The GDQ Method of Thermal Vibration Laminated Shell with Actuating Magnetostrictive Layers


  • C.C. Hong Hsiuping University of Science and Technology


magnetostrictive shell, thermal vibration, GDQ


The research of laminated magnetostrictive shell under thermal vibration was computed by using the generalized differential quadrature (GDQ) method. In the thermoelastic stress-strain equations that contain the terms linear temperature rise and the magnetostrictive material with velocity feedback control. The dynamic equilibrium differential equations with displacements were normalized and discretized into the dynamic discretized equations by the GDQ method. Two edges of laminated shell with clamped boundary conditions were considered. The values of interlaminar thermal stresses and center displacement of shell with and without velocity feedback control were calculated, respectively. The purpose of this research is to compute the time responses of displacement and stresses in the laminated magnetostrictive shell subjected to thermal vibration with suitable controlled gain values. The numerical GDQ results of displacement and stresses are also obtained and investigated. With velocity feedback and suitable control gain values are found to reduce the amplitude of displacement and stresses into a smaller value. The higher values of temperature get the higher amplitude of displacement and stresses. The GDQ results of actuating magnetostrictive shells can be applied in the field of morphing aircraft (adaptive structures and smart materials) to reduce and suppress the vibration when under aero-thermal flutter.


G. Xue, P. Zhang, Z. He, D. Li, Z. Yang and Z. Zhao, "Displacement model and driving voltage optimization for a giant magnetostrictive actuator used on a high-pressure common-rail injector," Materials and Design, vol. 95, pp. 501-509, 2016.

J. Ma, J. Jiao, C. Fang, X. Zhao and H. Luo, "High sensitive nonlinear modulation magnetoelectric magnetic sensors with a magnetostrictive metglas structure based on bell-shaped geometry," Journal of Magnetism and Magnetic Materials, vol. 405, pp. 225-230, 2016.

H. Yan, X. Zhao, C. Zhang, Z. Zhen, Z. Zhang, L. Li and D. Han, "A novel current fiber sensor with magnetostrictive material based on the plasmon response," Optik - International Journal for Light and Electron Optics, vol. 127, pp. 1323-1325, 2016.

Z. Yang, Z. He, D. Li, J. Yu, X. Cui and Z. Zhao, "Direct drive servo valve based on magnetostrictive actuator: Multi-coupled modeling and its compound control strategy," Sensors and Actuators A: Physical, vol. 235, pp. 119-130, 2015.

T. Sadowski, M. Bîrsan and D. Pietras, "Multilayered and FGM structural elements under mechanical and thermal loads. Part I: Comparison of finite elements and analytical models," Archives of Civil and Mechanical Engineering, vol. 15, pp. 1180-1192, 2015.

G. G. Sheng and X. Wang "An analytical study of the non-linear vibrations of functionally graded cylindrical shells subjected to thermal and axial loads," Composite Structures, vol. 97, pp. 261-268, 2013.

W. C. Sue, J. Y. Liou and J. C. Sung, "Investigation of the stress singularity of a magnetoelectroelastic bonded antiplane wedge," Applied Mathematical Modelling, vol. 31, pp. 2313-2331, 2007.

S. J. Lee, J. N. Reddy and F. Rostam-Abadi, "Nonlinear finite element analysis of laminated composite shells with actuating layers," Finite Elements in Analysis and Design, vol. 43, pp. 1-21, 2006.

J. S. Kumar, N. Ganesan, S. Swarnamani and C. Padmanabhan, "Active control of cylindrical shell with magnetostrictive layer," Journal of Sound and Vibration, vol. 262, pp. 577-589, 2003.

A. Sharma, R. Kumar, R. Vaish, V.S. Chauhan, "Active vibration control of space antenna reflector over wide temperature range," Composite Structures, vol. 128, pp. 291-304, 2015.

T. Zhang, B.T. Yang, H.G. Li, G. Meng, "Dynamic modeling and adaptive vibration control study for giant magnetostrictive actuators," Sensors and Actuators A: Physical, vol. 190, pp. 96-105, 2013.

A.G. Olabi, A. Grunwald," Design and application of magnetostrictive materials," Materials & Design, vol. 29, Issue 2, pp. 469-483, 2008.

C. C. Hong, "Rapid heating-induced vibration of composite magnetostrictive shells," Mechanics of Advanced Materials and Structures, vol. 23, pp. 415-422, 2016.

C. C. Hong, "Rapid heating induced vibration of circular cylindrical shells with magnetostrictive functionally graded material," Archives of Civil and Mechanical Engineering, vol. 14, pp. 710-720, 2014.

C. C. Hong, "Thermal vibration of magnetostrictive functionally graded material shells," European Journal of Mechanics-A/Solids, vol. 40, pp. 114-122, 2013.

C. Shu and H. Du, "Implementation of clamped and simply supported boundary conditions in the GDQ free vibration analyses of beams and plates," International Journal of Solids and Structures, vol. 34, pp. 819-835, 1997.

C. W. Bert, S. K. Jang and A. G. Striz, "Nonlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature," Computational Mechanics, vol. 5, pp. 217-226, 1989.




How to Cite

C. Hong, “The GDQ Method of Thermal Vibration Laminated Shell with Actuating Magnetostrictive Layers”, Int. j. eng. technol. innov., vol. 7, no. 3, pp. 188–200, Jun. 2017.