Rapid heating vibrations of FGM annular sector plates
Tóm tắt
In this paper, thermally induced vibration of annular sector plate made of functionally graded materials is analyzed. All of the thermomechanical properties of the FGM media are considered to be temperature dependent. Based on the uncoupled linear thermoelasticity theory, the one-dimensional transient Fourier type of heat conduction equation is established. The top and bottom surfaces of the plate are under various types of rapid heating boundary conditions. Due to the temperature dependency of the material properties, heat conduction equation becomes nonlinear. Therefore, a numerical method should be adopted. First, the generalized differential quadrature method (GDQM) is implemented to discretize the heat conduction equation across the plate thickness. Next, the governing system of time-dependent ordinary differential equations is solved using the successive Crank–Nicolson time marching technique. The obtained thermal force and thermal moment resultants at each time step from temperature profile are applied to the equations of motion. The equations of motion, based on the first-order shear deformation theory (FSDT), are derived with the aid of the Hamilton principle. Using the GDQM, two-dimensional domain of the sector plate and suitable boundary conditions are divided into a number of nodal points and differential equations are turned into a system of ordinary differential equations. To obtain the unknown displacement vector at any time, a direct integration method based on the Newmark time marching scheme is utilized. Comparison investigations are performed to validate the formulation and solution method of the present research. Various examples are demonstrated to discuss the influences of effective parameters such as power law index in the FGM formulation, thickness of the plate, temperature dependency, sector opening angle, values of the radius, in-plane boundary conditions, and type of rapid heating boundary conditions on thermally induced response of the FGM plate under thermal shock.
Tài liệu tham khảo
Boley BA (1956) Thermally induced vibrations of beams. J Aeronaut Sci 23(2):179–182
Boley BA, Barber AD (1957) Dynamic response of beams and plates to rapid heating. ASME J Appl Mech 24(3):413–416
Kraus H (1966) Thermally induced vibrations of thin nonshallow spherical shells. AIAA J 4(3):500–505
Stroud RC, Mayers J (1970) Dynamic response of rapidly heated plate elements. AIAA J 9(1):76–83
Nakajo Y, Hayashi K (1988) Response of simply supported and clamped circular plates to thermal impact. J Sound Vib 122(2):347–356
Kiani Y, Eslami MR (2014) Geometrically non-linear rapid heating of temperature-dependent circular FGM plates. J Therm Stress 37(12):1495–1518
Eslami MR (2018) Buckling and postbuckling of beams, plates, and shells. Springer, Berlin
Venkataramana J, Jana MK (1974) Thermally Forced Vibrations of Beams. J Sound Vib 37(2):291–295
Kidawa-Kukla J (2003) Application of the green functions to the problem of the thermally induced vibration of a beam. J Sound Vib 262(4):865–876
Brush JC, Adalis S, Sadek IS, Sloss JM (1993) Structural control of thermoelastic beams for vibration suppression. J Therm Stress 16(3):249–263
Manolis GD, Beskos DE (1980) Thermally induced vibrations of beam structures. Comput Methods Appl Mech Eng 21(3):337–355
Adam C, Heuer R, Raue A, Ziegler F (2000) Thermally induced vibrations of composite beams with interlayer slip. J Therm Stress 23(8):747–772
Zhang J, Xiang Z, Liu Y, Xue M (2014) Stability of thermally induced vibration of a beam subjected to solar heating. AIAA J 52(3):660–665
Malik P, Kadoli R (2017) Thermo-elastic response of SUS316-Al2O3 functionally graded beams under various heat loads. Int J Mech Sci 128–129:206–223
Ghiasian SE, Kiani Y, Eslami MR (2014) Nonlinear rapid heating of FGM beams. Int J Non-Linear Mech 67(1):74–84
Tauchert TR (1989) Thermal shock of orthotropic rectangular plates. J Therm Stress 12(2):241–258
Das S (1983) Vibrations of polygonal plates due to thermal shock. J Sound Vib 89(4):471–476
Tauchert TR, Ashidda F, Sakata S, Takahashi Y (2006) Control of temperature-induced plate vibrations based on speed feedback. J Therm Stress 29(6):585–606
Chang JS, Wang JH, Tsai TZ (1992) Thermally induced vibrations of thin laminated plates by finite element method. Comput Struct 42(1):117–128
Alipour SM, Kiani Y, Eslami MR (2016) Rapid heating of FGM rectangular plates. Acta Mech 227(2):421–436
Javani M, Kiani Y, Eslami MR (2019) Large amplitude thermally induced vibrations of temperature dependent annular FGM plates. Compos Part B 163(1):371–383
Javani M, Kiani Y, Eslami MR (2019) Geometrically nonlinear rapid surface heating of temperature-dependent FGM arches. Aerosp Sci Technol 90(1):264–274
Javani M, Kiani Y, Sadighi M, Eslami RM (2019) Nonlinear vibration behavior of rapidly heated temperature-dependent FGM shallow spherical shells. AIAA J. https://doi.org/10.2514/1.J058240
Javani M, Kiani Y, Eslami RM (2019) Nonlinear axisymmetric response of temperature-dependent FGM conical shells under rapid heating. Acta Mech. https://doi.org/10.1007/s00707-019-02459-y
Hill DL, Mazumdar J (1987) A study of the thermally induced large amplitude vibrations of viscoelastic plates and shallow shells. J Sound Vib 116(2):323–337
Mazumdar J, Hill D, Clements DL (1980) Thermally induced vibrations of a viscoelastic plate. J Sound Vib 73(1):31–39
Hill D, Mazumdar J, Clements DL (1982) Dynamic response of viscoelastic plates of arbitrary shape to rapid heating. Int J Solids Struct 18(11):937–945
Mazumdar J, Hill DL (1984) Thermally induced vibrations of viscoelastic shallow shell. J Sound Vib 93(2):189–200
Hong CC, Liao HW, Lee LT, Ke JB, Jane KC (2005) Thermally induced vibration of a thermal sleeve with the GDQ method. Int J Mech Sci 47(12):1789–1806
Esmaeili HR, Arvin H, Kiani Y (2019) Axisymmetric nonlinear rapid heating of FGM cylindrical shells. J Therm Stress 42(4):490–505
Huang NN, Tauchert TR (1992) Thermally induced vibration of doubly curved cross-ply laminated panels. J Sound Vib 154(3):485–494
Huang NN, Tauchert TR (1993) Large amplitude vibrations of graphite reinforced aluminum cylindrical panels subjected to rapid heating. Composit Eng 3(6):557–566
Keibolahi A, Kiani Y, Eslami MR (2018) Dynamic snap-through of shallow arches under thermal shock. Aerosp Sci Technol 77(1):545–554
Keibolahi A, Kiani Y, Eslami MR (2018) Nonlinear rapid heating of shallow arches. J Therm Stress 41(10–12):1244–1258
Khdeir AA (2001) Thermally induced vibration of cross-ply laminated shallow shells. Acta Mech 151(3–4):135–147
Khdeir AA (2001) Thermally induced vibration of cross-ply laminated shallow arches. J Therm Stress 24(11):1085–1096
Chang JS, Shyong JW (1994) Thermally induced vibration of laminated circular cylindrical shell panels. J Therm Stress 51(3):419–427
Raja S, Sinha PK, Prathap G, Dwarakanathan D (2004) Thermally induced vibration control of composite plates and shells with piezoelectric active damping. Smart Mater Struct 13(4):939–950
Kumar R, Mishra BK, Jain SC (2008) Thermally induced vibration control of cylindrical shell using piezoelectric sensor and actuator. Int J Adv Manuf Technol 38(5–6):551–562
Pandey S, Pradyumna S (2017) A finite element formulation for thermally induced vibrations of functionally graded material sandwich plates and shell panels. Compos Struct 160(1):877–886
Kiani Y, Eslami MR (2015) Thermal postbuckling of imperfect circular functionally graded material plates: examination of Yoigt, Mori-Tanaka, and self-consistent schemes. J Press Vessel Technol 137(2):021201
Ghiasian SE, Kiani Y, Eslami MR (2015) Nonlinear thermal dynamic buckling of FGM beams. Eur J Mech A/Solids 54(1):232–242
Kiani Y (2017) Axisymmetric static and dynamics snap-through phenomena in a thermally postbuckled temperature-dependent FGM circular plate. Int J Non-Linear Mech 89(1):1–13
Cong PH, Chien TM, Khoa ND, Duc ND (2018) Nonlinear thermo-mechanical buckling and post-buckling response of porous FGM plates using Reddy’s HSDT. J Aerosp Sci Technol 77:419–428
Quan TQ, Duc ND (2016) Nonlinear vibration and dynamic response of shear deformable imperfect functionally graded double curved shallow shells resting on elastic foundations in thermal environments. J Therm Stress 39(4):437–459
Duc ND, Quan TQ (2014) Nonlinear response of imperfect eccentrically stiffened FGM cylindrical panels on elastic foundation subjected to mechanical loads. Eur J Mech A/Solids 46:60–71
Duc ND (2013) Nonlinear dynamic response of imperfect eccentrically stiffened FGM double curved shallow shells on elastic foundation. Compos Struct 99:88–96
Duc ND (2016) Nonlinear thermal dynamic analysis of eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations using the Reddy’s third-order shear deformation shell theory. Eur J Mech A/Solids 58:10–30
Reddy JN, Chin CD (1998) Thermomechanical analysis of functionally graded cylinders and plates. J Therm Stress 21(6):593–626
Tornabene F, Viola E (2009) Free vibration analysis of functionally graded panels and shells of revolution. Meccanica 44(3):255–281
Tornabene F, Fantuzzi N, Ubertini F, Viola E (2015) Strong formulation finite element method based on differential quadrature: a survey. Appl Mech Rev 67(2):1–55
Tornabene F, Viola E (2009) Free vibrations of four-parameter functionally graded parabolic panels and shells of revolution european. Eur J Mech A/Solids 28(5):991–1013
Tornabene F, Viola E (2013) Static analysis of functionally graded doubly-curved shells and panels of revolution. Meccanica 48(4):901–930
Tornabene F, Fantuzzi N, Bacciocchi M (2018) Strong and weak formulations based on differential and integral quadrature methods for the free vibration analysis of composite plates and shells: convergence and accuracy. Eng Anal Bound Elem 92:3–37
Eslami MR (2014) Finite elements methods in mechanics. Springer, Berlin
Reddy JN (2004) An introduction to nonlinear finite element analysis. Oxford University Press, Oxford
Hetnarski RB, Eslami MR (2019) Thermal stresses. Advanced theory and applications, 2nd edn. Springer, Amsterdam
Mirtalaie SH, Hajabasi MA, Hejripour F (2012) Free vibration analysis of functionally graded moderately thick annular sector plates using differential quadrature method. Appl Mech Mater 110–116:2990–2998