Topology optimization of flextensional piezoelectric actuators with active control law

Abstract

Flextensional actuators assembled in association with piezoceramics feature the amplification of nanometric displacements generated by the ceramics energy conversion. For applications that require high precision positioning or vibration response attenuation, such as hard disc reading or atomic force microscopy, a response tracking control needs to be implemented. Shell and plate piezoactuators with vibration control have been extensively studied in literature, however the design of controlled piezoelectric systems by means of the Topology Optimization Method (TOM) has not been fully explored in literature yet, and is generally focused on the frequency domain transient analysis, which employs a model reduction method for the sake of computational implementation. Dealing with transient analysis of flextensional piezoelectric actuators, an active closed loop control design is more suited for the positioning and vibration problem, which consists on measuring the outputs of the system by the closed loop sensor layer, whose signal is modified by a control gain and eventually inputted into the actuator layer so the system response signal is modulated. Aiming to enhance the active feedback control in piezoelectric actuators (PEAs), this work targets the design of the flextensional microstructure considering an active velocity feedback control (AVFC), where the active piezoelectric sensing and actuating cycles imply in an extra damping to the system. Therefore, the flextensional mechanism compliance shall be distributed within the design domain by the allocation of void regions where there should be the flexible hinges. Such a design can be accomplished by means of the TOM, which employs a systematic analysis of the dynamic model through the finite element method (FEM). In this work, the finite element (FE) system model takes into account the piezoelectric ceramics intermediate nodes, what is denominated as non-collapsed piezoelectric nodes model, and whose induced voltage during the time domain dynamic response contributes to the active control of the system. The topology optimization (TO) problem is formulated for the system vibration suppression at the restoring position and at the actuated position (positioner) subject to material volume and design variables constraints. The TOM implemented is based on the solid isotropic material with penalization (SIMP), the dynamic adjoint sensitivity, and on the optimization solver known as sequential linear programming (SLP). To illustrate the method, bidimensional examples of optimized topologies are numerically obtained by employing different velocity feedback control gains, and the topologies efficiency are compared and contrasted.

A Review of Dielectric Elastomer Generator Systems

“…To demonstrate the operating principle of the system and validate analytical models, the authors built a prototype using acrylic VHB as the DE and operated it at low frequencies, achieving convertible power densities on the order of 2 mW cm À3 . Consistently with established results in the field of inertial energy harvesting, [73,145] they pointed out that the system delivers maximum power output when the vibrations excitation frequency equals a natural frequency of the system, i.e., in resonance conditions.…”

“…In applications, this allows the achievement of large DEG deformations with limited input forces and with no need for external static or dynamic negative-spring mechanisms for DEG's stiffness compensation. [44,61,73] Nonetheless, this elastomer has large hysteresis losses and non-negligible electrical conductivity, which limit the efficiency and the convertible energy in practical applications. The value of self-discharging time constant τ d suggests that this material is unsuitable for low-frequency applications (on the order of 10 À1 Hz).…”

“…Up until now, point absorber DEGS-based WECs have been the most widely investigated. [23,73,154,155] These systems generally rely on WEC layouts proposed in the past, [6] from which they differ in that they hold a DEG PTO instead of conventional generators. Their operating principle is schematically shown in Figure 18a.…”

A Multi-Parameter Perturbation Solution and Experimental Verification for Bending Problem of Piezoelectric Cantilever Beams

“…. ,18): From Equations (43)-(48) and (54), we may obtain the unknown functions of g II i (Z) and f II i (Z) 2,4,5,7,8,10,11,13,14,16,17) , (A17)…”

“…Piezoelectric polymers have been widely used in sensors, actuators, electronic information and intelligent structures because of its great force-electric coupling characteristics [1][2][3][4][5][6]. The piezoelectric polymers usually participate in the work of piezoelectric instruments in the form of piezoelectric sheets which usually are simplified to a piezoelectric cantilever beam [7][8][9].The problems of piezoelectric cantilever beams are usually difficult to be solved analytically due to the existence of the force-electric coupling constitutive relation. It is known that the design of piezoelectric instruments often requires the analytical expression of the problem of piezoelectric cantilever beams as a theoretical reference.…”