At present, numerical techniques allow the precise simulation of mechanical structures, but the results are limited by the knowledge of the material properties. In the case of piezoelectric ceramics, the full model determination in the linear range involves five elastic, three piezoelectric, and two dielectric complex parameters. A successful solution to obtaining piezoceramic properties consists of comparing the experimental measurement of the impedance curve and the results of a numerical model by using the finite element method (FEM). In the present work, a new systematic optimization method is proposed to adjust the full piezoelectric complex parameters in the FEM model. Once implemented, the method only requires the experimental data (impedance modulus and phase data acquired by an impedometer), material density, geometry, and initial values for the properties. This method combines a FEM routine implemented using an 8-noded axisymmetric element with a gradient-based optimization routine based on the method of moving asymptotes (MMA). The main objective of the optimization procedure is minimizing the quadratic difference between the experimental and numerical electrical conductance and resistance curves (to consider resonance and antiresonance frequencies). To assure the convergence of the optimization procedure, this work proposes restarting the optimization loop whenever the procedure ends in an undesired or an unfeasible solution. Two experimental examples using PZ27 and APC850 samples are presented to test the precision of the method and to check the dependency of the frequency range used, respectively.
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.
Piezoresistive sensors are commonly made of a piezoresistive membrane attached to a flexible substrate, a plate. They have been widely studied and used in several applications. It has been found that the size, position and geometry of the piezoresistive membrane may affect the performance of the sensors. Based on this remark, in this work, a topology optimization methodology for the design of piezoresistive plate-based sensors, for which both the piezoresistive membrane and the flexible substrate disposition can be optimized, is evaluated. Perfect coupling conditions between the substrate and the membrane based on the ‘layerwise’ theory for laminated plates, and a material model for the piezoresistive membrane based on the solid isotropic material with penalization model, are employed. The design goal is to obtain the configuration of material that maximizes the sensor sensitivity to external loading, as well as the stiffness of the sensor to particular loads, which depend on the case (application) studied. The proposed approach is evaluated by studying two distinct examples: the optimization of an atomic force microscope probe and a pressure sensor. The results suggest that the performance of the sensors can be improved by using the proposed approach.
Summary With the increasing advances in the oil and gas industry, seismic imaging near or under salt structures has become an important point in deep-water exploration. Detailed velocity models of these areas are particularly interesting not only to characterize hydrocarbon reservoirs but also to identify potential sites for hydrogen and carbon dioxide storage in offshore salt caverns. Thus, we study the Full Waveform Inversion (FWI) for the salt reconstruction in acoustic media with constant density considering the time-harmonic wave propagation in a Finite Element formulation using the Topology Optimization (TO) method. This problem is challenging due to the strong velocity contrast between salt bodies and the sedimentary background, in addition to the lack of low-frequency data and the inherent ill-posedness of the inverse problem. In this context, we incorporate techniques from the TO field, usually used in design applications, to overcome or reduce these known problems. We initially defined the squared slowness as a combination of two fields, one related to the salt shape and the other to the background. An interpolation rule based on the Solid Isotropic Material with Penalization (SIMP) method, combined with filtering and projection schemes, is used to find the shape of the salt bodies with increased sharpness interfaces. A Helmholtz-type filter is applied to modify the gradient aimed to regularize the problem and provide a more stable way for the salt shape to evolve during the inversion process. In particular, we demonstrate that the proposed approach may be relevant for reconstructing media with salt bodies when a suitable starting model is unavailable, and sharp interfaces are required. In addition, we present inversion results from synthetic data generated by a variable density model to demonstrate the approach capability when subjected to a reconstruction application.
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