Mechanical Coupling Coefficient Research Articles

Coupled vibration characteristics and optimization design of the cylindrical-exponential ultrasonic concentrator

Abstract In this study, the vibrations of cylindrical-exponential ultrasonic concentrators are investigated, with the objective of improving energy transfer efficiency. Traditional analyses, often one-dimensional, have been found to inadequately consider the effects of height on vibration behaviour. To address this gap, the equivalent elasticity method is employed to provide a more comprehensive understanding of vibrational phenomena. The coupled vibration of the concentrator is regarded as an interaction between a longitudinal vibration and a plane radial vibration. A mechanical coupling coefficient is introduced, establishing a link between these vibrational modes. Equivalent circuits for radial and longitudinal vibrations are derived, and input impedances are presented as functions of resonance frequency and mechanical coupling coefficient. These analyses enable an exploration of the impact of geometric dimensions on the vibrational characteristics. To validate our theoretical model, the finite element method is used to simulate the coupled vibration and the results confirm the efficacy of the approach.

Piezoelectric Hinged Beam with Arc Mass Stopper for Vibration and Human Motion Energy Harvesting.

Compact reliable structure and strong electromechanical coupling are hot pursuits in piezoelectric vibration energy harvester (PVEH) design. PVEH with a static arc stopper makes piezoelectric stress uniformly distributed and widens the frequency band by collision but wastes space. This Article proposes a hinged PVEH with two arc mass stoppers (AS-H-PVEH). Two arc stoppers as movable masses increase the vibration energy and the effective electromechanical coupling coefficient to achieve strong electromechanical coupling. AS-H-PVEH generates a 4.1 mW power output at 11.6-12.0 Hz and 0.2 g. AS-H-PVEH sustains 4 g acceleration vibration for 10 min without attenuation. To offset the resonance frequency increase caused by arc contact, we discuss the magnetic coupling, and axial force effects are discussed. The design of the arc stopper radius, nonlinear electromechanical coupling model, and system parameter identification method are presented. The displacement varied mechanical quality factor and effective electromechanical coupling coefficient are considered in the modified model for the first time. The model obtained good agreement under experiments. The power generation and driven wireless sensor performance of AS-H-PVEH was verified. This research has important theoretical and application value for the performance optimization of PVEH with an arc stopper.

Low-frequency directional wideband transducer based on lead-free piezoelectric ceramics

In recent years, lead-free piezoelectric ceramic devices have been extensively researched and applied in the high-frequency range, specifically above 20 kHz, for airborne acoustics applications. However, few applications have been reported on low-frequency underwater acoustic transducers, which are crucial in the fields of underwater acoustic communication, ocean resource development, etc., because this imposes more stringent requirements for lead-free piezoelectric ceramics in terms of size, mechanical coupling coefficient, piezoelectric coefficients, and temperature stability. This paper explores the application of high-performance potassium sodium niobate based lead-free piezoelectric ceramics in a low-frequency directional wideband transducer. It covers design, fabrication, and performance testing of the transducer. The transducer measures Φ236 × 83 mm2 and weighs 4.45 kg, which achieves wideband emission (3500–8200 Hz) and directional sound emission with a front-to-back sound pressure ratio exceeding 6 dB across a significant frequency range. Both the theoretical analysis and the experimental results confirm the competitiveness application of the lead-free piezoelectric ceramics in the field of low-frequency underwater acoustic transducers applications.

An analytical approach to design horns and boosters of ultrasonic welding machines

This paper presents a new design approach for two main components of an ultrasonic plastic welding machine, booster and horn, based on an analytical model. The design procedure is developed due to the lack of a comprehensive and precise analytical model for rapid design and analysis of these components. The previous analytical models use the one-dimensional wave equation that causes significant errors in designing components with large lateral dimensions. Three-dimensional vibrations are considered for developing an analytical model using the apparent elasticity method. In this way, longitudinal frequency equations are coupled with radial frequency equations by mechanical coupling coefficients. Also, the damping of materials is taken into account. The model can be adapted to calculate the resonant length of the components or calculate the resonant frequency. To verify the model, the results are compared to a numerical simulation. The difference between analytical and numerical resonance frequency is less than 0.02%. Moreover, an experimental modal analysis is performed, which shows 0.9% error with analytical results.Article highlightsA new design approach for boosters and horns has been developed based on an analytical model.Three-dimensional vibrations are considered in the model using the apparent elasticity method.The accuracy of calculating resonant frequencies is more than one-dimensional design method.

Evaluation of the role of beam homogeneity on the mechanical coupling of laser-ablation-generated impulse.

The material emitted from a target surface during laser ablation generates a net thrust (propulsion) in the opposite direction. The momentum generation efficiency of this laser-driven propulsion is given by the mechanical coupling coefficient (Cm). In this work, we considered nanosecond UV laser ablation of the aluminum 6061 alloy to study the Cm behavior with different irradiating conditions. This is done by systematically changing fluence, uniform/nonuniform intensity, and incident angle of the laser beam. In particular, we found that when dealing with nonuniform laser intensity, characterizing Cm exclusively in terms of fluence is not fully satisfactory because the energy distribution over the irradiated area plays a key role in the way material is removed-interplay between vaporization and phase explosion-and thrust is generated.

Study on the bending vibration of bimorph rectangular transducer based on type 2-2 piezoelectric composites

In order to improve the acoustic radiation capability of piezoelectric ultrasonic transducer in gas, a bimorph rectangular transducer based on type 2-2 piezoelectric composites is proposed in this paper, which is composed of two piezoelectric composite rectangular slices with thickness polarization. First, the bending vibration of the rectangular transducer is divided into two bending vibrations of the thin rods in the x and y directions using the equivalent elastic method. When the mechanical coupling coefficient is introduced and combined with the anisotropic piezoelectric equations, the resonance frequency equations of the thickness-polarized transducer are derived with simply supported boundary conditions. Then the bending vibration of the transducer is numerically simulated. The results show that the resonance frequency obtained by the analytical method is in good agreement with the numerical simulation results. Finally, the influence of geometrical size and two-phase volume ratio on the bending vibration performance of the transducer is analyzed. Compared with the piezoelectric bimorph transducer, the piezoelectric composite bimorph transducer has a larger bending vibration displacement amplitude, a larger transmitting voltage response, a lower resonant frequency and better acoustic radiation capability.

A piezoelectric micromachined ultrasonic transducer with mechanical grooves

This paper presents a novel architecture for annular and circular electrode piezoelectric micromachined ultrasound transducers (AC-PMUTs) with mechanical grooves. The mechanical grooves reduce stress and increase the vibration area of the membrane, resulting in enhanced vibrational deformation amplitude, transmission sensitivity, mechanical coupling coefficient (), quality factor (Q), and emission sound pressure level (SPL). Compared with conventional AC-PMUTs without mechanical grooves, the transmitting displacement sensitivity was measured as 419.4 NM V−1, which increased by 128.73%; the mechanical coupling coefficient () was measured as 6.09%, which increased by 116.43%; and the quality factor (Q) was measured as 90.68, which is an increase of 241.3%. The mechanical grooves also increased the emission SPL of PMUT at the same operating frequency. In the range of 10 kHz–70 kHz, the emission SPL of the optimum AC-PMUT with mechanical grooves can be improved in the range of 2.8 dB–28.8 dB. In general, AC-PMUTs with mechanical grooves have great potential in various emission ultrasound applications, such as distance measurement and object detection.

A novelly universal theory: Toward accurately evaluating radial vibration characteristics for radially sandwiched spherical piezoelectric transducer

With the development of ultrasonic technology, some ultrasonic processing technologies require a wide processing range. In this paper, a radially sandwiched spherical piezoelectric transducer is proposed and analyzed, which is composed of a spherical piezoelectric ceramic sandwiched by two concentric spherical metal shells. The electromechanical equivalent circuits of the spherically isotropic spherical shell and the spherical piezoelectric ceramic with arbitrary wall thickness are derived from their motion equations. According to the mechanical boundary conditions, the electromechanical equivalent circuits and frequency equation of various piezoelectric composite vibration systems can be obtained, including the radially sandwiched spherical piezoelectric transducer. The correctness of the proposed theory is verified via comparison with the finite element method and the previous theoretical model. In addition, the 2nd-order effective mechanical coupling coefficient for the radially sandwiched spherical piezoelectric transducer is higher than that of 1st-order within a specific range of wall thickness, which can be designed as the high-frequency transducer. The radially sandwiched spherical piezoelectric transducer is expected to be used in underwater sound, structural health monitoring, and high-frequency ultrasound.

Analysis on coupled vibration of piezoelectric ceramic stack with two piezoelectric ceramic elements.

A longitudinally polarized piezoelectric ceramic stack with two piezoelectric ceramic elements is an important part of sandwich piezoelectric transducers. The three-dimensional coupled vibration of piezoelectric ceramic stack is analyzed. Since the longitudinal and radial dimensions of particular piezoelectric ceramic stacks are approximately equal, one-dimensional theory cannot be used for analysis. The piezoelectric ceramic stack is analyzed by the equivalent elastic method, which is an approximate analytical method, and it is considered that the coupled vibration of a piezoelectric ceramic stack is composed of equivalent radial and longitudinal vibrations. These two equivalent vibrations are connected by a mechanical coupling coefficient. The radial and longitudinal electromechanical equivalent circuits are obtained, and the resonance frequency equations are derived. The dependency of the radial and longitudinal resonance frequencies on the geometrical dimensions for piezoelectric ceramic stack is analyzed. The height or radius has a large influence on the longitudinal resonance frequency or the radial resonance frequency. Two sets of piezoelectric ceramic stacks are fabricated. The experimental results, COMSOL simulated results, and theoretical results are in good agreement.

Electromechanical equivalent circuit of the radially polarized cylindrical piezoelectric transducer in coupled vibration.

Electromechanical equivalent circuit of the radially polarized cylindrical piezoelectric transducer in coupled vibration is obtained. The equivalent elasticity method is used to analyze the coupled vibration. It is an approximate analytical method, ignoring the shear and torsion stresses and strains, dividing the coupled vibration into the extensional radial and longitudinal vibrations. A mechanical coupling coefficient is introduced to connect these two equivalent vibrations. According to the electromechanical equivalent circuit, the resonance frequency equations as functions of the frequency and the mechanical coupling coefficient are acquired. The sound pressure level and far field sound pressure distribution for the transducer in water are simulated. It is demonstrated that the radiation range of the cylindrical transducer is larger than that of the ring-type transducer. Several prototypes of the transducer are fabricated; the radial and longitudinal resonance frequencies are measured. The experimental resonance frequencies are in good agreement with the analytical results. The acquisition of the electromechanical equivalent circuit contributes to analyzing the electromechanical characteristics of the radial polarized cylindrical transducer.

A 2D dual-mode composite ultrasonic transducer excited by a single piezoceramic stack

A 2D composite ultrasonic transducer with two resonance modes is proposed by using a central coupling metal block, a piezoceramic stack and four outer metal cylinders. With the introduction of the dual-mode equivalent mechanical coupling coefficient and the 2D longitudinal force transform coefficient, a novel equivalent circuit model is developed for the design and analysis of the 2D coupled vibration of the transducer. After verifying the proposed equivalent circuit model with the FE method and the corresponding experiments, the vibration characteristics of the proposed transducer are investigated by using the equivalent circuit mode, the FE methods, and the experiments. The results demonstrate that the proposed transducer has the advantage of generating 2D ultrasonic radiation with two different fundamental resonance modes, which is useful in some new ultrasonic applications such as ultrasonic emulsification, ultrasonic defoaming and ultrasonic sonochemistry where multi-frequency and multidimensional sound radiation is needed.

Electromechanical equivalent circuit and coupled vibration of the radially composite cylindrical piezoelectric transducer

Electromechanical equivalent circuit for the radially composite cylindrical piezoelectric transducer in coupled vibration is deduced. The transducer is composed of a piezoelectric cylinder sandwiched by two concentric metal cylinders. Equivalent elasticity method is used to study the coupled vibrations of the three cylinders. A ratio named the mechanical coupling coefficient is introduced to divide the coupled vibration into the radial and longitudinal vibrations. The electromechanical equivalent circuits for the transducer and the resonance frequency equations are obtained. When the height is close to the radius of the transducer, the coupling between the radial vibration and the longitudinal vibration is strong. The thicker is the piezoelectric cylinder, the larger is the effective electromechanical coupling coefficient. Several prototypes of the transducer are fabricated. It is demonstrated that the theoretical resonance frequencies are in good agreement with the numerical and experimental results.

Criteria determination to choose piezoelectric materials for BAW resonator applications via colored picosecond acoustics

A great number of piezoelectric materials which could be used in the fabrication of BAW resonators were investigated via colored picosecond acoustics technique in order to study the required parameters for designing and fabricating improved devices. These parameters concerns acoustic longitudinal velocity, vL, elastic stiffness constant, CD33, intrinsic mechanical loss, tanδ, and electromechanical coupling coefficient, k2t. We first quantify the effect of the ratio between the wavelength pulse of a femtosecond laser and the period of Brillouin oscillations, λp/T. It is found that CD33 depends linearly on λp/T. Then, we deduced novel relations for stiffness constant and mechanical coupling coefficient. Moreover, the determination of different parameters (density, refractive index and vL) of piezoelectric film is achieved, with good agreement with literature. The optimized conditions for the parameter choice of BAW resonators are found to be: 300 GPa < CD33 < 500 GPa and 1.7 GPa < e233/εs33 < 28.5 GPa with λp/T > 37 103 m/s where e33 and εs33 are the piezoelectric constant and the materials permittivity in the direction 3, respectively.

Analysis on the three-dimensional coupled vibration of composite cylindrical piezoelectric transducers.

Three-dimensional coupled vibration of the composite cylindrical piezoelectric transducer is analyzed. The composite cylindrical piezoelectric transducer consists of an inner axially polarized piezoelectric ceramic cylinder and an outer metal cylinder with the same height. Coupled vibration of the composite cylindrical piezoelectric transducer is analyzed by equivalent elasticity method, which is an approximate analytical approach. According to this method, coupled vibration of the cylindrical transducer is regarded as an interaction between a plane radial vibration and a longitudinal vibration. The radial and longitudinal electromechanical equivalent circuits of the piezoelectric transducer are acquired. Input impedances as functions of the resonance frequency and the mechanical coupling coefficient are derived to obtain resonance frequency equations. The analytical results are supported by experimental and numerical simulated results of two prototypes of the piezoelectric transducer. The composite cylindrical piezoelectric transducer presented in this paper is superior to single cylindrical piezoelectric transducers, composite ring-type, and tube-type transducers in the field of high output power and efficiency.

Analysis on Coupled Vibration of a Radially Polarized Piezoelectric Cylindrical Transducer.

Coupled vibration of a radially polarized piezoelectric cylindrical transducer is analyzed with the mechanical coupling coefficient method. The method has been utilized to analyze the metal cylindrical transducer and the axially polarized piezoelectric cylindrical transducer. In this method, the mechanical coupling coefficient is introduced and defined as the stress ratio in different directions. Coupled vibration of the cylindrical transducer is regarded as the interaction of the plane radial vibration of a ring and the longitudinal vibration of a tube. For the radially polarized piezoelectric cylindrical transducer, the radial and longitudinal electric admittances as functions of mechanical coupling coefficients and angular frequencies are derived, respectively. The resonance frequency equations are obtained. The dependence of resonance frequency and mechanical coupling coefficient on aspect ratio is studied. Vibrational distributions on the surfaces of the cylindrical transducer are presented with experimental measurement. On the support of experiments, this work is verified and provides a theoretical foundation for the analysis and design of the radially polarized piezoelectric cylindrical transducer.

Seismic control of a SDOF structure through electromagnetic resonant shunt tuned mass-damper-inerter and the exact H2 optimal solutions

This paper proposes a novel inerter-based component dynamic vibration absorber, namely, electromagnetic resonant shunt tuned mass-damper-inerter (ERS-TMDI). To analyze the performances of the ERS-TMDI, the combined ERS-TMDI and a single degree of freedom system are developed. The H2 norm performances of the ERS-TMDI, whose aim is to minimize the root mean square (RMS) value of structure damage under random ground acceleration excitation, are introduced in comparison with the energy-harvesting series electromagnetic tuned mass dampers (ERS-TMDs), tuned mass-damper-inerter (TMDI) and the classical tuned mass damper (TMD). The closed-form solutions, including the optimal mechanical tuning ratio, the optimal electrical damping ratio, the optimal electrical tuning ratio and the optimal electromagnetic mechanical coupling coefficient, are obtained. It is shown that the ERS-TMDI is superior to both the classical TMD and the ERS-TMD systems for protection from structure damage. Specifically, from the frequency-domain analyses, a case study is performed to illustrate the effectiveness, robustness of the ERS-TMDI and the sensitivity to the parameter changes. From the time-domain analyses, four types of earthquakes are studied to demonstrate the performances of vibration suppression.

Wind Induced Vibration Control and Energy Harvesting of Electromagnetic Resonant Shunt Tuned Mass-Damper-Inerter for Building Structures

This paper proposes a novel inerter-based dynamic vibration absorber, namely, electromagnetic resonant shunt tuned mass-damper-inerter (ERS-TMDI). To obtain the performances of the ERS-TMDI, the combined ERS-TMDI and a single degree of freedom system are introduced. H2 criteria performances of the ERS-TMDI are introduced in comparison with the classical tuned mass-damper (TMD), the electromagnetic resonant shunt series TMDs (ERS-TMDs), and series-type double-mass TMDs with the aim to minimize structure damage and simultaneously harvest energy under random wind excitation. The closed form solutions, including the mechanical tuning ratio, the electrical damping ratio, the electrical tuning ratio, and the electromagnetic mechanical coupling coefficient, are obtained. It is shown that the ERS-TMDI is superior to the classical TMD, ERS-TMDs, and series-type double-mass TMDs systems for protection from structure damage. Meanwhile, in the time domain, a case study of Taipei 101 tower is presented to demonstrate the dual functions of vibration suppression and energy harvesting based on the simulation fluctuating wind series, which is generated by the inverse fast Fourier transform method. The effectiveness and robustness of ERS-TMDI in the frequency and time domain are illustrated.

Nonlinear technique and self-powered circuit for efficient piezoelectric energy harvesting under unloaded cases

Vibration energy harvesting using piezoelectric materials has been intensively studied over the last few years, because of the wide availability of vibrational sources and the good integration and conversion abilities of piezoelectric materials. However, the power output of Piezoelectric Energy Harvesters (PEH) is still limited due to the relatively low mechanical quality factor and coupling coefficient of the electromechanical structure. Recently, nonlinear processes have been introduced to increase the energy extraction abilities of PEHs, showing impressive increase of the power output under monomodal excitation. However, their performance is limited when the structure is subjected to more complex signals or when considering the charge of a single capacitor (the latter operation reflecting well the typical use of self-powered systems). The purpose of this paper is to expose an enhancement of this technique, based on disabling the nonlinear process if no harvesting event has been done previously. This therefore allows better energy conversion abilities under multimodal excitation as it allows a better control of the trade-off between the number of switching events and the voltage values at the switching instant, as well as increasing the harvested energy in monochromatic case, as the damping effect is limited. Finally, in order to dispose of realistic devices, a self-powered version of the enhanced technique is proposed and validated through simulation analysis and experimental implementation.

Methodology for Characterizing Loss Factors of Piezoelectric Ceramics

The methodology to obtain the loss factors in piezoelectric ceramics is proposed in this paper. There are three hysteresis loss components for piezoelectric vibrators, i.e., dielectric, elastic and piezoelectric losses. The equations were derived about the relations between mechanical quality factors and all contributing loss factors by the complex analysis of the admittance/impedance expressions for specific piezoelectric vibrators. By characterizing mechanical quality factors and coupling coefficients in k31, kt, k33, kp, and k15 modes, 20 loss factors can be obtained for the piezoelectric ceramic with ∞mm or 6 mm crystal symmetry.

Frequency dependence of the magnetoelectric effect in a magnetostrictive-piezoelectric heterostructure

The frequency dependence of the magnetoelectric effect in a magnetostrictive-piezoelectric heterostructure is theoretically studied by solving combined magnetic, elastic, and electric equations with boundary conditions. Both the mechanical coupling coefficient and the losses of the magnetostrictive and piezoelectric phases are taken into account. The numerical result indicates that the magnetoelectric coefficient and the resonance frequency are determined by the mechanical coupling coefficient, losses, and geometric parameters. Moreover, at the electromechanical resonance frequency, the module of the magnetoelectric coefficient is mostly contributed by the imaginary part. The relationship between the real and the imaginary parts of the magnetoelectric coefficient fit well to the Cole—Cole circle. The magnetostrictive-piezoelectric heterostructure has a great potential application as miniature and no-secondary coil solid-state transformers.