In this paper, imperfection sensitivity in the vibration behavior of functionally graded arches with microstructural defects (porosity) has been studied. The temperature-dependent material properties of functionally graded arches are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. The formulations are based on the Reddy’s higher order shear deformation theory using finite element method. Convergence and comparison studies have been performed to describe the efficacy of the present formulation. The obtained results have been compared with the limited available literature. The parametric studies have been performed to study the influence of the temperature rise, volume fraction index, and porosity index on the frequency response of the functionally graded arches. The effect of various modes of initial geometrical imperfections has also been examined. The obtained numerical results can be used as benchmark solutions for future researches in this field of study.
GuptaATalhaM. Recent development in modeling and analysis of functionally graded materials and structures. Prog Aerosp Sci2015; 79: 1–14.
2.
KapuriaSPatniMYasinMY. A quadrilateral shallow shell element based on the third-order theory for functionally graded plates and shells and the inaccuracy of rule of mixtures. Eur J Mech A Solids2015; 49: 268–282.
3.
ChidamparamPLeissaAW. Vibrations of planar curved beams, rings, and arches. Appl Mech Rev1993; 46: 467–483.
4.
HowsonWPJemahAK. Exact dynamic stiffness method for planar natural frequencies of curved Timoshenko beams. Proc IMechE, Part C: J Mechanical Engineering Science1999; 213: 687–696.
5.
LüQLüCF. Exact two-dimensional solutions for in-plane natural frequencies of laminated circular arches. J Sound Vib2008; 318: 982–990.
6.
MalekzadehP. Two-dimensional in-plane free vibrations of functionally graded circular arches with temperature-dependent properties. Compos Struct2009; 91: 38–47.
7.
LimCWYangQLüCFet al.Two-dimensional elasticity solutions for temperature-dependent in-plane vibration of FGM circular arches. Compos Struct2009; 90: 323–329.
8.
AlashtiRAKashiriN. The effect of temperature variation of a simply supported curved sandwich beam with a flexible core. Proc IMechE, Part C: J Mechanical Engineering Science2010; 225: 537–547.
9.
MalekzadehPAtashiMMKaramiG. In-plane free vibration of functionally graded circular arches with temperature-dependent properties under thermal environment. J Sound Vib2009; 326: 837–851.
10.
NikkhooAKananipourH. Numerical solution for dynamic analysis of semicircular curved beams acted upon by moving loads. Proc IMechE, Part C: J Mechanical Engineering Science2014; 228: 2314–2322.
11.
AtaiAANikranjbarAKasiriA. Buckling and post-buckling behaviour of semicircular functionally graded material arches: A theoretical study. Proc IMechE, Part C: J Mechanical Engineering Science2012; 226: 607–614.
12.
FilipichCPPiovanMT. The dynamics of thick curved beams constructed with functionally graded materials. Mech Res Commun2010; 37: 565–570.
13.
BiglariHJafariAA. Static and free vibration analyses of doubly curved composite sandwich panels with soft core based on a new three-layered mixed theory. Proc IMechE, Part C: J Mechanical Engineering Science2010; 224: 2332–2349.
14.
Gupta A and Talha M. A new trigonometric higher-order shear and normal deformation theory for functionally graded plates. In: Proceedings of ASME IMECE, Phoenix, AZ, USA, 11–17 November 2016.
15.
Talha M and Singh BN. Nonlinear vibration analysis of shear deformable functionally graded ceramic-metal plates using an improved higher order theory. In: Proceedings of ASME, SMASIS, Philadelphia, PA, USA, 28 September to 1 October 2010.
16.
TalhaMSinghBN. Thermo-mechanical induced vibration characteristics of shear deformable functionally graded ceramic–metal plates using finite element method. Proc IMechE, Part C: J Mechanical Engineering Science2011; 225: 50–65.
17.
EbrahimiFBaratiMR. Size-dependent dynamic modeling of inhomogeneous curved nanobeams embedded in elastic medium based on nonlocal strain gradient theory. Proc IMechE, Part C: J Mechanical Engineering Science2016; 231: 4457–4469.
18.
WuHLYangJKitipornchaiS. Nonlinear vibration of functionally graded carbon nanotube reinforced composite beams with geometric imperfections. Compos Part B: Eng2016; 90: 86–96.
19.
SheinmanIAdanM. Imperfection sensitivity of a beam on a nonlinear elastic foundation. Int J Mech Sci1991; 33: 753–760.
20.
FangWWickertJA. Postbuckling of micromachined beams. J Micromach Microeng1994; 4: 116–122.
21.
Lacarbonara WA. Theoretical and experimental investigation of nonlinear vibrations of buckled beams. MS Thesis, Virginia Polytechnic Institute and State University, USA, 1997.
22.
VirginLN. Free vibrations of imperfect cantilever bars under self-weight loading. Proc IMechE, Part C: J Mechanical Engineering Science1987; 201: 345–347.
23.
EmamSA. A static and dynamic analysis of the postbuckling of geometrically imperfect composite beams. Compos Struct2009; 90: 247–253.
24.
YaghoobiHTorabiM. Post-buckling and nonlinear free vibration analysis of geometrically imperfect functionally graded beams resting on nonlinear elastic foundation. Appl Math Model2013; 37: 8324–8340.
25.
GhayeshMHFarokhiHGholipourA. Vibration analysis of geometrically imperfect three-layered shear-deformable microbeams. Int J Mech Sci2017; 122: 370–383.
26.
GhayeshMHFarokhiH. Global dynamics of imperfect axially forced microbeams. Int J Eng Sci2017; 115: 102–116.
WuHYangJKitipornchaiS. Imperfection sensitivity of postbuckling behaviour of functionally graded carbon nanotube-reinforced composite beams. Thin-Walled Struct2016; 108: 225–233.
29.
Dehrouyeh-SemnaniAMMostafaeiHDehrouyehMet al.Thermal pre- and post-snap-through buckling of a geometrically imperfect doubly-clamped microbeam made of temperature-dependent functionally graded materials. Compos Struct2017; 170: 122–134.
30.
WuHKitipornchaiSYangJ. Thermo-electro-mechanical postbuckling of piezo-electric FG-CNTRC beams with geometric imperfections. Smart Mater Struct2016; 25: 095022–095022. (14 pp).
31.
LiLTangHHuY. Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature. Compos Struct2018; 184: 1177–1188.
32.
TalhaMSinghBN. Stochastic vibration characteristics of finite element modelled functionally gradient plates. Compos Struct2015; 130: 95–106.
33.
TalhaMSinghBN. Nonlinear mechanical bending of functionally graded material plates under transverse loads with various boundary conditions. Int J Model Simul Sci Comput2011; 2: 237–258.
34.
ZhuJLaiZYinZet al.Fabrication of ZrO2– NiCr functionally graded material by powder metallurgy. Mater Chem Phys2001; 68: 130–135.
35.
WattanasakulpongNPrustyBGKellyDWet al.Free vibration analysis of layered functionally graded beams with experimental validation. Mater Des2012; 36: 182–190.
36.
EbrahimiFJafariA. A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities. J Eng2016; 2016: 1–20.
37.
EbrahimiFGhasemiFSalariEr. Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities. Meccanica2016; 51: 223–249.
38.
GuptaATalhaM. Influence of porosity on the flexural and free vibration responses of functionally graded plates in thermal environment. Int J Struct Stab Dyn2018; 18: 1850013–1850013. (31 pp).
39.
MechabIMechabBBenaissaSet al.Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories. J Braz Soc Mech Sci Eng2016; 38(8): 1–19.
40.
KamranfardMRSaidiARNaderiA. Analytical solution for vibration and buckling of annular sectorial porous plates under in-plane uniform compressive loading. Proc IMechE, Part C: J Mechanical Engineering Science2017; 232(12): 2211–2228.
41.
EbrahimiFMokhtariM. Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method. J Braz Soc Mech Sci Eng2015; 37: 1435–1444.
42.
Magnucka-BlandziE. Vibration of a porous-cellular circular plate. Proc Appl Math Mech2006; 6: 243–244.
43.
MojahedinAJoubanehEFJabbariM. Thermal and mechanical stability of a circular porous plate with piezoelectric actuators. Acta Mech2014; 83: 57–64.
44.
WangYQZuJW. Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment. Aerosp Sci Technol2017; 69: 550–562.
45.
WangYQZuJW. Large-amplitude vibration of sigmoid functionally graded thin plates with porosities. Thin-Walled Struct2017; 119: 911–924.
46.
Amir M and Talha M. Free vibration analysis of functionally graded porous circular arch in thermal environment. In: Proceedings of ICTACEM, IIT Kharagpur, India, 28–30 December 2017.
47.
BaratiMR. Porosity-dependent vibration and dynamic stability of compositionally gradient nanofilms using nonlocal strain gradient theory. Proc IMechE, Part C: J Mechanical Engineering Science2017.
48.
EbrahimiFJafariA. Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory. Struct Eng Mech2016; 59: 343–371.
49.
WadeeMA. Effects of periodic and localized imperfections on struts on nonlinear foundations and compression sandwich panels. Int J Solids Struct2000; 37: 1191–1209.
50.
HeiligerPRReddyJN. A higher order beam finite element for bending and vibration problems. J Sound Vib1988; 126: 309–326.
51.
GroverNMaitiDKSinghBN. An efficient C0 finite element modeling of an inverse hyperbolic shear deformation theory for the flexural and stability analysis of laminated composite and sandwich plates. Finite Elem Anal Des2014; 80: 11–22.
52.
SuZJinGYeT. Vibration analysis and transient response of a functionally graded piezoelectric curved beam with general boundary conditions. Smart Mater Struct2016; 25: 065003–065003. (14 pp).
53.
QatuMS. Vibration of laminated shells and plates, Amsterdam: Elsevier, 2004, pp. 82–88.
54.
WuJSChiangLK. A new approach for free vibration analysis of arches with effects of shear deformation and rotary inertia considered. J Sound Vib2004; 277: 49–71.
55.
LitewkaPRakowskiJ. Free vibrations of shear-flexible and compressible arches by FEM. Int J Num Method Eng2001; 52: 273–286.
56.
ErogluU. In-plane free vibrations of circular beams made of functionally graded material in thermal environment: Beam theory approach. Compos Struct2015; 122: 217–228.
