Patel","year":"2002","journal-title":"Compos. Struct."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.compositesb.2016.05.037","article-title":"Vibration of composite cylindrical shallow shells subjected to hygrothermal loading-experimental and numerical results","volume":"98","author":"Biswal","year":"2016","journal-title":"Compos. Part B Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"112887","DOI":"10.1016\/j.compstruct.2020.112887","article-title":"Parametric resonances of rotating composite laminated nonlinear cylindrical shells under periodic axial loads and hygrothermal environment","volume":"255","author":"Li","year":"2021","journal-title":"Compos. Struct."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1016\/j.compstruct.2016.06.057","article-title":"Flapwise free vibration characteristics of a rotating composite thin-walled beam under aerodynamic force and hygrothermal environment","volume":"153","author":"Qin","year":"2016","journal-title":"Compos. Struct."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.ymssp.2016.12.041","article-title":"Influences of hygrothermal environment and installation mode on vibration characteristics of a rotating laminated composite beam","volume":"91","author":"Qin","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/j.compstruct.2016.02.006","article-title":"Transient response of delaminated composite conical shells due to multiple low velocity impacts in hygrothermal environment","volume":"143","author":"Bandyopadhyay","year":"2016","journal-title":"Compos. Struct."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.ijmecsci.2018.01.026","article-title":"Multiphase nanocomposite viscoelastic laminated conical shells subjected to magneto-hygrothermal loads: Dynamic buckling analysis","volume":"137","author":"Hajmohammad","year":"2018","journal-title":"Int. J. Mech. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1565","DOI":"10.1007\/s00366-019-00903-0","article-title":"Nonlinear free vibration analysis of composite conical shell panel with cluster of delamination in hygrothermal environment","volume":"37","author":"Parhi","year":"2019","journal-title":"Eng. Comput."},{"key":"ref_40","unstructured":"Love, A.E.H. (2013). A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Jones, R.M. (1975). Mechanics of Composite Materials, Scripta Book Company.","DOI":"10.1115\/1.3423688"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/0022-460X(90)90852-Q","article-title":"Resonant phenomena of a rotating cylindrical shell subjected to a harmonic moving load","volume":"136","author":"Huang","year":"1990","journal-title":"J. Sound Vib."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1693","DOI":"10.1007\/s11071-014-1410-5","article-title":"Nonlinear vibration of a rotating laminated composite circular cylindrical shell: Traveling wave vibration","volume":"77","author":"Wang","year":"2014","journal-title":"Nonlinear Dyn."},{"key":"ref_44","unstructured":"Soedel, W. (1981). Vibrations of Shells and Plates, Marcel Dekker Incorporated."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"2866","DOI":"10.1016\/j.jsv.2014.02.020","article-title":"Parametric resonance of truncated conical shells rotating at periodically varying angular speed","volume":"333","author":"Han","year":"2014","journal-title":"J. Sound Vib."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/7\/1369\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,15]],"date-time":"2025-01-15T00:13:26Z","timestamp":1736900006000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/7\/1369"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,3]]},"references-count":45,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["sym14071369"],"URL":"https:\/\/doi.org\/10.3390\/sym14071369","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,7,3]]}}}