Abstract
In this paper, flexural vibrations of rectangular plates and beams which are consisted of functionally inhomogeneous materials due to cyclic loadings of external force and temperature change are analyzed mathematically. Interference between the flexural vibration due to cyclic loading and that due to cyclic heating is discussed. The amplification effect by loading frequency is also discussed for the deflection and stresses of the beam and the plate. Furthermore, a control problem of the flexural vibration of the FGM beam by the method of wave control is considered. In order to remove progressive wave in flexural waves excited by cyclic loading, intensity and phase lag of control force are derived on the basis of the active sink method. Then, the validity of wave control for the flexural vibration suppression of the FGM beam is discussed
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Kawamura R, Tanigawa Y, Hetnarski RB(2003) Thermally induced vibration of an inhomogeneous beam due to a cyclic heating. 177–186 In: Watanabe K, Ziegler F(eds) IUTAM Symposium on Advanced Materials and Smart Structures, Solid mechanics and its applications Vol. 106, Kluwer, Dordrecht.
Kawamura R, Kusuki S, Matsumoto N(2008) Fundamental thermo-elasticity equations for thermally induced flexural vibration problems for inhomogeneous plates and thermo-elastic dynamical responses to a sinusoidally varying surface temperature. Journal of Engineering Mathematics, Vol. 61, No. 2–4, 143–160.
Kawamura R, Tanigawa Y, Matsumoto N(2008) Thermally induced vibration of inho-mogeneous material rectangular plate due to cyclic variation of thermal and mechanical loads. AIP conference proceedings, Vol. 973, 694–699.
Tanaka N, Kikushima Y(1990) Flexural wave control of a flexible beam —Proposition of the active sink method. Transactions of the Japan Society of Mechanical Engineers Series C, Vol. 56, No. 522, 351–359(in Japanese).
Tanaka N, Kikushima Y(1990) Flexural wave control of flexible beam —Fundamental characteristics of an active sink system and its verification. Transactions of the Japan Society of Mechanical Engineers Series C, Vol. 56, No. 530, 2575–2582(in Japanese).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag/Wien
About this chapter
Cite this chapter
Kawamura, R., Fujita, H., Heguri, K., Tanigawa, Y. (2010). Mathematical Analysis of Flexural Vibration for a Functionally Graded Material Plate and Vibration Suppression by Flexural Wave Control. In: Irschik, H., Krommer, M., Watanabe, K., Furukawa, T. (eds) Mechanics and Model-Based Control of Smart Materials and Structures. Springer, Vienna. https://doi.org/10.1007/978-3-211-99484-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-211-99484-9_12
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-99483-2
Online ISBN: 978-3-211-99484-9
eBook Packages: EngineeringEngineering (R0)