Abstract
In this work, the finite element model of a cantilevered plate is derived using Hamilton’s principle. A cantilevered plate structure instrumented with one piezoelectric sensor patch and one piezoelectric actuator patch is taken as a case study. Quadrilateral plate finite element having three degrees of freedom at each node is employed to divide the plate into finite elements. Thereafter, Hamilton’s principle is used to derive equations of motion of the smart plate. The finite element model is reduced to the first three modes using orthonormal modal truncation, and subsequently, the reduced finite element model is converted into a state-space model.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Kheiri Sarabi B, Sharma M, Kaur D (2014) Techniques for creating mathematical model of structures for active vibration control. IEEE, Recent Adv Eng Comput Sci (RAECS)
Benjeddou A (2000) Advances in piezoelectric finite element modeling of adaptive structural elements: a survey. Comput Struct 76:347–363
Allemang RJ (1983) Experimental modal analysis for vibrating structures
Moita JMS, Soares CMM, Soares CAM (2002) Geometrically non-linear analysis of composite structures with integrated piezoelectric sensors and actuators. Compos Struct 57:253–261
Reddy JN (2007) Theory and analysis of elastic plates and shells, 2nd edn. CRC Press, Boca Raton
Park SK, Gao XL (2006) Bernoulli-Euler beam model based on a modified couple stress theory. J Micromech Microeng 16:2355
Umesh K, Ganguli R (2009) Shape and vibration control of a smart composite plate with matrix cracks. Smart Mater Struct 18:1–13
Heidary F, Eslami MR (2004) Dynamic analysis of distributed piezothermoelastic composite plate using first-order shear deformation theory. J Therm Stresses 27:587–605
Peng XQ, Lam KY, Liu GR (1998) Active vibration control of composite beams with piezoelectrics: a finite element model with third order theory. J Sound Vib 209:635–650
Kulkarni SA, Bajoria KM (2003) Finite element modeling of smart plates/shells using higher order shear deformation theory. Compos Struct 62:41–50
Robbins DH, Reddy JN (1991) Analysis of piezoelecrically actuated beams using a layer-wise displacement theory. Comput Struct 41:265–279
Reddy JN (1999) On laminated composite plate with integrated sensors and actuators. Eng Struct 21:568–593
Kheiri Sarabi B, Sharma M, Kaur D (2016) Simulation of a new technique for vibration tests, based upon active vibration control. IETE J Res 63:1–9
Kheiri Sarabi B, Sharma M, Kaur D, Kumar N (2016) A novel technique for generating desired vibrations in structure. Integr Ferroelectr 176:236–250
Kheiri Sarabi B, Sharma M, Kaur D, Kumar N (2017) An optimal control based technique for generating desired vibrations in a structure. Iran J Sci Technol Trans Electr Eng 41:219–228
Petyt M (1990) Introduction to finite element vibration analysis, 2nd edn. Cambridge University Press, New York
Acharjee S, Zabaras N (2007) A non-intrusive stochastic Galerkin approach for modeling uncertainty propagation in deformation processes. Comput Struct 85:244–254
Pradhan KK, Chakraverty S (2013) Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh-Ritz method. Compos B Eng 51:175–184
Dovstam K (1995) Augmented Hooke’s law in frequency domain. A three dimensional, material damping formulation. Int J Solids Struct 32:2835–2852
Tzou HS, Howard RV (1994) A piezothermoelastic thin shell theory applied to active structures. J Vibr Acoust 116:295–302
Sharma S, Vig R, Kumar N (2015) Active vibration control: considering effect of electric field on coefficients of PZT patches. Smart Struct Syst 16:1091–1105
Smittakorn W, Heyliger PR (2000) A discrete-layer model of laminated hygrothermopiezoelectric plates. Mech Compos Mater Struct 7:79–104
Dyke SJ, Spencer BF, Sain MK, Carlson JD (1996) Modeling and control of magnetorheological dampers for seismic response reduction. Smart Mater Struct 5:565
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Kheiri Sarabi, B., Sharma, M., Kaur, D. (2018). Mathematical Model of Cantilever Plate Using Finite Element Technique Based on Hamilton’s Principle. In: Nandi, A., Sujatha, N., Menaka, R., Alex, J. (eds) Computational Signal Processing and Analysis. Lecture Notes in Electrical Engineering, vol 490. Springer, Singapore. https://doi.org/10.1007/978-981-10-8354-9_16
Download citation
DOI: https://doi.org/10.1007/978-981-10-8354-9_16
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-8353-2
Online ISBN: 978-981-10-8354-9
eBook Packages: EngineeringEngineering (R0)