Document Type : Research Paper

**Authors**

School of Mechanical Engineering, College of Engineering, University of Tehran, Iran

**Abstract**

Energy harvesting is a conventional method to collect the dissipated energy of a system. In this paper, we investigate the optimal location of a piezoelectric element to harvest maximum power concerning different excitation frequencies of a vibrating cantilever beam. The cantilever beam oscillates by a concentrated sinusoidal tip force, and a piezoelectric patch is integrated on the beam to generate electrical energy. To this end, the system is modeled with analytical governing equations, then a Deep Neural Network (DNN)-based surrogate model is developed to appropriately model the system within the range of its first three natural frequencies. The surrogate model has significantly abated the computation cost. Thus, the optimization time is reduced drastically. Our investigations led to an optimal piezoelectric location for different excitation frequencies, which can result in maximum electrical output power. This location is highly dependent on the excitation frequency. When excitation frequency equals to natural frequencies, the maximum harvested power increases considerably.

**Keywords**

[1] Mitcheson, P.D., et al., MEMS electrostatic micropower generator for low frequency operation. 2004. 115(2-3): p. 523-529.

[2] Williams, C., R.B.J.s. Yates, and a.A. Physical, Analysis of a micro-electric generator for microsystems. 1996. 52(1-3): p. 8-11.

[3] Anton, S.R., H.A.J.S.m. Sodano, and Structures, A review of power harvesting using piezoelectric materials (2003–2006). 2007. 16(3): p. R1.

[4] Cook-Chennault, K.A., et al., Powering MEMS portable devices—a review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems. 2008. 17(4): p. 043001.

[5] Qaisi, M.I.J.A.A., Application of the harmonic balance principle to the nonlinear free vibration of beams. 1993. 40(2): p. 141-151.

[6] Zohoor, H. and F.J.S.I. Kakavand, Vibration of Euler–Bernoulli and Timoshenko beams in large overall motion on flying support using finite element method. 2012. 19(4): p. 1105-1116.

[7] Azrar, L., et al., Semi-analytical approach to the non-linear dynamic response problem of S–S and C–C beams at large vibration amplitudes Part I: general theory and application to the single mode approach to free and forced vibration analysis. 1999. 224(2): p. 183-207.

[8] Jahani, K., M.M. Rafiei, and R. Aghazadeh Ayoubi, Development of a laboratory system to investigate and store electrical energy from the vibrations of a piezoelectric beam %J Energy Equipment and Systems. 2016. 4(2): p. 161-168.

[9] Mateu, L., F.J.J.o.I.M.S. Moll, and Structures, Optimum piezoelectric bending beam structures for energy harvesting using shoe inserts. 2005. 16(10): p. 835-845.

[10] Anderson, T.A. and D.W. Sexton. A vibration energy harvesting sensor platform for increased industrial efficiency. In Smart Structures and Materials 2006: Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems. 2006. International Society for Optics and Photonics.

[11] Jiang, S., et al., Performance of a piezoelectric bimorph for scavenging vibration energy. 2005. 14(4): p. 769.

[12] de Almeida, B.V., R.J.J.o.A. Pavanello, and C. Mechanics, Topology Optimization of the Thickness Profile of Bimorph Piezoelectric Energy Harvesting Devices. 2019. 5(1): p. 113-127.

[13] Mohammadi, A., et al. Passive vibration control of a cantilever beam using shunted piezoelectric element. in 2017 5th RSI International Conference on Robotics and Mechatronics (ICRoM). 2017. IEEE.

[14] Roundy, S., et al., Improving power output for vibration-based energy scavengers. 2005. 4(1): p. 28-36.

[15] Park, J., et al., Design optimization of piezoelectric energy harvester subject to tip excitation. 2012. 26(1): p. 137-143.

[16] Perera, A., et al., Machine learning methods to assist energy system optimization. 2019. 243: p. 191-205.

[17] Nguyen, T.H., D. Nong, and K.J.E.M. Paustian, Surrogate-based multi-objective optimization of management options for agricultural landscapes using artificial neural networks. 2019. 400: p. 1-13.

[18] Jeon, K., et al., Development of surrogate model using CFD and deep neural networks to optimize gas detector layout. 2019. 36(3): p. 325-332.

[19] Mousavi, S.M. and S.M. Rahnama, Shape optimization of impingement and film cooling holes on a flat plate using a feedforward ANN and GA %J Energy Equipment and Systems. 2018. 6(3): p. 247-259.

[20] Palagi, L., E. Sciubba, and L.J.A.E. Tocci, A neural network approach to the combined multi-objective optimization of the thermodynamic cycle and the radial inflow turbine for Organic Rankine cycle applications. 2019. 237: p. 210-226.

[21] White, D.A., et al., Multiscale topology optimization using neural network surrogate models. 2019. 346: p. 1118-1135.

[22] Villarrubia, G., et al., Artificial neural networks used in optimization problems. 2018. 272: p. 10-16.

[23] Hagood, N.W., et al., Modelling of piezoelectric actuator dynamics for active structural control. 1990. 1(3): p. 327-354.

[24] Meitzler, A., H. Tiersten, and D.J.N.Y.I.-A. Berlincourt, IEEE standard on piezoelectricity: an american national standard. 1988.

[25] Park, C.-H.J.J.o.S. and vibration, Dynamics modelling of beams with shunted piezoelectric elements. 2003. 268(1): p. 115-129.

[26] Inman, D.J., Vibration with control. 2006: Wiley Online Library.

[27] MacDonald, J.J.P.R., Successive approximations by the Rayleigh-Ritz variation method. 1933. 43(10): p. 830.

[28] Bengio, Y.J.F. and t.i.M. Learning, Learning deep architectures for AI. 2009. 2(1): p. 1-127.

[29] Moré, J.J., The Levenberg-Marquardt algorithm: implementation and theory, in Numerical analysis. 1978, Springer. p. 105-116.