Design of quasistatic piezoelectric plate based transducers by using topology optimization

摘要

Sensors and actuators based on piezoelectric plates have shown relevance in the field of smart structures. Recently, modern design techniques such as the topology optimization method have been applied to design laminated piezoelectric transducers, and design requirements such as maximizing static displacements (actuator design) and output voltages (sensor design) have been employed. However, it may be desirable to keep the transducer working range before its first resonance frequency. In this case, the (displacement or voltage) amplitude is expected to be constant with excitation frequency, which may not be the case when only static design requirements are employed. Thus, considering sensor design, if the amplitude is constant, an undetected change in the excitation frequency would cause a small measurement error. Regarding actuators, on the other hand, if the first resonance frequency is small, oscillations in the response to a step excitation (which is usually applied in quasi-static applications, i.e. applications in which the transducer operates under the first resonance frequency) could be high, ultimately causing overshoot, for instance. Thus, in this work, the topology optimization method has been applied to design piezoelectric transducers considering quasi-static operation, by distributing piezoelectric material over a metallic plate and by selecting the material polarization sign, in order to fulfil quasi-static design requirements. This is achieved by maximizing an objective function that depends on both displacements (for actuators) or output voltages (for sensors), and first resonance frequencies. The applied methodology, which encompasses the optimization problem formulation and numerical implementation, is presented. The achieved computational results, corresponding to the design of different types of transducers, clearly show the potential of the proposed methodology to increase the quasi-static working frequency range.