Abstract
This investigation describes the computational characteristics of two-directional functionally graded beams under the hygrothermal effect. A prismatic two-directional functionally graded beam (FGM) is used in this work. Temperature and moisture are applied to this FGM beam. Stainless steel (SUS304) and silicon nitride (Si3N4) are the materials used in their construction. Finite element method (FEM) software calculates the eigenfrequencies of two-directional FGM (COMSOL Multiphysics). The power law governs the material properties. The Euler–Bernoulli beam theory (EBT) is used in this study. The mechanical parameters are varied in longitudinal and transverse directions. The eigenfrequencies of two-directional FGM beams are affected by the material gradient parameter, the boundary condition, and the aspect ratio under the influence of the hygrothermal effect. The results obtained for reduced cases are used to validate the results computed with the FEM. The natural frequencies decrease with increased moisture concentration and temperature variation under clamped–clamped (C–C) boundary conditions and increase under clamped-free (C–F) boundary conditions. It is also observed that natural frequencies increase with the increase in material gradient parameters in the z-direction (nz) and decrease with the increase in material gradient parameters in the x-direction (nx) under C–C and C–F end conditions. With the increase in aspect ratio, the natural frequency increases under C–C and C–F boundary conditions.
Similar content being viewed by others
References
Aria, A.I., Friswell, M.I.: A nonlocal finite element model for buckling and vibration of functionally graded nanobeams. Compos. B Eng. 1(166), 233–246 (2019)
Wang, Y., Ren, H., Fu, T., Shi, C.: Hygrothermal mechanical behaviors of axially functionally graded microbeams using a refined first order shear deformation theory. Acta Astronaut. 1(166), 306–316 (2020)
Nguyen, T.K., Nguyen, B.D., Vo, T.P., et al.: Hygro-thermal effects on vibration and thermal buckling behaviors of functionally graded beams. Compos. Struct. 176, 1050–1060 (2017)
Rajasekaran, S., Tochaei, E.N.: Free vibration analysis of axially functionally graded tapered Timoshenko beams using differential transformation element method and differential quadrature element method of lowest-order. Meccanica 49(4), 995–1009 (2014)
Sharma, P., Singh, R., Hussain, M.: On modal analysis of axially functionally graded material beam under hygrothermal effect. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 234(5), 1085–1101 (2020)
Chen, W.R., Chang, H.: Vibration analysis of bidirectional functionally graded Timoshenko beams using Chebyshev collocation method. Int. J. Struct. Stab. Dyn. 21(01), 2150009 (2021)
Karamanl, A.: Free vibration analysis of two directional functionally graded beams using a third order shear deformation theory. Compos. Struct. 1(189), 127–136 (2018)
Trinh, L.C., Vo, T.P., Thai, H.T., Nguyen, T.K.: Size-dependent vibration of bi-directional functionally graded microbeams with arbitrary boundary conditions. Compos. B Eng. 1(134), 225–245 (2018)
Gupta, B., Sharma, P., Rathore, S.K.: A new numerical modeling of an axially functionally graded piezoelectric beam. J. Vib. Eng. Technol. 13, 1–6 (2022)
Sharma, P., Gupta, B., Rathore, S.K., Khinchi, A., Gautam, M.: Computational characteristics of an exponentially functionally graded piezoelectric beam. Int. J. Interact. Des. Manuf. (IJIDeM) 31, 1–7 (2022)
Parashar, S.K., Sharma, P.: Modal analysis of shear-induced flexural vibration of FGPM beam using Generalized Differential Quadrature method. Compos. Struct. 139, 222–232 (2016)
Sharma, P., Parashar, S.K.: Free vibration analysis of shear-induced flexural vibration of FGPM annular plate using generalized differential quadrature method. Compos. Struct. 1(155), 213–222 (2016)
Sharma, P.: Efficacy of Harmonic Differential Quadrature method to vibration analysis of FGPM beam. Compos. Struct. 1(189), 107–116 (2018)
Sharma, P.: Vibration Analysis of Functionally Graded Piezoelectric Actuators. Springer, New York (2019)
Singh, R., Sharma, P.: Vibration analysis of an axially functionally graded material non prismatic beam under axial thermal variation in humid environment. J. Vib. Control 28(23–24), 3608–3621 (2021)
Sharma, P., Gautam, M., Chaturvedi, M.: Vibration analysis of EFGM beam using GDQ method. Int. J. Interact. Des. Manuf. (IJIDeM) 26, 1–9 (2022)
Mohammadnejad, M.: Free vibration analysis of axially functionally graded beams using Fredholm integral equations. Arch. Appl. Mech. 5, 1–6 (2022)
Zghal, S., Ataoui, D., Dammak, F.: Free vibration analysis of porous beams with gradually varying mechanical properties. Proc. Inst. Mech. Eng. Part M J. Eng. Marit. Environ. 236(3), 800–812 (2022)
Balireddy, S.N., Pitchaimani, J.: Stability and dynamic behaviour of bi-directional functionally graded beam subjected to variable axial load. Mater. Today Commun. 1(32), 104043 (2022)
Nejad, M.Z., Hadi, A.: Non-local analysis of free vibration of bi-directional functionally graded Euler–Bernoulli nano-beams. Int. J. Eng. Sci. 1(105), 1–1 (2016)
Sharma, P., Kataria, S.D., Khinchi, A.: On modal analysis of bi-direction FGM beam under general end conditions. Mater. Today Proc. 1(44), 1853–1856 (2021)
Sharma, P., Khinchi, A.: On frequency investigation of bi-directional FGM beam under thermal effect. Mater. Today Proc. 1(47), 6089–6092 (2021)
Khinchi, A., Sharma, P.: A convergence behavior of HDQ and GDQ methods to analyze vibration characteristics of different configurations of FGM beams. Mater. Today: Proc. 62, 2670–3674 (2022)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Sharma, P., Khinchi, A. Finite element modeling of two-directional FGM beams under hygrothermal effect. Int J Interact Des Manuf (2023). https://doi.org/10.1007/s12008-022-01190-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12008-022-01190-8