Mode Electromechanical Coupling Factor Research Articles

Optimal placement of thin piezoelectric patches for maximum modal coupling

The aim of this paper is to present an innovative approach for optimal placement of piezoelectric patches in the context of vibration control or energy harvesting applications. Targeting a specific mode shape and assuming that the addition of thin surface-bonded piezoelectric layers has a sufficiently weak influence, the analysis of the stress or strain fields over the bare structure directly provides the best areas for maximized piezoelectric coupling. The area extension of a patch is then optimized based on the modal electromechanical coupling factor. The whole process only requires a standard finite element model, without the need of any piezoelectric elements. Three criteria of increasing complexity are proposed and numerically validated on a benchmark structure which offers a non-standard geometry. Such criteria and methods may have a strong interest in an industrial context where coupled models or specific expertise in piezoelectric coupling are not always available.

Enhanced piezoelectric properties of KNN-based ceramics by synergistic modulation of phase constitution, grain size and domain configurations

Despite significant advancements in KNN-based piezoelectric ceramics, controlling their grain size remains a challenge, impacting reproducibility of piezoelectric properties. Here, we address this issue by initially investigating the defect chemistry of a ternary system 0.96 K0.48Na0.52Nb0.96Sb0.04O3-0.04Bi0.5Na0.5ZrO3-ABO3 (KNNS-BNZ-ABO3). The ABO3 dopant not only influences the phase constitution, but also induces different charge compensation mechanisms, affecting the grain size and domain configurations of ceramics. Furthermore, the relationship between the grain size and the piezoelectric properties is investigated. The superior piezoelectric charge coefficient (d33) of 435 pC/N, ultra-high planar mode electromechanical coupling factor (kp) of 0.62 and preferable temperature stability are obtained in KNN-based ceramics with large grain size (∼50 μm) and hierarchical domain structures. Finally, we elucidated the intrinsic and extrinsic contribution of the grain size on piezoelectric properties of KNN-based piezoceramics based on Rayleigh analysis. Our work provides an effective paradigm for the development of lead-free piezoelectric ceramics for industrial applications.

Achieving ultrahigh electromechanical properties with high TC in PNN-PZT textured ceramics

<001> textured Pb(Ni1/3Nb2/3)O3-PbZrO3-PbTiO3 (PNN-PZT) ceramics were prepared by templated grain growth (TGG) technique using 0.36PNN-xPZ-(0.64-x)PT (x = 0.23, 0.25 and 0.27) powder matrix. Optimum template content was derived to achieve the best electromechanical properties of textured ceramics. The piezoelectric coefficient d33 = 1165 pC/N, Curie temperature TC = 197 °C, longitudinal mode electromechanical coupling factor k33 = 0.86 and a very large effective piezoelectric strain coefficient d33* = 2041 pm/V were simultaneously achieved at the morphotropic phase boundary (MPB) composition (x = 0.25) with 3 vol.% BaTiO3 (BT) templates. Domain structures of textured ceramics were analyzed in detail to reveal the origin of these high piezoelectric and electromechanical properties.

Nonlinear modal electromechanical coupling factor for piezoelectric structures containing nonlinearities

Within the linear framework, the Modal Electromechanical Coupling Factor (MEMCF) is an important indicator to quantify the dynamic conversion of mechanical energy and electrical energy of piezoelectric structures. It is also an important tool to guide the piezoelectric damping design of linear structures. Advanced aircraft often fly in maneuvers, and the variable working conditions induce drastic changes in the load level on structures. Geometric and contact nonlinearities of thin-walled structures and joint structures are often activated. To achieve a good vibration reduction effect covering all working conditions, one cannot directly use linear electromechanical coupling theory to instruct the piezoelectric damping design for nonlinear structures. Therefore, this paper defines the Nonlinear Modal Electromechanical Coupling Factor (NMEMCF) and proposes the corresponding numerical method for the first time to quantitatively evaluate the electromechanical coupling capability of nonlinear piezoelectric structures. Three candidate definitions of the NMEMCF are given, including two frequency definitions and one energy definition. The energy definition is the most promising one. It is not only applicable to both conservative and dissipative nonlinear structures but also compatible with the linear MEMCF. In addition, based on the energy formula, the NMEMCF can be obtained by only performing one nonlinear modal analysis in the open-circuit state. The analytical findings and the numerical tool are validated against two piezoelectric structures with different types of nonlinearities. A strong correlation among the NMEMCF, geometric parameters, and energy dissipation is observed. The results confirm that the proposed NMEMCF captures the physics of the electromechanical coupling phenomenon associated with nonlinear piezoelectric structures and can be used as an essential design indicator of piezoelectric damping, especially for variable working conditions.

Energy harvesting efficiency of unimorph piezoelectric acoustic black hole cantilever shunted by resistive and inductive circuits

A unimorph piezoelectric cantilever equipped with an Acoustic Black Hole (ABH) termination is designed for broadband energy harvesting. The ABH termination, with its tapered region, induces a focusing of the flexural vibrations which can be used to increase the efficiency of an energy harvesting device. A modal-based analytical model is presented, providing an explicit form of the electro-mechanical coupling for each beam eigenmode. Closed-form expressions for the coupled mechanical response and electrical outputs are obtained, allowing one to draw out a complete parametric study to optimize the device. The optimization procedure is conducted following two steps: first, optimal location and dimensions of a single piezoelectric patch are achieved by maximizing the modal electro-mechanical coupling factor (MEMCF) for each structural mode. Thanks to the proposed analytical approach, it is clearly shown that by putting the piezoelectric patch at the maximum of the strain field in the tapered termination, and by adjusting its length in accordance with the focalization created by the ABH effect, the ABH cantilever produces much higher MEMCFs over a wide frequency range and thus outperforms those of a uniform beam. Second, optimization of the shunted circuit is comprehensively performed for a circuit with only resistance, or both resistance and inductance, in series or in parallel. Analytical results show that the key design rule resides in matching the time scale of the circuit with that of the forcing frequency. Addition of the inductance allows enhancing the performance, but on a narrow frequency band. Finally, broadband advantages can be further obtained by considering multiple piezoelectric patches, in which the optimum is obtained when the shunted circuit in each patch is tuned targeting an eigenmode of the ABH beam.

High piezoelectricity after field cooling AC poling in temperature stable ternary single crystals manufactured by continuous-feeding Bridgman method

After field cooling (FC) alternating current poling (ACP), we investigated the dielectric and piezoelectric properties of [001]pc-oriented 0.24Pb(In1/2Nb1/2)O3 (PIN)-0.46Pb(Mg1/3Nb2/3)O3 (PMN)-0.30PbTiO3 (PT) (PIMN-0.30PT) single crystals (SCs), which were manufactured by continuous-feeding Bridgman (CF BM) within morphotropic phase boundary (MPB) region. By ACP with 4 kVrms/cm from 100 to 70 °C, the PIMN-0.30PT SC attained high dielectric permittivity (ε33T/ε0) of 8330, piezoelectric coefficient (d33) of 2750 pC/N, bar mode electromechanical coupling factor k33 of 0.96 with higher phase change temperature (Tpc) of 103 °C, and high Curie temperature (TC) of 180 °C. These values are the highest ever reported as PIMN-xPT SC system with Tpc > 100 °C. The enhancement of these properties is attributed to the induced low symmetry multi-phase supported by phase analysis. This work indicates that FC ACP is a smart and promising method to enhance piezoelectric properties of relaxor-PT ferroelectric SCs including PIMN-xPT, and provides a route to a wide range of piezoelectric device applications.

Vibration control with piezoelectric elements: The indirect measurement of the modal capacitance and coupling factor

The knowledge of the modal capacitance and electro-mechanical coupling factor is essential for a proper design of systems with embedded piezoelectric transducers and materials. In light of this, this paper presents two indirect methods for measuring the piezoelectric modal capacitance and a method to estimate the modal electro-mechanical coupling factor. All methods rely on simple vibration measurements of the structure with the piezoelectric transducer connected to a proper shunt impedance, thus avoiding measurements of piezoelectric current and voltage by expensive equipment. For the modal electro-mechanical coupling factor, the proposed method guarantees reduced uncertainty compared to traditional experimental estimation procedures. Upon introduction of the underlying theory, the paper experimentally demonstrates the reliability and effectiveness of the methods by comparison with well-established procedures.

Design of wave-like dry friction and piezoelectric hybrid dampers for thin-walled structures

This paper proposes a wave-like hybrid damper containing both dry friction and piezoelectric damping mechanisms for thin-walled structures. The idea is to distribute piezoelectric material on the wave-like friction plate, so that the elastic deformation of the plate can be further utilized to generate additional shunted piezoelectric damping. The proposed damper has the following advantages: simple structure, easy installation and maintenance, convenient to adjust the normal preload, and feasible to mount piezoelectric materials. Combined with damped nonlinear normal modes (dNNMs), the nonlinear modal electromechanical coupling factor (nonlinear MEMCF) is proposed, and its relationship with piezoelectric damping is established for electromechanically coupled systems with contact nonlinearities. Based on the extended periodic motion concept (E-PMC) of dNNMs for non-conservative systems, the preliminary design guidelines of wave-like hybrid dampers are given through nonlinear modal analyses. The modal damping ratio and the nonlinear MEMCF are used to evaluate the damping generated by friction and piezoelectric mechanisms, respectively. The damping effect is also verified by steady-state response analyses through the Multi-Harmonic Balance Method (MHBM). By using a cantilever beam finite element (FE) model, the spatial distribution of piezoelectric material is optimized for a single wave-like hybrid damper. Four optimized hybrid dampers are then implemented to an industrial thin-walled structure. Taking the normal preload as an example, the influence of parameter distribution patterns at different interfaces on the damping effect is also discussed. Compared with the underlying friction damper, the wave-like hybrid damper not only provides greater damping, but is also less sensitive to the variation of excitation amplitude and the normal preload. Whether friction or piezoelectric damping is inactive, the proposed damper can still generate considerable damping.

Design of dry friction and piezoelectric hybrid ring dampers for integrally bladed disks based on complex nonlinear modes

This paper investigates a new passive damper coupling the energy dissipative mechanisms of dry friction and piezoelectric shunting circuit for Integrally Bladed Disks (blisks). The idea is to distribute piezoelectric material to the dry friction ring so that the elastic deformation of the dry friction ring is utilized to generate additional damping. Mounting piezoelectric material on the additional structure instead of the host structure is a more practical alternative to install piezoelectric damping devices to realistic mechanical systems. This improves the reliability and maintainability of both dampers and host structures. Based on the concept of Complex Nonlinear Modes (CNMs), the dry friction damping effect of the proposed damper is measured through the modal damping ratio for target modes. Modal Electromechanical Coupling Factor (MEMCF) is extended to nonlinear electromechanical coupling systems in order to quantify the additional piezoelectric damping ratio. The damping effect of the hybrid damper is also evaluated by the maximal response amplitude in the frequency domain by the forced response analysis. On one hand, it validates the results from the nonlinear modal analysis, on the other hand, it serves as a reference to choose the optimum design parameters of the hybrid damper. Steady-state response of the cyclic symmetric structure under engine-order excitation is calculated by the Multi-Harmonic Balance Method (MHBM). A phenomenological lumped parameter model representing a blisk with a hybrid ring damper is firstly studied to demonstrate the methodology. Then a blisk finite element model is used as a demonstrator to quantitatively verify the effectiveness of the idea. It is shown that for those modes that can be damped by the dry friction damper, the addition of piezoelectric material further enhances the damping effect.

Dielectric and piezoelectric properties of Pb[(Mg1/3Nb2/3)0.52(Yb1/2Nb1/2)0.15Ti0.33]O3 single-crystal rectangular plate and beam mode transducers poled by alternate current poling

The dielectric, piezoelectric and physical properties of the [001]-oriented rectangular plate and beam mode of Pb[(Mg1/3Nb2/3)0.52(Yb1/2Nb1/2)0.15Ti0.33]O3 (PMN-PYbN-PT) ternary single crystals (SC) poled by alternate current poling (ACP) were investigated. The dielectric permittivity and average piezoelectric coefficient d33 were 6800 and 2490 pC/N, respectively, for the rectangular plate sample after ACP, which were 31% and 41% larger than those of the same sample after conventional direct current poling. The highest value of d33 reached 2750 pC N−1. The dielectric loss was reduced by 31%; nevertheless, the d33 improved after ACP. The beam mode electromechanical coupling factor () was 91% by using ACP, showing the highest value among all relaxor-PT SC systems reported so far. The regular periodic stripe domains were observed in ACP samples, showing high domain wall density and uniform domain size. This work demonstrates that the high performance after ACP is an effective method of improving the relaxor-PT SC transducers.

Structure and enhanced electrical properties of high-temperature BiFeO3-PbTiO3-BaZrO3 ceramics with bismuth excess

0.54BiFeO3–0.36PbTiO3–0.1BaZrO3 (BF-PT-BZ) ceramics with various amounts of excess Bi were fabricated by conventional solid-state method and the microstructure and electrical properties were researched to estimate the role of excess Bi on the structure and properties in sintering process. XRD results indicate that tetragonal distortion declined monotonously with the increasing amount of Bi. SEM images reflect that the grain size was enlarged by excess Bi addition. The dielectric, ferroelectric and piezoelectric properties of BF-PT-BZ ceramics were improved effectively. Remnant polarization Pr, piezoelectric coefficient d33 and planar mode electromechanical coupling factor kp of BF-PT-BZ ceramics with 1 mol% Bi excess are 20 μC/cm2, 197 pC/N and 0.448, improved by 20%, 30% and 39%, respectively. The temperature of the maximum dielectric constant Tm of 445 °C for BF-PT-BZ-1 mol% Bi shows tremendous potential for high temperature piezoelectric applications.

Wave Electromechanical Coupling Factor for the Guided Waves in Piezoelectric Composites

A novel metrics termed the ‘wave electromechanical coupling factor’ (WEMCF) is proposed in this paper, to quantify the coupling strength between the mechanical and electric fields during the passage of a wave in piezoelectric composites. Two definitions of WEMCF are proposed, leading to a frequency formula and two energy formulas for the calculation of such a factor. The frequency formula is naturally consistent with the conventional modal electromechanical coupling factor (MEMCF) but the implementation is difficult. The energy formulas do not need the complicated wave matching required in the frequency formula, therefore are suitable for computing. We demonstrated that the WEMCF based on the energy formula is consistent with the MEMCF, provided that an appropriate indicator is chosen for the electric energy. In this way, both the theoretical closure and the computational feasibility are achieved. A numerical tool based on the wave and finite element method (WFEM) is developed to implement the energy formulas, and it allows the calculation of WEMCF for complex one-dimensional piezoelectric composites. A reduced model is proposed to accelerate the computing of the wave modes and the energies. The analytical findings and the reduced model are numerically validated against two piezoelectric composites with different complexity. Eventually an application is given, concerning the use of the shunted piezoelectric composite for vibration isolation. A strong correlation among the WEMCF, the geometric parameters and the energy transmission loss are observed. These results confirm that the proposed WEMCF captures the physics of the electromechanical coupling phenomenon associated with the guided waves, and can be used to understand, evaluate and design the piezoelectric composites for a variety of applications.

Li-modified Ba0.99Ca0.01Zr0.02Ti0.98O3 lead-free ceramics with highly improved piezoelectricity

In this paper, Ba0.99Ca0.01Zr0.02Ti0.98O3 lead-free ceramics with highly enhanced piezoelectricity have been obtained at an optimized Li+ ion doping content by means of elaborately adjusting the microstructure. The introduction of Li+ ions significantly improves the sinterability due to the emergence of oxygen vacancies and the formation of eutectic liquid phase. The sintering temperature is reduced by 100–150 °C compared with other literatures. The highest piezoelectric coefficient d33 and planar mode electromechanical coupling factor kp can be increased up to 340 pC/N and 44%, which are stem from outstanding ferroelectric activity (Pr = 9.8 μC/cm2, Ec = 220 V/mm) and dielectric property (εr = 2250, tan δ = 1.35%). In addition, the Curie temperature Tc is still maintained about 120 °C. A plausible mechanism concerning the defect dipoles, polarization rotation, and ferroelectric phase transition is constructed in this work to well state above mentioned phenomena.

Effects of cobalt and sintering temperature on electrical properties of Ba0.98Ca0.02Zr0.02Ti0.98O3 lead-free ceramics

Lead-free (Ba0.98Ca0.02)(Zr0.02Ti0.98)O3-xmol% (x = 0–1.6) cobalt ceramics (BCZT-xCo) have been fabricated by the traditional solid-state reaction technique and the effects of Co and sintering temperature on ferroelectric, dielectric and piezoelectric properties of (Ba0.98Ca0.02)(Zr0.02Ti0.98)O3 lead-free ceramics have been studied systematically. The orthorhombic–tetragonal (T O–T) transition shift towards lower temperature with increasing Co addition, while Curie temperature (T c) remained at relatively high value of 107 °C. And the Main piezoelectric parameters are optimized at x = 0.8 mol% with a high piezoelectric coefficient (d 33 = 330 pC/N), a planar mode electromechanical coupling factor (k p = 46.7 %), a high dielectric constant (e r = 2,675) and a low dielectric loss (tanδ = 0.90 %) at 1kHZ. Besides these, high remnant polarization (P r) and low coercive field (E c) of 11.5 μC/cm2, 0.31 kV/cm are also obtained at (Ba0.98Ca0.02)(Zr0.02Ti0.98)O3-0.8 mol%Co lead-free ceramics. Furthermore, greatly enhanced temperature stability of the piezoelectric properties was obtained in the temperature range from 20 to 90 °C. The above results indicate that BCZT-Co ceramics are promising lead-free materials for practical applications.

Topology optimization of shunted piezoelectric elements for structural vibration reduction

Passive structural vibration reduction by means of shunted piezoelectric patches is addressed in this article. The concept of topology optimization, based on the solid isotropic material with penalization method, is employed in this work to optimize, in terms of damping efficiency, the geometry of piezoelectric patches, as well as their placement on the host elastic structure. The proposed optimization procedure consists of distributing the piezoelectric material in such a way as to maximize the modal electromechanical coupling factor of the mechanical vibration mode to which the shunt is tuned. An original finite element formulation, suitable to any elastic structures with surface-mounted piezoelectric patches, is proposed to solve the electromechanical problem. Numerical examples validate and demonstrate the potential of the proposed approach for the design of piezoelectric shunt devices.

Sintering and electrical properties of La-modified (Na0.52K0.45Li0.03)1−3xLax(Nb0.88Sb0.09Ta0.03)O3 lead-free ceramics

(Na0.52K0.45Li0.03)1−3xLax(Nb0.88Sb0.09Ta0.03)O3 (NKLLxNST) lead-free ceramics were prepared by normal sintering and their dielectric and piezoelectric properties were investigated. The X-ray methods indicate that the NKLLxNST ceramics with x≤0.003 present a pure perovskite phase at room temperature. The bulk density of NKLLxNST ceramics increases with proper amount of La2O3 contents, and reaches its highest value of 4.544g/cm3 with the addition of 0.3mol% La2O3. At x=0.003, remnant polarization Pr, piezoelectric constant d33 and planar mode electromechanical coupling factor kp of NKLLxNST ceramics reach the highest values of 37.80μC/cm2, 346pC/N and 40%, respectively, exhibiting excellent “soft” piezoelectric characteristics, demonstrating a tremendous potential of the compositions studied for device applications.

Inter-Pillar 진동 모드를 고려한 1-3형 압전복합체의 구조 최적화

Department of Mechanical Engineering, Kyungpook National University, Daegu 702-010, Korea (Received May 21, 2013; Revised May 24, 2013; Accepted May 24, 2013)Abstract: With polymer properties and ceramic volume fraction as design variables, the optimal structure of 1-3 piezocomposites has been determined to maximize the thickness mode electromechanical coupling factor. When the piezocomposite vibrates in a thickness mode, inter-pillar resonant modes are likely to occur between lattice-structured piezoceramic pillars and polymer matrix, which significantly deteriorates the performance of the piezocomposite. In this work, a new method to design the structure of the 1-3 type piezocomposite is proposed to maximize the thickness mode electromechanical coupling factor while preventing the occurrence of the inter-pillar modes. Genetic algorithm was used for the optimal design, and the finite element analysis method was used for the analysis of the inter-pillar mode.Keywords: 1-3 piezocomposite, Inter-pillar mode, Optimization

Polymorphic phase transition and enhanced piezoelectric properties in (Ba0.9Ca0.1)(Ti1−xSnx)O3 lead-free ceramics

Lead-free (Ba0.9Ca0.1)(Ti1−xSnx)O3 (BCTS) (x=0.02–0.1) ceramics were fabricated using conventional solid state reaction method. The effects of Sn substitution on structure and electrical properties of the BCTS ceramics were researched. At room temperature, a polymorphic phase transition (PPT) from tetragonal phase to rhombohedral phase is identified from XRD patterns with increasing Sn content. High piezoelectric coefficient of d33=405pC/N and planar mode electromechanical coupling factor of kp=43.2% are obtained for the sample at x=0.06. The ceramic for x=0.06 also shows uniform microstructure that contributes to the excellent electrical properties. These results indicate that this BCTS system with optimal composition is a promising lead-free piezoelectric material.

Placement and dimension optimization of shunted piezoelectric patches for vibration reduction

Passive structural vibration reduction by means of shunted piezoelectric patches is addressed in this paper. We present a strategy to optimize, in terms of damping efficiency, the geometry of piezoelectric patches as well as their placement on the host elastic structure. This procedure is based on the maximization of the modal electro-mechanical coupling factor (MEMCF) of the mechanical vibration mode to which the shunt is tuned. To illustrate the method, a general analytical model of a laminated beam is proposed. Two particular configurations are investigated: (i) a beam with two collocated piezoelectric patches connected in series or in parallel to the shunt and (ii) a cantilever beam with one patch. After a modal expansion, original closed-form solutions of the MEMCF are exhibited, which enables to compute optimal values for the placement, length and thickness of the piezoelectric patches that maximize the MEMCF. A dimensionless model is used so that this study can be used to design any smart beam, whatever be its dimensions. More general results about the coupling mechanisms between the piezoelectric patches and the host structure are also raised. In particular, it is found that the patches thickness is an essential parameter and that several configurations are possible, depending on the considered vibration mode. Experiments are also proposed to validate the model.

Sensitivity Characteristics of Acoustic Emission (AE) Sensor Using Thickness-Shear-Mode Piezoelectric Device

In this study, Acoustic Emission (AE) sensor was fabricated with the rectangular type Pb(Mg1/2W1/2)O3-Pb(Ni1/3Nb2/3)O3-Pb(Zr0.5Ti0.5)O3 (abbreviated as PMW-PNN-PZT) ceramic piezoelectric device using thickness shear mode. From the results of ATILA simulation, the specimen with the size of 8 × 6 × 8 mm3 was determined as the experimental piezoelectric device which shows the excellent thickness shear mode. Electromechanical coupling factor kp, piezoelectric constant d33 and g33 of PMW-PNN-PZT ceramics showed the excellent values of 0.63, 573 [pC/N], and 29.81 [10−3V·m/N], respectively, suitable for AE sensor device application. Thickness shear mode electromechanical coupling factor k15 was 0.61 at the specimen with the size of 8 × 6 × 8 mm3. The peak sensitivity of AE sensor using this thickness–shear-mode piezoelectric device showed 79 [dB] at 29.4 [kHz].