Abstract
Based on the first-order shear deformation theory taking into account geometrical nonlinearity, initial geometrical imperfection, vibration and nonlinear dynamic analysis of the sandwich laminated composite panel characterized by a continuous thickness variation in thermal environment and resting on an elastic foundation are considered in this paper. Variable thickness could affect the design of composite panel since it allows to tailor the stiffness features in the most stressed areas within the domain, keeping the weight constant. As a consequence, an improved dynamic behavior of the structure may be exhibited. The motion equations of dynamic analysis are determined due to Galerkin method and the obtained equation is numerically solved by using Runge–Kutta method. In numerical results, the effects of initial geometrical imperfections and geometrical parameters, material properties, coefficients of foundation, mechanical loads, temperature and the variable thickness on the nonlinear dynamic response and vibration of the laminated composite panel are investigated.
References
1. | Kang, JH, Leissa, AW. Three-dimensional vibrations of thick spherical shell segments with variable thickness. Int J Solids Struct 2000; 37: 4811–4823. Google Scholar | Crossref | ISI |
2. | Kang, JH, Leissa, AW. Free vibration analysis of complete paraboloidal shells of revolution with variable thickness and solid paraboloids from a three-dimensional theory. Comput Struct 2005; 83: 2594–2608. Google Scholar | Crossref |
3. | Xu, Y, Zhou, D. Three-dimensional elasticity solution of functionally graded rectangular plates with variable thickness. Compos Struct 2009; 91: 56–65. Google Scholar | Crossref |
4. | Tajeddini, V, Ohadi, A, Sadighi, M. Three-dimensional free vibration of variable thickness thick circular and annular isotropic and functionally graded plates on Pasternak foundation. Int J Mech Sci 2011; 53: 300–308. Google Scholar | Crossref |
5. | Behravan, RA, Shariyat, M. Three-dimensional magneto-elastic analysis of asymmetric variable thickness porous FGM circular plates with non-uniform tractions and Kerr elastic foundations. Compos Struct 2015; 125: 558–574. Google Scholar | Crossref |
6. | Wael, A, Tabey, A. (8 September 2014). Vibration analysis of laminated composite variable thickness plate using finite strip transition matrix technique and MATLAB verifications, MATLAB applications for the practical engineer, Kelly Bennett, IntechOpen, DOI: 10.5772/57384. Google Scholar |
7. | Dhurvey, P. Buckling analysis of composite laminated skew plate of variable thickness. Volume 4, Issue 9, 2017, Pages 9732-9736. In: International conference on recent trends in engineering and material sciences (ICEMS-2016), Jaipur, India, 17–19 March 2016, pp. 9732–9736. Vol. 4. Netherlands: Elsevier, https://www.sciencedirect.com/science/article/pii/S2214785317310520?via%3Dihub Google Scholar |
8. | Wu, Z, Raju, G, Weaver, PM. Optimization of postbuckling behaviour of variable thickness composite panels with variable angle tows: towards “Buckle-Free” design concept. Int J Solids Struct 2018; 132–133: 66–67. Google Scholar | Crossref |
9. | Wei, Z, Zonghong, X, Wang, Xet al. Buckling behavior of stiffened composite panels with variable thickness skin under compression. J Mech Adv Mater Struct 2019; 26: 215–223. Google Scholar | Crossref |
10. | Bacciocchi, M, Eisenberger, M, Fantuzzi, Net al. Vibration analysis of variable thickness plates and shells by the generalized differential quadrature method. Compos Struct 2016; 156: 218–237. Google Scholar | Crossref |
11. | Wu, TY, Liu, GR. Free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule. Int J Solids Struct 2001; 38: 7967–7980. Google Scholar | Crossref | ISI |
12. | Jiang, W, Redekop, D. Static and vibration analysis of orthotropic toroidal shells of variable thickness by differential quadrature. Thin Wall Struct 2003; 41: 461–478. Google Scholar | Crossref |
13. | Liang, B, Zhang, SF, Chen, DY. Natural frequencies of circular annular plates with variable thickness by a new method. Int J Pres Vessel Pip 2007; 84: 293–297. Google Scholar | Crossref |
14. | Eisenberger, M, Jabareen, M. Axisymmetric vibrations of circular and annular plates with variable thickness. Int J Struct Stab Dyn 2001; 1: 195–206. Google Scholar | Crossref |
15. | Ahmad, BR, Mohammad, S. Thermo-magneto-elasticity analysis of variable thickness annular FGM plates with asymmetric shear and normal loads and non-uniform elastic foundations. Arch Civil Mech Eng 2016; 16: 448–466. Google Scholar | Crossref |
16. | Duan, WH, Koh, CG. Axisymmetric transverse vibrations of circular cylindrical shells with variable thickness. J Sound Vib 2008; 317: 1035–1041. Google Scholar | Crossref | ISI |
17. | Thang, PT, Trung, NT, Lee, J. Closed-form expression for nonlinear analysis of imperfect sigmoid-FGM plates with variable thickness resting on elastic medium. Compos Struct 2016; 143: 143–150. Google Scholar | Crossref |
18. | Thang, PT, Duc, ND, Trung, NT. Effects of variable thickness and imperfection on nonlinear buckling of Sigmoid-functionally graded cylindrical panels. Compos Struct 2016; 155: 99–106. Google Scholar | Crossref |
19. | Shufrin, I, Eisenberger, M. Vibration of shear deformable plates with variable thickness – first-order and higher-order analyses. J Sound Vib 2006; 290: 465–489. Google Scholar | Crossref | ISI |
20. | Duc, ND, Hadavinia, H, Thu, PVet al. Vibration and nonlinear dynamic response of imperfect three-phase polymer nanocomposite panel resting on elastic foundations under hydrodynamic loads. Compos Struct 2015; 131: 229–237. Google Scholar | Crossref |
21. | Quan, TQ, Tran, P, Tuan, NDet al. Nonlinear dynamical analysis and vibration of shear deformable eccentrically stiffened S-FGM cylindrical panels with metal-ceramic-metal layers resting on elastic foundations. Compos Struct 2015; 126: 16–33. Google Scholar | Crossref | ISI |
22. | Bich, DH, Dung, DV, Nam, VH. Nonlinear dynamical analysis of eccentrically stiffened functionally graded cylindrical panels. Compos Struct 2012; 94: 2465–2473. Google Scholar | Crossref | ISI |
23. | Tran, P, Tuan, DN, Abdallah, G. Numerical modelling of hybrid elastomeric composite panels subjected to blast loadings. Compos Struct 2016; 153: 108–122. Google Scholar | Crossref |
24. | Kiani, Y. Free vibration of FG –CNT reinforced composite spherical shell panels using Gram–Schmidt shape functions. Compos Struct 2017; 159: 368–381. Google Scholar | Crossref |
25. | Mahapatra, TR, Panda, SK, Kar, VR. Nonlinear hygro-thermo-elastic vibration analysis of doubly curved composite shell panel using finite element micromechanical model. Mech Adv Mater Struct 2018; 23: 1343–1359. Google Scholar | Crossref |
26. | Hirwani, CK, Mahapatra, TR, Panda, SKet al. Nonlinear free vibration analysis of laminated carbon/epoxy curved panels. Def Sci J 2017; 67: 207–218. Google Scholar | Crossref |
27. | Hirwani, CK, Panda, SK, Mahapatra, TR. Nonlinear finite element analysis of transient behavior of delaminated composite plate. J Vib Acoust 2017; 140: 021001. Google Scholar | Crossref |
28. | Mahapatra, TR, Kar, VR, Panda, SK. Large amplitude vibration analysis of laminated composite spherical panels under hygrothermal environment. Int J Struct Stab Dyn 2016; 16: 1450105. Google Scholar | Crossref |
29. | Hassanli, S, Samali, B. Buckling analysis of laminated composite curved panels reinforced with linear and non – linear distribution of shape memory alloys. Thin Wall Struct 2016; 106: 9–17. Google Scholar | Crossref |
30. | Sahoo, SS, Panda, SK, Singh, VKet al. Numerical investigation on the nonlinear flexural behavior of wrapped glass/epoxy laminated composite panel and experimental validation. Arch Appl Mech 2017; 87: 315–333. Google Scholar | Crossref |
31. | Akbaş, SD. Hygrothermal post-buckling analysis of laminated composite beams. Int J Appl Mech 2019; 11: 1950009. Google Scholar | Crossref |
32. | Akbaş, SD. Nonlinear thermal displacements of laminated composite beams. Coupled Syst Mech 2018; 7: 691–705. Google Scholar |
33. | Akbaş, SD. Thermal post-buckling analysis of a laminated composite beam. Struct Eng Mech 2018; 67: 337–346. Google Scholar |
34. | Akbaş, SD. Free vibration analysis of a cross-ply laminated plate in thermal environment. Int J Eng 2018; 10: 176–189. Google Scholar |
35. | Tung, HV. Nonlinear thermo-mechanical response of pressure-loaded doubly curved functionally graded material sandwich panels in thermal environments including tangential edge constraints. J Sandw Struct Mater 2018; 20(8): 974–1008. Google Scholar | SAGE Journals |
36. | Arefi, M, Zenkour, A. A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermo-electric environment. J Sandw Struct Mater 2016; 18: 624–651. Google Scholar | SAGE Journals | ISI |
37. | Zenkour, A, Allam, MNM, Sobhy, M. Bending analysis of FG viscoelastic sandwich beams with elastic cores resting on Pasternak’s elastic foundations. Acta Mech 2010; 212: 233–252. Google Scholar | Crossref | ISI |
38. | Akbaş, SD. Thermal effects on the vibration of functionally graded deep beams with porosity. Int J Appl Mech 2017; 9: 1750076. Google Scholar | Crossref |
39. | Akbaş, SD, Kocatürk, T. Post-buckling analysis of functionally graded three-dimensional beams under the influence of temperature. J Therm Stress 2013; 36: 1233–1254. Google Scholar | Crossref |
40. | Bennai, R, Hassen, A, Tounsi, A. A new higher-order shear and normal deformation theory for functionally graded sandwich beams. Steel Compos Struct 2015; 19: 521–546. Google Scholar | Crossref |
41. | Wang, ZX, Shen, H-S. Nonlinear analysis of sandwich plates with FGM face sheets resting on elastic foundations. Compos Struct 2011; 93: 2521–2532. Google Scholar | Crossref | ISI |
42. | Duc, ND, Bich, DH, Vtt, A. On the nonlinear stability of eccentrically stiffened functionally graded annular spherical segment shells. J Thin Wall Struct 2016; 106: 258–267. Google Scholar | Crossref |
43. | Anh, VTT, Duc, ND. The nonlinear stability of axisymmetric FGM annular spherical shells under thermo-mechanical load. J Mech Adv Mater Struct 2015; 23: 1421–1429. Google Scholar | Crossref |
44. | Chan, DQ, Anh, VTT, Duc, ND. Vibration and nonlinear dynamic response of eccentrically stiffened functionally graded composite truncated conical shells in thermal environments. Acta Mech 2019; 230: 157–178. Google Scholar | Crossref |
45. | Trung, TT, Nam, NH, Thom, DVet al. Bending and thermal buckling of unsymmetric functionally graded sandwich beams in high temperature environment based on a new third order shear deformation theory. J Sandw Struct Mater. Epub ahead of print 12 May 2019. DOI: 10.1177/1099636219849268. Google Scholar |
46. | Thanh, NV, Quang, VD, Khoa, NDet al. Nonlinear dynamic response and vibration of FG CNTRC shear deformable circular cylindrical shell with temperature dependent material properties and surrounded on elastic foundations. J Sandw Struct Mater 2019; 21(7). Google Scholar |
47. | Duc, ND. Nonlinear thermo-electro-mechanical dynamic response of shear deformable piezoelectric Sigmoid functionally graded sandwich circular cylindrical shells on elastic foundations. J Sandw Struct Mater 2018; 20(3). Google Scholar |
48. | Thu, PV, Duc, ND. Nonlinear dynamic response and vibration of an imperfect three – phase laminated nanocomposite cylindrical panel resting on elastic foundation in thermal environments. Sci Eng Compos Mater 2015; 24(6): 951–962. Google Scholar |
49. | Thinh, TI, Trung, NV, Cuong, NM. Free vibration of fluid – filled laminated composite cylindrical shells on elastic foundations. In: Proceeding of the third international conference on engineering mechanics and automation (ICEMA3), Hanoi, 15 October 2014. Google Scholar |