Abstract
Basically, the piezoelectric coupling coefficient is represented by the symbol \(d_{ij}\). The subscript i implies the direction of applied electric field, while j denotes the direction of induced strain. In piezoceramics, a high DC voltage is applied between a pair of electroded faces to establish the initial polarization within the piezoelectric material along the three axes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
A part of results in this chapter are already published [10].
References
Parashar SK, Wagner UV, Hagedorn P (2005) Nonlinear shear-induced flexural vibrations of piezoceramic actuators: experiments and modeling. J Sound Vib 285:989–1014
Sun CT, Zhang XD (1995) Use of thickness-shear mode in adaptive sandwich structures. Smart Mater Struct 4:202–206
Benjeddou A, Trindade MA, Ohayon R (1997) A unified beam finite element model for extension and shear piezoelectric actuation mechanisms. J Intell Mater Syst Struct 8:1012–1025
Trindade MA, Benjeddou A, Ohayon R (1999) Parametric analysis of the vibration control of sandwich beams through shear-based piezoelectric actuation. J Intell Mater Syst Struct 10:377–85
Aldraihem OJ, Khdeir AA (2000) Smart beams with extension and thickness-shear piezoelectric actuators. Smart Mater Struct 9:1–9
Shindo Y, Narita F, Mikami M, Saito F (2006) Nonlinear dynamic bending and domain wall motion in functionally graded piezoelectric actuators under AC electric fields: simulation and experiment. JSME Int J Ser A 49(2):188–94
Su Z, Jin G, Ye T (2016) Vibration analysis and transient response of a functionally graded piezoelectric curved beam with general boundary conditions. Smart Mater Struct 25(6):065003
Mindlin RD, Tiersten HF (1962) Effects of couple-stresses in linear elasticity. Arch Rat Mech Anal 11(1):415–48
Tadi Beni Y (2016) Size-dependent electromechanical bending, buckling, and free vibration analysis of functionally graded piezoelectric nanobeams. J Intell Mater Syst Struct 27(16):2199–215
Parashar SK, Sharma P (2016) Modal analysis of shear-induced flexural vibration of FGPM beam using generalized differential quadrature method. Compos Structures 1(139):222–32
Parashar SK, DasGupta A, Wagner UV, Hagedorn P (2005) Nonlinear shear vibrations of piezoceramic actuators. Int J Non-Linear Mech 40(4):429–43
Wang Q, Quek ST (2000) Flexural vibration analysis of sandwich beam coupled with piezoelectric actuator. Smart Mater Struct 9:103–9
Liu X, Wang Q, Quek ST (2002) Analytical solution for free vibration of piezoelectric coupled moderately thick circular plates. Int J Solids Struct 39:2129–51
Rodriguez-Fortun JM, Orus J, Buil F, Castellanos JA (2010) General bond graph model for piezoelectric actuators and methodology for experimental identification. Mechatronics 20(2):303–14
Parashar SK, Wagner UV, Hagedorn P (2004) A modified Timoshenko beam theory for nonlinear shear-induced flexural vibrations of piezoceramic continua. Nonlinear Dyn 37:181–205
Sharma P, Parashar SK (2016) Exact analytical solution of shear-induced flexural vibration of functionally graded piezoelectric beam. In: AIP conference proceedings 2016 May 6, vol 1728, No. 1. AIP Publishing, New York, p 020167
Yang J, Xiang HJ (2007) Thermo-electro-mechanical characteristics of functionally graded piezoelectric actuators. Smart Mater Struct 16:784–97
Li YS, Feng WJ, Cai ZY (2014) Bending and free vibration of functionally graded piezoelectric beam based on modified strain gradient theory. Compos Struct 115:41–50
Chi SH, Chung YL (2006) Mechanical behavior of functionally graded material plates under transverse load– Part I: Analysis. Int J Solids Struct 43(13):3657–74
Bert CW, Malik M (1996) Differential quadrature method in computational mechanics: a review. Appl Mech Rev 49(1):1–28
Wang X, Gan L, Wang Y (2006) A differential quadrature analysis of vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses. J Sound Vib 298:420–31
Sharma P (2017) Vibration analysis of FGPM actuators excited under the shear effect. Submitted to Rajasthan Technical University Kota, Thesis
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Sharma, P. (2019). Vibration Analysis of FGPM Beam. In: Vibration Analysis of Functionally Graded Piezoelectric Actuators. SpringerBriefs in Applied Sciences and Technology(). Springer, Singapore. https://doi.org/10.1007/978-981-13-3717-8_5
Download citation
DOI: https://doi.org/10.1007/978-981-13-3717-8_5
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-3716-1
Online ISBN: 978-981-13-3717-8
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)