Flexural Vibration Modes Research Articles

Acoustic black hole immersed sonoreactor for high-efficiency cavitation treatment

Developing innovative sonoreactors to enhance acoustic processing efficiency holds immense importance in the field of sonochemistry. Traditional immersed sonoreactors (TISs) mainly produce cavitation at the probe tip, with a relatively weak cavitation around the probe, resulting in posing challenges for high-efficiency cavitation treatment. Here we propose an acoustic black hole immersed sonoreactor (ABHIS) in longitudinal-flexural coupled vibration, enabling high-efficiency cavitation treatment by unleashing the cavitation potential of the probe. The symmetrical structure of the probe is altered to introduce a coupling of flexural vibration mode, and an acoustic black hole (ABH) profile is integrated to further enhance both flexural wave number and amplitude. In this paper, we present a systematic theoretical design method for ABHIS and compare its performance with TIS using finite element method (FEM). An ABHIS prototype is fabricated and subjected to experimental tests and cavitation observation. The results demonstrate that our theoretical analysis model accurately predicts the frequency characteristics of ABHIS. The proposed ABHIS exhibits satisfactory dynamic characteristics, with significantly increased vibration displacement and acoustic radiation ability compared to TIS. Importantly, the ABH design significantly expands ultrasonic cavitation regions and enhances acoustic radiation intensity of ABHIS resulting in a substantial improvement in acoustic processing efficiency.

Passive Design of Nonlinearity in Specific Modes of Flexural Vibrations in Thin Plates through Topology Optimization

Passive Design of Nonlinearity in Specific Modes of Flexural Vibrations in Thin Plates through Topology Optimization

Ultrasonic liquid crystal tunable light diffuser

Conventional light diffusers have periodic surface profiles, periodic refractive index distributions, or light scattering layers containing colloids. In all such structures the optical directivity of the light diffuser is cannot typically be controlled. Here we propose an electrically tunable light diffuser based on the application of ultrasound to a nematic liquid crystal (LC) material. The ultrasonic LC diffuser consists of an LC layer sandwiched by two glass discs and an ultrasonic transducer. The electrodes of the transducer are divided in a circumferential direction so that a resonant non-coaxial flexural vibration mode can be generated on the diffuser by controlling the electrical input signals. A continuous reversed-phase sinusoidal electric signal to the transducer generates the non-coaxial resonant flexural vibration mode on the glass disc, inducing an acoustic radiation force acting on the boundary between the LC layer and glass discs. This effect changes the molecular orientation of the LC and the transmitted light distribution. The diffusion angle of the transmitted light depends on the input voltage amplitude, and the diffusion angle was maximized at 16.0 V. The vibrational distribution and the diffusion directivity could be rotated by adjusting the input voltages to different electrodes, meaning that an ultrasonic LC diffuser with a thin structure and no moving mechanical parts provided a tunable light-diffusing functionality with rotatable directivity.

A Flexural Ultrasonic Transducer for Inducing Acoustic Cavitation on Material Surfaces

Abstract Purpose This paper proposes a flexural ultrasonic transducer specifically designed for surface treatment of materials with delicate surfaces such as skin by acoustic cavitation at low frequencies. The goal of this preliminary study is to assess the resonance frequencies and the output sound pressure of the proposed transducer and confirm generation of acoustic cavitation on the surface of an artificial skin phantom. Methods A transducer prototype was designed based on structural-acoustic simulation and fabricated. The proposed design employs a concave-shaped acoustic resonator with a spherical cavity, which is driven by flexural vibration of a piezoelectric ceramic disk actuator. The transducer prototype has compact dimensions of 15 mm in diameter and 8 mm in axial length, working at frequencies around flexural vibration modes of the piezoelectric disk with a thickness of 1 mm. Results The maximum sound pressure amplitude reached 125 kPa with an input voltage amplitude of 10 V at the second resonance frequency of 167 kHz, where the third axisymmetric eigenmode was excited. Despite enhancing the maximum pressure, the sound pressure outside the resonator attenuates because the near-field distance of the irradiated sound wave is smaller than the height of the resonator. This implies that the proposed method provides the cavitation effect on material surfaces, possibly minimizing the side effect of ultrasound irradiation on the underlying structure. Cavitation generation on a urethane gel surface was directly observed by using a high-speed video camera. Conclusion We confirmed that acoustic cavitation was generated and propelled to the target surface. It concludes that ultrasound irradiation using the proposed ultrasonic transducer could be a promising alternative for effective and safe ultrasound treatment of material surfaces.

Detection of air- and water-filled cavities beneath concrete plate using electromagnetic and acoustic waves

Underground excavation and tunneling may result in cavities filled with air or water. This study aims to detect cavities beneath underground concrete walls or tunnel linings and assess their risks by estimating the cavity thickness and width using electromagnetic and acoustic waves. In this study, air- and water-filled cavities are simulated, and nondestructive testing methods such as ground penetrating radar (GPR), time domain reflectometry (TDR), and microphones are used to investigate the thickness and width of a cavity beneath a reinforced concrete plate. The results show that GPR signals converted from temporal to spatial scales, combined with TDR measurements, can be used to accurately examine the cavity thickness. However, the examination of the cavity width based on GPR signals remains challenging because of the strong parabolic patterns caused by steel bars. Therefore, this study employs flexibility, which is the ratio of the particle velocity of the structure to the load signal according to the frequency. The flexibility of the concrete plate calculated using microphone signals increases in the cavity section for both air- and water-filled cavities because the flexural vibration mode prevails at the cavity–concrete plate interface. The characteristics of the microphone signals analyzed in the context of flexibility enabled the prediction of the cavity width beneath the concrete plate in both air- and water-filled cavities. GPR and TDR signatures combined with microphone signals can be used for the detection and risk assessment of cavities beneath underground structures when subjected to variations in the groundwater level.

Free vibration analysis employing strain gradient notation four-node plane elements and considering the effects of parasitic shear

In this work, plane stress free vibration is performed using four-node elements formulated using strain gradient notation. Accurate results are sought, and the effects of parasitic shear are investigated. By applying strain gradient notation, which is a physically interpretable notation, parasitic shear terms are identified a priori in the shear strain expressions of the four-node plane element. Parasitic shear is the source of shear locking in that element, and the a priori removal of the parasitic shear terms corrects the element for locking. Several studies in the literature show that this modeling error causes improper behavior of the element in bending, which affects the computed results of stress and displacements of the structure. Based on this, this work applies strain gradient notation to examine the effects of parasitic shear on the natural frequencies and corresponding mode shapes of plane stress structures. The results are compared with literature results, and with the isoparametric FEM formulation modeled by ANSYS software. It is observed that parasitic shear has a higher preponderance in coarse meshes of flexural vibration modes. Furthermore, the deleterious effects are emphasized as bending deformation becomes more important in the model. Strain gradient notation shows advantages in the numerical aspect and successfully eliminates the parasitic shear terms from the four-node element. The problems studied here display accurate results.

Measuring Vibrational Modes in Living Human Cells

The question of whether human living cells in physiological conditions exhibit mechanical resonances has remained unresolved for more than 70 years. We here construct a theoretical model to predict how these hypothetical vibration modes of a living cell can modify the stochastic response of a supporting micromechanical resonator. The key signatures that demonstrate the existence of these vibration modes are then searched for experimentally. To this aim, single human breast epithelial cells were attached to the surface of compliant small microcantilevers. Close examination of the frequency spectra of the thermal fluctuations of the microcantilever over a high-frequency range of 1 kHz–1 MHz revealed anomalies that are consistent with our theoretical predictions. We identify the stochastic coupling of the first and third vibration modes of the cell with the torsional and flexural vibration modes of the cantilever, respectively. These mechanical resonances are very broad and are located at 10–30 kHz and 150–180 kHz, respectively. The analysis of the experiments allows us to obtain information on the temporal evolution of several physical properties of the cell, in addition to the resonance frequencies, during the adhesion process—such as the mass, viscoelasticity, and contact area. These results open multiple avenues in our understanding of single cell mechanobiology, vibrational spectrometry of living cells and mechanical destruction of cancerous cells by targeting specific cell frequencies. Published by the American Physical Society 2024

Investigation on Gas-Liquid Two-Phase Flow-Induced Vibrations of a Horizontal Elastic Pipe

Abstract This paper is concerned with experimental analyses on the vibration behaviors of a horizontal pipe containing gas–liquid two-phase flow with different flow patterns. The effects of flow patterns and superficial velocities on pressure fluctuations and structural responses are evaluated in detail. Numerical simulations on the fluid–structure interactions within the pipe are carried out using the volume of fluid method and the finite element method. A strongly partitioned coupling method is adopted to ensure the compatibility and equilibrium interface conditions between the fluid and the elastic pipe. The accuracy of the numerical solutions is confirmed by comparing with experimental results. It is found that the fluctuation frequency of the pressure fluctuations of the two-phase flow ranges from 0 Hz to 5 Hz. The standard deviation (STD) value of the pressure fluctuation of the two-phase flow increases with an increase in the superficial liquid velocity, and the maximum magnitude appears in slug flows. The vibration responses of the pipe exhibit strong dependence on the momentum flux of the two-phase flow, which mainly excites the fundamental flexural vibration mode of the pipe. The magnitude of vertical vibration response of the pipe is equal to that of the lateral vibration response, and the vibration response measured at the middle of the pipe does not contain the second-order operating mode. Moreover, the STD value of the structural responses of the pipe increases proportionally with an increase in the gas flowrate, while the predominant vibration frequency of the pipe slightly increases.

Effect of ultrasonic vibration on the orientation of C2C12 cells

Control of orientation direction of tissues is important for regenerative medicine techniques. This paper investigates effects of ultrasound vibration on a culture dish on the orientation of myoblast C2C12 cells. A piezoelectric ultrasonic transducer (PZT) was fixed to the bottom of a culture dish. A continuous sinusoidal signal with 10 to 30 Vpp at the resonant frequency of 86kHz was input to the transducer to generate a concentric flexural vibration mode on the bottom surface of the dish. C2C12 cells were cultured on the dish for 2 days under continuous ultrasonic vibration. The ultrasound excitation was then stopped, resulting in the differentiation of the cells into myotube cells through 7 days. The orientation distribution of the cells on the dish was evaluated by spatial Fourier transform in the microscopic images. Compared with the control, the orientation of C2C12 cells was changed significantly under ultrasonication; the concentric pattern of the cell orientation appeared, which corresponds to the concentric vibration mode generated on the bottom of the dish. Larger vibrational amplitude of the dish gave a larger effect on the cell orientation.

Quantifying Shallow-Depth Concrete Delamination using Impact-Echo

Corrosion-induced concrete deck delamination is quite common in bridges. Locating these embedded delaminations is important to assess the extent of the damage, the remaining member capacity and any necessary rehabilitation. The impact-echo (IE) is a simple and straightforward non-destructive testing (NDT) technique by which the depth and extent of concrete delamination may be estimated. It is effective in detecting the location and determining the depth of relatively deep delaminations in concrete. Delaminations that occur near the concrete surface can also be detected by the IE method. However, the exact depth cannot be quantified due to difficulties in analysing the flexural mode that dominates the vibration response over the corresponding delaminated region. This study developed an IE-based procedure to quantitatively estimate the depth of shallow depth delaminations in concrete slab members. Four slab specimens were prepared, each with three artificial delaminations with varying shapes and sizes at shallow depths. The frequency contour maps showed good agreement with the actual location of the delaminations. The perimeter-to-depth ratio of the delaminated region can be used to analyze the flexural mode vibration frequency. Two equations are proposed that relate the depth of arbitrarily shaped delaminations to the flexural mode vibration frequency measured over the shallow-depth delaminations. Keywords: impact echo, concrete delamination, concrete slabs, flexural mode vibration, non-destructive evaluation (NDE)

Impact acoustic inspection of interfacial debonding defects in concrete-filled steel tubes

Concrete-filled steel tube (CFST) structures are commonly used in the construction of high-rise buildings and bridges. However, the presence of debonding defects at the steel–concrete interface of CFST structures due to poor construction quality and concrete shrinkage can significantly reduce their load-bearing capacity. In this paper, an impact acoustic method based on the flexural vibration mode is proposed to detect interfacial debonding in CFST structures. A portable instrument comprising a hammer and a data recording and analysis module is developed for real-time inspection. A vibration energy ratio (VER) criterion, which compares the energy distribution between flexural vibration and thickness stretch modes, is proposed to evaluate the degree of debonding. The effectiveness of the proposed method is verified using a CFST column specimen with debonding defects. The laboratory experimental results demonstrate that the proposed method can detect and roughly pinpoint the debonding area. Additionally, the proposed method is applied to evaluate debonding defects in the CFST columns of the Shenzhen SEG Building, which experienced abnormal shaking on May 18–20, 2021. Impact acoustic measurements were conducted along 27 circumferential rings of nine CFST columns, revealing serious debonding damage to the building with a comprehensive debonding rate of 50.4%. It is concluded that that the proposed impact acoustic method can detect and locate debonding defects in CFST structures, and has a broad application prospect for rapid inspection in civil engineering due to its high efficiency.

Design and analysis of longitudinal–flexural hybrid transducer for ultrasonic peen forming

Ultrasonic peen forming (UPF) is an emerging technology that exhibits great superiority in both its flexible operating modes and the deep residual stress that it produces compared with conventional plastic forming methods. Although ultrasonic transducers with longitudinal vibration have been widely studied, they have seldom been incorporated into UPF devices for machining in confined spaces. To meet the requirements of this type of machining, a sandwich-type piezoelectric transducer with coupled longitudinal–flexural vibrational modes is proposed. The basic structure of the transducer is designed to obtain large vibrational amplitudes in both modes. Experimental results obtained with a prototype device demonstrate the feasibility of the proposed transducer. The measured vibrational amplitude for the working face in the longitudinal vibrational mode is 1.0 μm, and electrical matching increases this amplitude by 40%. The flexural vibration characteristics of the same prototype transducer are also tested and are found to be slightly smaller than those of longitudinal mode. The resultant working strokes of the UPF impact pins reach 1.7 mm and 1.2 mm in the longitudinal and flexural modes, respectively. The forming capability of the prototype has been evaluated via 15-min machining on standard 2024-T351 aluminum plates. After UPF, an improved surface morphology with lower surface roughness is obtained. The aluminum plate test piece has an apparent upper deformation with an arc height of 0.64 mm. The measured peak value of the compressive residual stress is around 250 MPa, appearing at a depth of 100 μm. The proposed longitudinal–flexural hybrid transducer thus provides a high-performance tool for plate peen forming in confined spaces.

Interlaminar shear modulus of cardboard obtained by torsional and flexural vibration tests

Abstract The interlaminar shear modulus of cardboards was measured using torsional vibration (TV) and flexural vibration (FV) methods. In the TV method, the sample widths were decreased during the tests, and the interlaminar and in-plane shear moduli were determined using the data obtained based on the different widths. By contrast, in the FV method, the resonance frequencies from the first to third FV modes were measured using samples of various lengths, and the interlaminar shear modulus and Young’s modulus in the length direction were calculated using Timoshenko’s vibration theory. In addition to the experiment, modal analyses based on the finite element (FE) method were performed, and the sample configurations used to accurately obtain the interlaminar shear modulus were experimentally and numerically investigated. The TV method did not allow the interlaminar shear modulus to be obtained appropriately because the vibration behavior often deviated from that theoretically derived by the TV equation. By contrast, the FV method allowed the interlaminar shear modulus to be obtained appropriately for a wide range of sample lengths.

Local-Resonance-Induced Dual-Band Topological Corner States of Flexural Waves in a Perforated Metaplate

Despite their proven effectiveness in localizing and steering subwavelength elastic waves, locally resonant elastic topological insulators (TIs) with surface-mounted or embedded resonators are often challenged because of their structural complexity and the difficulty in realizing multiple topological band gaps. Here we present a second-order elastic TI (SETI), made of a perforated metaplate with a series of etched C-shaped slots, to achieve dual-band topological corner states. The etched slots in the metaplate form a type of cantileverlike oscillator, the multimodal bending resonances of which couple with the flexural vibration modes of the metaplate, resulting in multiple locally resonant band gaps. Judiciously configuring these slots in a ${C}_{4v}$-symmetric lattice enables topologically distinct metastructures and creates a SETI. We numerically and experimentally observe the dual-band corner states in two broad topological band gaps. Our platform for observing the topological effects in a perforated metaplate greatly simplifies the fabrication of metastructures for implementing locally resonant elastic TIs, benefiting applications of TIs at the subwavelength scale such as elastic wave trapping and energy amplification.

Method for efficient excitation of selective vibration modes in pulsed laser photothermal actuation

Photothermal excitation based on thermoelastic mechanisms is widely used in non-destructive testing, precision operations, and driving micro-resonators. The narrow drive bandwidth of the high vibration mode in photothermal excitation limits its application to multi-mode drives. Controlling the laser’s irradiation position is an effective solution. In this study, we build a theoretical model to achieve selective and efficient excitation of different flexural vibration modes of beams with different supports. The model can be extended to other thermal and physical boundaries, which is validated by numerical simulations and experimental results. The results show that higher modes with complex periodic shapes can be efficiently excited by focusing the laser at the peak of the absolute value of the second derivative of the flexural mode while focusing the laser at the inflection point of the mode shape will result in extremely small amplitudes. Our study indicates that the thermal gradient plays a vital role in the oscillation of the beam. The conventional view assumes that the resonance of the photo-thermal excitation beam is caused by the local expansion and contraction of the material, which cannot completely explain the dependence principle of the photothermal vibration on the laser irradiation position. To investigate the mechanism of beam resonance under laser excitation, three excitation modes, unidirectional excitation, bidirectional in-phase excitation, and bidirectional anti-phase excitation, were established, and the conversion process of optical energy to mechanical energy under laser excitation was analyzed. These results provide new options for optimal excitation and multi-mode energy flow control in photothermal driving.

Transfer of Energy from Flexural to Torsional Modes for the Fish-Bone Suspension Bridge Model

We consider a conservative coupled oscillators system which arises as a simplified model of the interaction of flexural and torsional modes of vibration along the deck of the so-called fish-bone (Berchio and Gazzola in Nonlinear Anal 121:54–72, 2015) model of suspension bridges. The elastic response of the cables is supposed to be asymptotically linear under traction, and asymptotically constant when compressed (a generalization of the slackening regime). We show that for vibrations of sufficiently large amplitude, transfer of energy from flexural modes to torsional modes may occur provided a certain condition on the parameters is satisfied. The main result is a non-trivial extension of a theorem in Marchionna and Panizzi (Nonlinear Anal 140:12–28, 2016) to the case when the frequencies of the normal modes are no more supposed to be the same. Several numerical computations of instability diagrams for various slackening models respecting our assumptions are presented.

A thin acoustic touchless sensor using flexural vibration

This paper investigates a thin sensor used to detect the position of an object in front of an ultrasonic transducer using changes in the radiation impedance. The sensor consists of a rectangular plate and a piezoelectric transducer, and the configuration is determined based on the results of a finite element analysis simulation. Stripe flexural vibration modes are generated on the plate, radiating sound waves into the air between the plate and the object. The radiation angle of these sound waves is dependent on the driving frequency, resulting in a change in the sound field and the electrical admittance characteristics. The sensing performance is examined using two resonant vibration modes. The sensor can determine the position of an object uniquely within a two-dimensional area, and the lower resonant mode gave a wider measurable range. The sensitivity is improved six-fold over that of our conventional sensor using the same sensing mechanism.

How to fix an ultrasonic variable-focus liquid crystal lens for substrate-mountable applications

This paper proposed a board-mounted ultrasonic variable-focus liquid crystal (LC) lens. The lens controls the focus using the acoustic radiation force generated by the resonant flexural vibration mode. The LC lens was fixed to an aluminum substrate with a hole whose aperture corresponded to the inner diameter of the transducer. The part of the LC lens attached to the substrates functioned as a fixed condition, and the flexural vibration mode was successfully generated. The fixed lens exhibited a gradual focal change with current, confirming that fixing the condition affected the rate of focal change.

Acoustic touchless sensor using the flexural vibration of a plate

This paper investigates a method to detect the position of an object in front of an ultrasonic vibrator using changes in the radiation impedance. This acoustic touchless sensor is composed of a rectangular vibrating plate (width: 30 mm; length: 200 mm; thickness: 3 mm) and two bolt-clamped Langevin-type transducers with stepped horns. The sensor configuration was determined based on the results of a finite element analysis simulation. When a stripe flexural vibration mode excited on the plate was generated an acoustic standing-wave field in the air, the electrical impedance of the ultrasound transducers changed dramatically, thus indicating that the radiation impedance of the sensor was dependent on the object position. By measuring the amplitude of the input current to the transducers and the phase difference between the input current and the voltage applied to the sensor, the 40 mm long object’s position could be determined uniquely within a two-dimensional area of 160 × 7 mm2.

Detection of Delaminations in Concrete Plates Using a Laser Ablation Impact Echo Technique

This study investigates the non-destructive detection of delaminations in concrete plates using non-contact laser ablation, instead of the conventional hammer excitation, as part of the impact echo method. We performed tests on five concrete specimens of different sizes, two of which contained artificial delaminations. A range of steel ball hammers was used as reference impulse sources, the responses of which were compared with wave excitation generated by a 7 ns pulsed 1064 nm Nd:YAG laser with 150 mJ pulse energy. Signals were recorded by surface-mounted accelerometers and two contactless methods: microphones and a laser Doppler vibrometer. The laser generates frequencies across a broad range of frequencies (0 to 150 kHz) but with much less energy than the hammers' narrower frequency spectra; the laser pulse energy transferred into the specimen is 0.07 mJ, corresponding to about 0.5 ‰ of the impulse source energy. Because of this, the thick intact plates' characteristic thickness stretch resonance frequency can be reliably detected by the hammer excitations but not when using laser excitation. However, the laser can excite low-frequency flexural vibration modes over a shallow delamination at 3 cm depth. The low-frequency flexural vibration results are verified by numerical natural frequency analysis.