Laminated composite panels are extensively used in various engineering applications. Piezoelectric transducers can be integrated into such composite structures for a variety of vibration control and energy harvesting applications. Analyzing the structural dynamics of such electromechanical systems requires precise modeling tools which properly consider the coupling between the piezoelectric elements and the laminates. Although previous analytical models in the literature cover vibration analysis of laminated composite plates with fully covered piezoelectric layers, they do not provide a formulation for modeling the piezoelectric patches that partially cover the plate surface. In this study, a methodology for vibration analysis of laminated composite plates with surface-bonded piezo-patches is developed. Rayleigh–Ritz method is used for solving the modal analysis and obtaining the frequency response functions. The developed model includes mass and stiffness contribution of the piezo-patches as well as the two-way electromechanical coupling effect. Moreover, an accelerated method is developed for reducing the computation time of the modal analysis solution. For validations, system-level finite element simulations are performed in ANSYS software. The results show that the developed analytical model can be utilized for accurate and efficient analysis and design of laminated composite plates with surface-bonded piezo-patches.
AghakhaniABasdoganI (2017) Equivalent impedance electroelastic modeling of multiple piezo-patch energy harvesters on a thin plate with AC-DC conversion. IEEE/ASME Transactions on Mechatronics22(4): 1575–1584.
2.
AridoganUBasdoganIErturkA (2014) Analytical modeling and experimental validation of a structurally integrated piezoelectric energy harvester on a thin plate. Smart Materials and Structures23(4): 45039.
3.
AridoganUBasdoganIErturkA (2016) Random vibration energy harvesting on thin plates using multiple piezopatches. Journal of Intelligent Material Systems and Structures27: 1–13.
4.
ArrietaAFHagedornPErturkAet al. (2010) A piezoelectric bistable plate for nonlinear broadband energy harvesting. Applied Physics Letters97(10): 104102.
5.
BallhauseDD’OttavioMKröplinBet al. (2005) A unified formulation to assess multilayered theories for piezoelectric plates. Computers & Structures83: 1217–1235.
6.
BatraRCLiangXQ (1997) The vibration of a rectangular laminated elastic plate with embedded piezoelectric sensors and actuators. Computers & Structures63(2): 203–216.
7.
BayikBAghakhaniABasdoganIet al. (2016) Equivalent circuit modeling of a piezo-patch energy harvester on a thin plate with AC-DC conversion. Smart Materials and Structures25(5): 55015.
8.
BenjeddouADeüJFLetombeS (2002) Free vibrations of simply-supported piezoelectric adaptive plates: an exact sandwich formulation. Thin-walled Structures40: 573–593.
9.
BhatRB (1985) Natural frequencies of rectangular plates using characteristic orthogonal polynomials in Rayleigh–Ritz method. Journal of Sound and Vibration102(4): 493–499.
10.
ChandrashekharaKAgarwalAN (1993) Active vibration control of laminated composite plates using piezoelectric devices: a finite element approach. Journal of Intelligent Material Systems and Structures4(4): 496–508.
11.
Cook-ChennaultKAThambiNSastryAM (2008) Powering MEMS portable devices—a review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems. Smart Materials and Structures17(4): 043001.
12.
CorreiaVMFGomesMAASulemanAet al. (2000) Modelling and design of adaptive composite structures. Computer Methods in Applied Mechanics and Engineering185: 325–346.
13.
De GodoyTCTrindadeM (2011) Modeling and analysis of laminate composite plates with embedded active—passive piezoelectric networks. Journal of Sound and Vibration330: 194–216.
14.
GohariSSharifiSVrceljS (2016) New explicit solution for static shape control of smart laminated cantilever piezo-composite-hybrid plates/beams under thermo-electro-mechanical loads using piezoelectric actuators. Composite Structures145: 89–112.
15.
GurdalZHaftkaRTHajelaP (1999) Design and Optimization of Laminated Composite Materials. New York: John Wiley & Sons.
16.
HeyligerPDASaravanos (1995) Exact free-vibration analysis of laminated plates with embedded piezoelectric layers. The Journal of the Acoustical Society of America98(3): 1547–1557.
17.
JiangSLiWLYangTet al. (2016) Free vibration analysis of doubly curved shallow shells reinforced by any number of beams with arbitrary lengths. Journal of Vibration and Control22(2): 570–584.
18.
LamKYPengXQLiuGRet al. (1997) A finite-element model for piezoelectric composite laminates. Smart Materials and Structures6: 583–591.
19.
LiuGRPengXQLamKYet al. (1999) Vibration Control Simulation of Laminated Composite Plates with Integrated Piezoelectrics. Journal of Sound and Vibration220(5): 827–846.
20.
MeirovitchL (2001) Fundamentals of Vibrations. New York: McGraw-Hill.
21.
ParkJHHwangJHLeeCSet al. (2001) Stacking sequence design of composite laminates for maximum strength using genetic algorithms. Composite Structures52(2): 217–231.
22.
Phung-VanPDe LorenzisLThaiCHet al. (2015) Analysis of laminated composite plates integrated with piezoelectric sensors and actuators using higher-order shear deformation theory and isogeometric finite elements. Computational Materials Science96: 495–505.
23.
ReddyJN (1999) On laminated plates with integrated sensors and actuators. Engineering Structures21: 568–593.
24.
RuppCJEvgrafovAMauteKet al. (2009) Design of piezoelectric energy harvesting systems: a topology optimization approach based on multilayer plates and shells. Journal of Intelligent Material Systems and Structures20(16): 1923–1939.
25.
SaravanosDA (1999) Damped vibration of composite plates with passive piezoelectric-resistor elements. Journal of Sound and Vibration221(5): 867–885.
26.
SaravanosDAHeyligerPRHopkinsDA (1997) Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates. International Journal of Solids and Structures34(3): 359–378.
27.
ShojaeeSValizadehNIzadpanahEet al. (2012) Free vibration and buckling analysis of laminated composite plates using the NURBS-based isogeometric finite element method. Composite Structures94(5): 1677–1693.
28.
SodanoHAInmanDJParkG (2004) A review of power harvesting from vibration using piezoelectric materials. Shock and Vibration Digest36(3): 197–206.
29.
SulemanAVenkayaVB (1995) A simple finite element formulation for a laminated composite plate with piezoelectric layers. Journal of Intelligent Material Systems and Structures6(6): 776–782.
30.
XingYFLiuB (2009) New exact solutions for free vibrations of thin orthotropic rectangular plates. Composite Structures89(4): 567–574.
31.
YoonHYounBDKimHS (2016) Kirchhoff plate theory-based electromechanically-coupled analytical model considering inertia and stiffness effects of a surface-bonded piezoelectric patch. Smart Materials and Structures25(2): 25017.
32.
ZhangZFengCLiewKM (2006) Three-dimensional vibration analysis of multilayered piezoelectric composite plates. International Journal of Engineering Science44: 397–408.
