Abstract
In this paper, a frequency-domain spectral finite element model (SFEM) is developed for dynamic analysis of piezoelectric laminated composite beams. The displacement field of the beam is represented by the first-order shear deformation theory (FSDT). The electric potential for the piezoelectric layer is expressed in two ways: (i) distributed linearly through the thickness and (ii) layerwise through thickness distribution consistent with the FSDT. The governing differential equation of motion for piezoelectric laminated composite beam is obtained using Hamilton’s principle. These time-domain equations are transformed to frequency domain using the Fourier transformation. The spectral element is derived from the exact solution of the frequency domain governing equations of motion. The formulation is validated by comparing the results of the natural frequencies with the published finite element method (FEM) results. The developed element is used to perform dispersion, free vibration analysis, and elastic wave propagation in laminated composite beam fully or partially covered with surface-bonded piezoelectric layer.
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References
Gopalakrishnan S, Chakraborty A, Mahapatra DR (2007) Spectral finite element method. Springer, London
Doyle JF (1997) Wave propagation in Structures. Springer, New York
Patera AT (1984) Spectral element method for fluid dynamics: laminar flow in a channel expansion. J Comput Phys 54:468–488
Peng H, Ye L, Meng G, Mustapha S, Li F (2010) Concise analysis of wave propagation using the spectral element method and identification of delamination in CF/EP composite beams. Smart Mater Struct 19:085018
Li F, Peng H, Sun X, Wamg J, Meng G (2012) Wave propagation analysis in composite laminates containing a delamination using a three-dimensional; spectral element method. Math Prob Eng 1:1–19
Kudela P, Zak A, Krawczuk M, Ostachowicz W (2007) Modelling of wave propagation in composite plates using the time domain spectral element method. J Sound Vib 302:728–745
Zak A, Krawczuk M, Ostachowicz W (2006) Propagation of in-plane elastic waves in a composite panel. Finite Elem Anal Design 43:145–154
Doyle JF (1988) A spectrally formulated finite element for longitudinal wave propagation. Int J Anal Exp Modal Anal 3:1–5
Doyle JF, Farris TN (1990) A spectrally formulated finite element for flexural wave propagation in beams. Int J Anal Exp Modal Anal 5:13–23
Gopalakrishnan S, Martin M, Doyle JF (1992) A matrix methodology for spectral analysis of wave propagation in multiple connected Timoshenko beams. J Sound Vib 158:11–24
Lee U, Kim J, Leung AYT (2000) The spectral element method in structural dynamics. The Shock Vib Digest 32:451–465
Mahapatra DR, Gopalakrishnan S, Shankar TS (2000) Spectral element based solution for wave propagation analysis of multiply connected unsymmetric laminated composite beams. J Sound Vib 237:819–836
Ruotolo R (2004) A spectral element for laminated composite beams: theory and application to pyroshock analysis. J Sound Vib 270:149–169
Mitra M, Gopalakrishnan S (2005) Spectrally formulated wavelet finite element for wave propagation and impact force identification in connected 1D waveguides. Int J Solids Struct 42:4695–4721
Lee U, Jang I (2010) Spectral element model for axially loaded bending-shear-torsion coupled composite Timoshenko beams. Compos Struct 92:2860–2870
Nanda N, Kapuria S, Gopalakrishnan S (2014) Spectral finite element based on an efficient layerwise theory for wave propagation analysis of composite and sandwich beams. J Sound Vib 333:3120–3137
Smaratunga D, Jha R, Gopalakrishnan S (2014) Wave propagation analysis in laminated composite plates with transverse cracks using the wavelet spectral finite element method. Finite Elem Anal Des 89:19–32
Lee HJ, Saravanos DA (1996) Coupled layerwise analysis of thermopiezoelectric composite beams. AIAA J 34:1231–1237
Kapuria S, Alam N (2006) Efficient layerwise finite element model for dynamic analysis of laminated piezoelectric beams. Comput Methods Appl Mech Eng 195:2742–2760
Bendary IM, Elshafei MA, Riad AM (2010) Finite element model of smart beams with distributed piezoelectric actuators. J Intell Mater Syst Struct 21:747–758
Sulbhewar LN, Raveendranath P (2016) A Timoshenko piezoelectric beam finite element with consistent performance irrespective of geometric and material configurations. Lat Am J Solids Struct 13:992–1015
Lee U, Kim D, Park I (2013) Dynamic modeling and analysis of the PZT-bonded composite Timoshenko beams: Spectral element method. J Sound Vib 332:1585–1609
Song Y, Kim S, Park I, Lee U (2015) Dynamics of two layer smart composite Timoshenko beams: Frequency domain spectral element analysis. Thin-Walled Struct 89:84–92
Acknowledgements
The author gratefully acknowledges the financial assistance by the Science and Engineering Research Board, Department of Science and Technology, New Delhi, under Start-up grant for Young Scientists.
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Nanda, N. (2020). Spectral Finite Element for Dynamic Analysis of Piezoelectric Laminated Composite Beams. In: Singh, B., Roy, A., Maiti, D. (eds) Recent Advances in Theoretical, Applied, Computational and Experimental Mechanics. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-1189-9_7
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DOI: https://doi.org/10.1007/978-981-15-1189-9_7
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