Geometric nonlinear finite element and genetic algorithm based optimal vibration energy harvesting from nonprismatic axially functionally graded piezolaminated beam

Abstract

The present article deals with optimal vibration energy harvesting from an axially functionally graded (FG) non-prismatic piezolaminated beam using genetic algorithm (GA). Geometric nonlinear based finite element (FE) formulation using Newmark method in conjunction with Newton-Raphson method is formulated to solve the obtained governing equation. A two noded beam element with two degrees of freedom (DOF) at each node is used in the present FE formulation. The FG material (i.e. non-homogeneity) in the axial direction is considered which varies (continuously decreasing from root to tip of such cantilever beam) using a proposed power law formula. The various cross section profiles (such as linear, parabolic and cubic) are modelled using the Euler-Bernoulli beam theory. The effects of nonlinearity on the responses (such as displacement, voltage and output power) are deliberated with arbitrary power gradient index. The effects of tapers (both width and height in length directions) on the output power and voltage are analysed. A real-coded genetic algorithm based constrained optimization technique is also proposed to determine the best possible design variables for optimal power harvesting within the allowable limits of ultimate stress of beam and breakdown voltage of PZT sensor.

Keywords

Geometric nonlinearity axially functionally graded (FG) beam electromechanical coupling nonprismatic beam finite element analysis genetic algorithm optimal energy harvesting

Get full access to this article

View all access options for this article.

References

Abdelkefi

(2016) Aeroelastic energy harvesting: A review. International Journal of Engineering Science 100: 112–135.

Abdelkefi

Barsallo

(2016) Nonlinear analysis and power improvement of broadband low-frequency piezomagnetoelastic energy harvesters. Nonlinear Dynamics 83: 41–56.

Abdelkefi

Hajj

Nayfeh

(2013) Piezoelectric energy harvesting from transverse galloping of bluff bodies. Smart materials and structures 22: 015014.

Abdelkefi

Najar

Nayfeh

et al. (2011) An energy harvester using piezoelectric cantilever beams undergoing coupled bending–torsion vibrations. Smart materials and structures 20: 115007.

Abdelkefi

Nayfeh

Hajj

(2012) Effects of nonlinear piezoelectric coupling on energy harvesters under direct excitation. Nonlinear Dynamics 67: 1221–1232.

Abdelmoula

Abdelkefi

(2016) Piezoaeroelastic investigation on the control and energy harvesting of galloping systems. 57th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. 0209.

Ajitsaria

Choe

S-Y

Shen

et al. (2007) Modeling and analysis of a bimorph piezoelectric cantilever beam for voltage generation. Smart materials and structures 16: 447.

Alshorbagy

Eltaher

Mahmoud

(2011) Free vibration characteristics of a functionally graded beam by finite element method. Applied Mathematical Modelling 35: 412–425.

Anton

Sodano

(2007) A review of power harvesting using piezoelectric materials (2003–2006). Smart materials and structures 16: R1–R21.

10.

Arora

Tulshyan

Deb

(2010) Parallelization of binary and real-coded genetic algorithms on GPU using CUDA. Evolutionary Computation (CEC), 2010 IEEE Congress on. IEEE, pp. 1–8.

11.

Aydogdu

(2008) Semi-inverse method for vibration and buckling of axially functionally graded beams. Journal of Reinforced Plastics and Composites 27: 683–691.

12.

Ayed

Abdelkefi

Najar

et al. (2013) Design and performance of variable-shaped piezoelectric energy harvesters. Journal of intelligent material systems and structures 25: 174–186.

13.

Benasciutti

Moro

Zelenika

et al. (2010) Vibration energy scavenging via piezoelectric bimorphs of optimized shapes. Microsystem Technologies 16: 657–668.

14.

Bibo

Abdelkefi

Daqaq

(2015) Modeling and characterization of a piezoelectric energy harvester under Combined Aerodynamic and Base Excitations. Journal of Vibration and Acoustics 137: 031017.

15.

Bibo

Daqaq

(2013) Energy harvesting under combined aerodynamic and base excitations. Journal of sound and vibration 332: 5086–5102.

16.

Bichiou

Abdelkefi

Hajj

(2016) Nonlinear aeroelastic characterization of wind turbine blades. Journal of Vibration and Control 22: 621–631.

17.

Bruch

Jr Sloss

Adali

et al. (2000) Optimal piezo-actuator locations/lengths and applied voltage for shape control of beams. Smart materials and structures 9: 205.

18.

Castagnetti

(2013) A wideband fractal-inspired piezoelectric energy converter: design, simulation and experimental characterization. Smart materials and structures 22: 094024.

19.

Castagnetti

(2014) Comparison Between a Wideband Fractal-Inspired and a Traditional Multicantilever Piezoelectric Energy Converter. Journal of Vibration and Acoustics 137: 011006.

20.

Chuang

Y-C

Chen

C-T

Hwang

(2016) A simple and efficient real-coded genetic algorithm for constrained optimization. Applied Soft Computing 38: 87–105.

21.

Dai

Abdelkefi

Wang

(2014) Piezoelectric energy harvesting from concurrent vortex-induced vibrations and base excitations. Nonlinear Dynamics 77: 967–981.

22.

de Paula

Balthazar

Felix

JLP

(2013) Some comments on the nonlinear dynamics of a portal frame under base excitation. Shock and Vibration 20: 1093–1101.

23.

Deb

(2001) Multi-objective optimization using evolutionary algorithms, New York: John Wiley & Sons.

24.

Eggborn T. (2003) Analytical models to predict power harvesting with piezoelectric materials. MS Thesis, Virginia Polytechnic Institute and State University.

25.

Elishakoff

Candan

(2001) Apparently first closed-form solution for vibrating: inhomogeneous beams. International Journal of Solids and Structures 38: 3411–3441.

26.

Elishakoff

Guede

(2004) Analytical polynomial solutions for vibrating axially graded beams. Mechanics of Advanced Materials and Structures 11: 517–533.

27.

Elvin

Choi

(2003) A self-powered damage detection sensor. The Journal of Strain Analysis for Engineering Design 38: 115–124.

28.

Elvin

Spector

(2001) A self-powered mechanical strain energy sensor. Smart materials and structures 10: 293–299.

29.

Erturk

Inman

(2009) An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations. Smart materials and structures 18: 025009.

30.

Flynn

Sanders

(2002) Fundamental limits on energy transfer and circuit considerations for piezoelectric transformers. Power Electronics, IEEE Transactions on 17: 8–14.

31.

Gere

Timoshenko

(2001) Mechanics of materials Brooks. Cole, Pacific Grove, CA, 815–839.

32.

Herrera

Lozano

Sánchez

(2003) A taxonomy for the crossover operator for real‐coded genetic algorithms: An experimental study. International Journal of Intelligent Systems 18: 309–338.

33.

Huang

X-F

(2010) A new approach for free vibration of axially functionally graded beams with non-uniform cross-section. Journal of sound and vibration 329: 2291–2303.

34.

Hwang

W-S

Park

(1993) Finite element modeling of piezoelectric sensors and actuators. AIAA journal 31: 930–937.

35.

Iliuk

Balthazar

Tusset

et al. (2013a) A non-ideal portal frame energy harvester controlled using a pendulum. The European Physical Journal Special Topics 222: 1575–1586.

36.

Iliuk

Balthazar

Tusset

et al. (2013b) Application of passive control to energy harvester efficiency using a nonideal portal frame structural support system. Journal of intelligent material systems and structures 25: 417–429.

37.

Javed

Abdelkefi

Akhtar

(2016) An improved stability characterization for aeroelastic energy harvesting applications. Communications in Nonlinear Science and Numerical Simulation 36: 252–265.

38.

Jiang

Guo

et al. (2005) Performance of a piezoelectric bimorph for scavenging vibration energy. Smart materials and structures 14: 769–774.

39.

Korla

Leon

Tansel

et al. (2011) Design and testing of an efficient and compact piezoelectric energy harvester. Microelectronics Journal 42: 265–270.

40.

Leung A, Zhou W, Lim C, Yuen R and Lee U (2001) Dynamic stiffness for piecewise non-uniform Timoshenko column by power series – part I: Conservative axial force. International Journal for Numerical Methods in Engineering 51: 505–529.

41.

Masana

Daqaq

(2011) Electromechanical modeling and nonlinear analysis of axially loaded energy harvesters. Journal of Vibration and Acoustics 133: 011007.

42.

Mehraeen

Jagannathan

Corzine

(2010) Energy harvesting from vibration with alternate scavenging circuitry and tapered cantilever beam. Industrial Electronics, IEEE Transactions on 57: 820–830.

43.

Mukherjee

Chaudhuri

(2002) Piezolaminated beams with large deformations. International Journal of Solids and Structures 39: 4567–4582.

44.

Murin

Aminbaghai

Kutiš

(2010) Exact solution of the bending vibration problem of FGM beams with variation of material properties. Engineering structures 32: 1631–1640.

45.

Reddy

(2014) An Introduction to Nonlinear Finite Element Analysis: with applications to heat transfer, fluid mechanics, and solid mechanics, Oxford: OUP.

46.

Rosa

De Marqui Junior

(2014) Modeling and analysis of a piezoelectric energy harvester with varying cross-sectional area. Shock and Vibration. 2014.

47.

Roundy

Leland

Baker

et al. (2005) Improving power output for vibration-based energy scavengers. Pervasive Computing, IEEE 4: 28–36.

48.

Roundy

Wright

(2004) A piezoelectric vibration based generator for wireless electronics. Smart materials and structures 13: 1131.

49.

Roy

Chakraborty

(2008) GA-LQR based optimal vibration control of smart FRP composite structures with bonded PZT patches. Journal of Reinforced Plastics and Composites 28: 1383–1404.

50.

Roy

Chakraborty

(2009a) Genetic algorithm based optimal control of smart composite shell structures under mechanical loading and thermal gradient. Smart materials and structures 18: 115006.

51.

Roy

Chakraborty

(2009b) Optimal vibration control of smart fiber reinforced composite shell structures using improved genetic algorithm. Journal of sound and vibration 319: 15–40.

52.

Roy

Manikandan

Chakraborty

(2010) Improved shell finite element for piezothermoelastic analysis of smart fiber reinforced composite structures. Finite elements in analysis and design 46: 710–720.

53.

Sankar

(2001) An elasticity solution for functionally graded beams. Composites Science and Technology 61: 689–696.

54.

Shahba

Attarnejad

Hajilar

(2011a) Free vibration and stability of axially functionally graded tapered Euler-Bernoulli beams. Shock and Vibration 18: 683–696.

55.

Shahba

Attarnejad

Marvi

et al. (2011b) Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions. Composites Part B: Engineering 42: 801–808.

56.

Shahba

Rajasekaran

(2012) Free vibration and stability of tapered Euler–Bernoulli beams made of axially functionally graded materials. Applied Mathematical Modelling 36: 3094–3111.

57.

Sharpes

Abdelkefi

Priya

(2015) Two-dimensional concentrated-stress low-frequency piezoelectric vibration energy harvesters. Applied Physics Letters 107: 093901.

58.

Shenck

Paradiso

(2001) Energy scavenging with shoe-mounted piezoelectrics. IEEE micro 21: 30–42.

59.

Tusset

Piccirillo

Bueno

et al. (2015) Chaos control and sensitivity analysis of a double pendulum arm excited by an RLC circuit based nonlinear shaker. Journal of Vibration and Control 22: 3621–3637.

60.

Tzou

(1996) Analysis of piezoelastic structures with laminated piezoelectric triangle shell elements. AIAA journal 34: 110–115.

61.

Wahrhaftig AdM Brasil

Balthazar

(2013) The first frequency of cantilevered bars with geometric effect: a mathematical and experimental evaluation. Journal of the Brazilian Society of Mechanical Sciences and Engineering 35: 457–467.

62.

Wankhade

Bajoria

(2013) Free vibration and stability analysis of piezolaminated plates using the finite element method. Smart materials and structures 22: 125040.

63.

Wang

Q-s

Elishakoff

(2005) Semi-inverse method for axially functionally graded beams with an anti-symmetric vibration mode. Journal of sound and vibration 284: 1190–1202.