Structural and Multidisciplinary Optimization https://doi.org/10.1007/s00158-020-02714-0 RESEARCH PAPER Optimization of beam profiles for improved piezoelectric energy harvesting efficiency C. Volkan Karadag 1 · Seyda Ertarla 1 · Nezih Topaloglu 1 · A. Fethi Okyar 1 Received: 2 April 2020 / Revised: 11 July 2020 / Accepted: 5 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract Piezoelectric cantilever beams are among the most popular vibration energy harvesting devices. Homogenization of the spatial distribution of axial strain along those beams increases harvesting efficiency. The general approach to minimize axial strain variation is to use triangular or trapezoidal width profiles. In this study, a width profile function that includes curved shapes is proposed and a finite element–based optimization scheme is constructed to maximize harvesting efficiency. A distribution parameter is defined for quantifying the strain uniformity. Optimization is performed for various tip mass values, using this parameter as the objective function. It is shown that curved beam profiles exhibit less variation in axial strain, compared to triangular and rectangular beams. Optimized shapes for minimal strain variation at resonance are determined. Experimental results also validate the findings of the optimization. At least 22% increase in strain uniformity is obtained with the optimized-shaped beam, compared to a triangular beam when no tip mass is used. The increase in strain uniformity becomes 29% when the tip mass is increased to 5 g. The results indicate the potential of employing beam-type piezoelectric energy harvesters with optimized width profiles. Keywords Shape optimization · Vibration energy harvesting · Finite element method · Piezoelectric energy harvesting · Deflection measurement 1 Introduction Research on vibration energy harvesting has increased in recent years. Applications of vibration energy harvesters (VEH) hold up as wireless sensor networks, body sensor networks, and portable electronic devices for today and future (Senthilkumar et al. 2019). Electromagnetism (Foisal et al. 2012), electrostatics (Lee et al. 2009), and piezo- electricity (Karadag and Topaloglu 2016; Pasharavesh et al. 2017) are three common methods that generate energy from vibration. Among vibration energy harvesting meth- ods, piezoelectric cantilever beam–based energy harvesting is a common and effective approach. Responsible Editor: Byeng D Youn This research has been funded by TUBITAK (The Scientific and Technological Research Council of Turkey) under Grant No. 117M101.  Nezih Topaloglu nezih.topaloglu@yeditepe.edu.tr 1 Yeditepe University, Faculty of Engineering, Atasehir, 34755, Istanbul, Turkey Optimization of the performance of vibration energy har- vesters has been a major topic of research. As an example, a robust genetic algorithm–based optimization that maxi- mizes the power transmissibility and bandwidth of a bistable electromagnetic energy harvester (Yang and Zhou 2019) was presented. The effects of parameter uncertainties were considered, and an experimental verification was given. Dai and Harne (2018) assessed the effect of harmonic base exci- tation frequency, stiffness nonlinearity, and stochastic base excitation on output electrical power and determined the optimal load resistance resulting in maximum output power. Cai and Harne (2019a) constructed an analytical model of a piezoelectric energy harvester with power conditioning circuitry. The influence of output impedance, excitation fre- quency, and the duty cycle of the buck-boost converter was analyzed, and the optimal duty cycle for maximum DC power delivery was obtained. Franco and Varoto (2017) employed sequential quadratic planning and found the opti- mal beam length, piezo-layer length, tip mass height, and load resistance that maximizes the output voltage and power within a predefined excitation frequency range. The effect of parameter uncertainties was also investigated by intro- ducing random perturbations in the optimal parameters and