## 1 Introduction
In recent years, researchers have been studying piezoelectric plate actuators for use in active vibration cancelation, for example, in the articles [9; 10; 11]. However, most piezoelectric actuators are generally limited to either discrete rectangular patches or a single thin sheet of material in order to provide adequate actuated performance. In the discrete patch system, one of the major drawbacks is the management of higher modes, which results in highly involved control schemes that are difficult to implement, as mentioned by [12]. The same source also stated that a single sheet form exhibits modal phase cancellation, which severely restricts the ability to control the structure's higher vibration modes. The voltage-strain sensitivity of a single piezoelectric patch, whether one-sided or bimorph, is rather low, so it is unable to generate considerable control force [13]. Increasing the actuator sensitivity can be achieved by using very high input voltages, but this can lead to problems such as patch burning and extra safety requirements for working with high voltages, as confirmed by the same source. In addition, the high voltages are not usually supplied by the work environment. Considered the abovementioned limitations, multi-layer piezoelectric actuators (MPA) were suggested by [12; 13] as enhanced vibration control actuators. According to these two sources, the MPA is a simple method that uses a larger number of layers at the same point, one below the other in the thickness direction, and drives the same input voltage for every layer. The research by [12] performed active control experiments on a cantilever honeycomb sandwich panel (CHSP) using an MPA. These experiments included the resonant vibration control and the sinusoidal sweep of the control system for different piezoelectric layer numbers. The results showed that the MPA could effectively control the vibration of the high damping HSP, and the control performance per voltage by the proposed actuator could be improved significantly by increasing the piezoelectric patch number. Consequently, the MPA exhibited better actuation capability than that with only a single layer. The work [13] investigated the voltage moment sensitivity of the MPA for vibration control, embedded into the surface of thin-walled beam-type structures. It was indicated that the MPA could increase the actuation performance for a low input voltage and, to a lesser extent, alter the mass, stiffness, and strength of the structure it controlled. While the multilayer piezoelectric actuator (MPL) exhibits excellent actuation performance, unfortunately, researchers have not investigated the actuation performance of layers of different materials versus layers of the same materials, nor the cost-effectiveness of designing MPL actuators with only high-quality piezoelectric materials. These are the main motives of this article. Therefore, this article examines the relative performance of two pairs of piezoelectric plates. The candidate plate pairs are plates of the same dimensions/different materials and plates of the same material/different dimensions as shown in Figures 1a and 1b, respectively, so that both actuation performance and cost requirements are met. Therefore, the primary objective of this article is to design and recommend a high-performance piezoelectric actuator for active vibration cancellation. In order to accomplish this main objective, this article addresses the selection of the optimal material for piezoelectric plate actuators and performs multiphysics modeling of individual piezoelectric plates and pairs of piezoelectric plates. This article uses two methods of multicriteria decision making (MCDM) to select materials, namely figure of merit (FOM) and technique for order preference by similarity to ideal solutions (TOPSIS). The goal of the multiphysics modeling in this article is to identify the superior pair of piezoelectric plates from the two candidates mentioned above.