In this paper, the location of masses and of a piezoelectric patch for energy harvesting reported onto a vibrating cantilever beam is studied and optimized. To this aim, a genetic algorithm is adapted and utilized to optimize the voltage amplitude generated by the piezoelectric patches by choosing attachment mass, attachment mass moment of inertia, attachment location, piezoelectric patch location and force location on the beam as parameters. While an analytical approach is proposed to evaluate the voltage amplitude, a multi-layer perceptron neural network is trained by the derived characteristic matrix to obtain an approximate function for natural frequencies based on the attachment parameters. The trained network is then used in the core of genetic algorithm to find the best optimization variables for any excitation frequency. Numerical simulation by COMSOL Multiphysics finite element software validates the calculated voltage by analytical approach. The optimization method successfully matches the natural frequency of the beam with the excitation frequency which therefore maximizes the output energy. On the other hand, the superiority of the optimized design over the conventional configuration in harvesting the energy at high frequency excitation is also approved.

Piezoelectric materials based actuators are highly recognized for the development of microrobotic systems thanks to their high bandwidth, high resolution and high force density. However, one of their main drawback is the low relative stroke (0.1% of actuator's size) that limits the actuator motion range. Overcoming this limitation is challenging but would increase the achievable working space of microrobots. In this paper, topology optimization method is used to maximize the actuator stroke. Instead of optimizing only the material density, we also consider the optimization of the electrodes polarity. This approach allows to combine both material expansion and compression in order to increase the actuator output displacement. To demonstrate this approach, two actuators were designed starting from a full domain considered as a basic reference piezoelectric actuator. The first design considered only the density optimization while the second one took into account the optimization of the topology of electrodes. Both simulation and experiment showed a good agreement between the obtained designs and the fabricated prototypes. The result revealed that the optimized design with polarization has an improved factors of 2.8 and 2.02 compared to full plate and actuator without electrodes optimization, respectively.

In this paper, piezoelectric plate energy harvesters are designed by using topology optimization algorithm to harvest the excitation from different directions. The goal is to minimize the volume and weight of the whole structure so the harvesters can be used in small scale applications. To this aim, the profile of polarization is optimized by the topology optimization to overcome charge cancellation which is the main challenge in random direction excitation. Two optimized designs with uniform and non-uniform polarization profiles are obtained. Separated electrodes in the surfaces of the optimized design with non-uniform polarization are used to simulate the polarization profile. Numerical simulations by COMSOL multi-physics software show that the optimized design with separated electrodes can provide 3 times higher voltage and power than those obtained with non-optimized piezoelectric plate. Experimental investigation demonstrated that the same design with separated electrodes can have 2.17 and 1.98 times higher voltage than the full plate for out of plane and in-plane forces respectively.

Currently, most of the piezoelectric structures are designed under deterministic conditions, where the influence of uncertain factors on the output motion accuracy is ignored. In this work, a probabilistic reliability-based topology optimization method for piezoelectric structure is proposed to deal with the working voltage uncertainty. A nested double-loop optimization algorithm of minimizing the total volume while satisfying the reliability requirement of the displacement performance is established, where the PEMAP-P (piezoelectric material with penalization and polarization) model is used for parameterization of stiffness matrix, piezoelectric coupling matrix, and polarization direction. This strategy consists of an inner loop for reliability analysis and an outer loop for topology optimization. The reliability index approach based on most probable point (MPP) is used for realizing the evaluation of reliability constraint in reliability analysis. The sensitivities of reliability constraint with respect to the random variables and design variables are detailed using the adjoint variable method. Typical examples are performed to illustrate the effectiveness of the proposed RBTO method. A comparison of the optimization results for different reliability indexes, standard deviations of the voltage, spring stiffnesses, and displacement limits are conducted, as well as the deterministic topology optimization results.