Analysis of Thermo-Magneto-Elastic Nonlinear Dynamic Response of Shallow Conical Shells
- 1 School of Mechanics and Construction Engineering, Jinan University, Guangzhou, China
- 2 School of Mechanics and Construction Engineering, Jinan University, Guangzhou, China
Abstract
The dynamic response study on thermo-magneto-elastic behavior of shallow conical shell in a time-dependent magnetic field is investigated, and the dynamic responses of displacement of shallow conical shell under mechanical loads, electromagnetic fields and temperature field coupling are analyzed. Based on Maxwell’s equations, heat conduction equation and nonlinear equations of classical plates and shells, the nonlinear dynamic response governing equations are derived. The electromagnetic field and temperature field equations are solved using variable separating technique, the nonlinear elastic field equations are solved by Galerkin method. The variation of temperature, magnetic field intensity and displacement with time under the coupling effect of the applied magnetic field and the surface uniform load were obtained. The influence of frequency of the applied magnetic field on the displacement wave forms is discussed.
- Zhou, Y.H. and Zheng, X.J. (1999) Electromagnetic Solid Structural Mechanics. Science Press, Peking.
- Bai, X.Z. (2006) Magnetic Base Plate and Shell Elasticity. Science Press, Peking.
- Xing, Y.F. and Liu, B. (2010) A Differential Quadrature Analysis of Dynamic and Quasi-Static Magneto-Thermo-Elastic Stresses in a Conducting Rectangular Plate Subjected to an Arbitrary Variation of Magnetic Field. International Journal of Engineering Science, 48, 1944-1960. https://doi.org/10.1016/j.ijengsci.2010.06.010
- Higuchi, M., Tanigawa, Y. and Kawamura, R. (2007) Magneto-Thermo-Elastic Stresses Induced by a Transient Magnetic Field in a Conducting Solid Circular Cylinder. Journal of Thermal Stresses, 44, 5316-5335.
- Tanigawa, Y., Higuchi, M. and Kawamura, R. (2008) Dynamic and Quasi-Static Behaviors of Magneto-Thermo-Elastic Stresses in a Conducting Hollow Circular Cylinder Subjected to an Arbitrary Variation of Magnetic Field. International Journal of Mechanical Sciences, 50, 365-379. https://doi.org/10.1016/j.ijmecsci.2007.11.001
- Tu, J.X., Wang, Z.R., Li, Y.Z. and Wang, P. (2014) Nonlinear Random Vibration of a Current Carrying Circular Plate in a Magnetic Field. Journal of Mechanical Strength, 36, 504-509.
- Wang, P., Chen, S.M. and Wang, Z.R. (2013) Bifurcation and Chaos of a Thin Rectangular Plate Simply Supported with Large Deflection in a Coupled Environment of Heating, Force and Magnetic Field. Journal of Vibration and Shock, 32, 129-134.
- Milazzo, A. (2013) A One-Dimensional Model for Dynamic Analysis of Generally Layered Magneto-Electro-Elastic Beams. Journal of Sound and Vibration, 332, 465-483. https://doi.org/10.1016/j.jsv.2012.09.004
- Lang, Z. and Li, X. (2013) Buckling and Vibration Analysis of Functionally Graded Magneto-Electro-Thermo-Elastic Circular Cylindrical Shells. Applied Mathematical Modelling, 37, 2279-2292. https://doi.org/10.1016/j.apm.2012.05.023
- Kattimani, S.C. and Ray, M.C. (2015) Control of Geometrically Nonlinear Vibrations of Functionally Graded Magneto-Electro-Elastic Plates. International Journal of Mechanical Sciences, 99, 154-167. https://doi.org/10.1016/j.ijmecsci.2015.05.012