Order Flexural Modes Research Articles

Multi-resonant TVA formed by a tree of deflated composite beams with core structured fabrics

Abstract This paper presents a study on a multi-resonant tuneable vibration absorber for the control of flexural vibrations of thin structures in a low frequency band where the response is characterized by distinct lightly damped resonances of low order flexural modes. The absorber is formed by a tree of deflated composite beams made by a core structured fabric wrapped on a plastic skin. The beams have increasingly smaller length and are fixed in the middle on a mast that works as a base-post and vacuum-junction too. The fabric in each beam is made by a lattice of interlocked truss-like rigid particles. The uniform pressure exerted by the deflated skin forces the particles to jam such that the fabric moves from its natural fluid-like state to a solid state whose rigidity depends on the confining pressure exerted by the skin. Hence, each beam is characterized by a fundamental flapping vibration mode whose response resembles that of a classical mass-spring-damper vibration absorber and can be suitably tuned by adjusting the level of vacuum. The paper first analyses the working principles of single-beam and three-beams absorbers with respect to their vibration transmissibility and base impedance frequency response functions. Then, it presents the vibration control generated by the single-beam and the three-beams absorbers tuned to minimise the resonant responses of a single or three low order flexural modes of a thin plate. The paper shows that the operational frequency of each beam-absorber can be suitably adapted in a band of 8 Hz by varying the vacuum pressure in a 5 – 80 kPa range. Also, it shows that the single-beam or multi-beams absorbers reduce the resonant response of the target flexural modes by 10 to 20 dB.

Shunted piezoelectric patch adaptive vibration absorber set to maximise electric power absorption: A comparison between parallel and series RL-shunts

This paper presents a comparative study on two types of shunted piezoelectric patch adaptive vibration absorbers, which can be bonded in batches on thin-walled structures to control the broad-band resonant response of low order flexural modes. The self-contained control units are formed by a thin piezoelectric patch connected either to a series or to a parallel resistive-inductive (RL) network. The two components of the shunt are adapted online in such a way as to maximise the time-averaged electric power absorbed by the shunt, which corresponds to minimising the time-averaged total flexural response of the hosting structure. The study considers a practical demonstrator formed by a thin rectangular plate with five piezoelectric patches connected to digital RL-shunts, which is excited in bending by a stationary white noise point force. The aim of the paper is to contrast the tuning and vibration control properties of the series and parallel RL shunts. More specifically, the online implementation of a recursive two-paths tuning strategy along R-constant and L-constant paths with an extremum seeking gradient search algorithm is analysed first for the two types of shunts. Then, the vibration control performance produced by the two types of shunts is investigated for the case where they are tuned to control the resonant response of the first flexural mode of the plate.

Measurement of thermal properties of liquid analytes using microfluidic resonators via photothermal modulation

Understanding the thermal properties of fluids at the nanoscale with high spatial, temporal, and thermal resolution are on great demand in the fields of MEMS, drug development, biomedical devices, and analytical systems. Microfluidic channel-integrated cantilevers are considered as an established benchtop sensor platform for physical and thermal characterization of materials at the picogram amount of analytes. This paper reports analysis of thermal characteristics of liquid analytes using photothermal heating effect of the microfluidic cantilever. Using real-time tracking of frequency shift of microfluidic resonator, the thermal properties of liquid samples can be estimated whilst the liquid analytes in the cantilever are locally heated by laser-induced irradiation. The heating results in the expansion of the liquid inside the channel which induces thermal stress on the walls of the channel. This thermal stress contributes to the rise of the resonance frequency of the microfluidic resonator and, therefore, the frequency shift is linearly dependent on the volumetric coefficient expansion of the liquid. A threefold improved sensitivity is observed when the second order flexural vibration mode is analyzed compared to that of the fundamental resonance. This approach, which combines photothermal heating and the dynamic mode of operation, can serve as a platform for the development of a portable, lab on a chip device for the use of real time detection of thermomechanical properties of fluids at low cost.

A novel looped space tether transportation system with multiple climbers for high efficiency

This paper proposes a novel concept of looped tether transportation system with multiple climbers for highly efficient transportation of payloads. It is formed by connecting two parallel tether transportation systems or partial space elevators with multiple climbers per tether at upper and lower ends. A high-fidelity and accurate model for the system is built up to capture the high order flexural modes of tethers based on the nodal position finite element method in the arbitrary Lagrangian-Eulerian description. Numerical analysis is conducted to understand the dynamic characteristics of the looped tether transportation system compared to the tether transportation system with a single tether. The results show that the high-order flexural modes of tethers must be considered in the system's engineering analysis. The analysis also shows the interaction between two tethers caused by climbers on different tethers moving in different directions could be beneficial. It will reduce the overall libration of the system while keeping the magnitude of tether tension comparable to the tether transportation system with a single tether. In addition, the analysis of high order flexural modes of tether indicates that there exists a risk of tether collision in the payload transportation, which indicates again the necessity to include the high order flexural modes of tether in the analysis. Finally, the study shows the risk of tether collision could be avoided by optimizing the number of climbers per tether, the climber's moving profiles, and the distance between climbers using the optimal control methodology.

Application of Ultrasonic Guided Waves for Inspection of High Density Polyethylene Pipe Systems

The structural integrity assessment of thermoplastic pipes has become an interesting area of research due to its elevated usage in the liquid/gas transportation industry. Ultrasonic guided wave testing has gained higher attention from industry for the inspection of elongated structures due to the reduced inspection time and cost associated with conventional non-destructive testing techniques, e.g., ultrasonic testing, radiography, and visual inspection. Current research addresses the inspection of thermoplastic pipes using ultrasonic guided waves as a low cost and permanently installed structural health-monitoring tool. Laboratory and numerical investigations were conducted to study the potential of using ultrasonic guided waves to assess the structural health of thermoplastic pipe structures in order to define optimum frequency range for inspection, array design, and length of inspection. In order to achieve a better surface contact, flexible Macro-Fiber Composite transducers were used in this investigation, and the Teletest® Focus+ system was used as the pulser/receiver. Optimum frequency range of inspection was at 15−25 kHz due to the level of attenuation at higher frequencies and the larger dead zone at lower frequencies due to the pulse length. A minimum of 14 transducers around the circumference of a 3 inch pipe were required to suppress higher order flexural modes at 16 kHz. According to the studied condition, 1.84 m of inspection coverage could be achieved at a single direction for pulse-echo, which could be improved by using a higher number of transducers for excitation and using pitch-catch configuration.

Panel with self-tuning shunted piezoelectric patches for broadband flexural vibration control

Abstract A practical approach based on maximisation of vibration power dissipation is proposed for the self-tuning of single- and multi-resonant shunts connected to piezoelectric patches, which are bonded on thin rectangular panels to reduce the broadband flexural vibrations produced by stochastic disturbances at low audio-frequencies. The single- and multi-resonant shunts are formed either by one or by multiple resistance-inductance-capacitance (RLC) branches connected in parallel. The proposed self-tuning approach sequentially adapts the RL elements in the branches of each shunt in such a way as to maximise the vibration power dissipation from the resonant response of the flexural modes of the hosting structure that resonate in a target frequency band. The vibration power dissipated is estimated from the measured electric power dissipated by each shunt so that self-tuning can be implemented locally and independently in each shunt without the need of system identification or on-line measurement of the vibration response of the hosting structure. Therefore, on-line tuning can be implemented to control the vibrations of distributed structures, also in those cases where they are characterised by time-varying dynamics, generated, for example, by tensioning effects, mass variations, moving loads, uneven constraints, etc. To start with, the paper presents a parametric study on a thin rectangular panel with two piezoelectric patches connected to multi-resonant shunts, which shows that, the time-averaged total flexural kinetic energy of the smart panel and the time-averaged electric power dissipated by each shunt are characterised by matching local minima and maxima, which identify the optimal RL parameters in the branches of each shunt necessary to control the resonant responses of the panel low order flexural modes. A practical iterative approach, based on the maximisation of the time-averaged electric power dissipated by each shunt, is then introduced to find on-line these optimal RL parameters. Finally, a brief survey is presented to show the flexural vibration control effects produced in the panel by increasingly larger arrays of piezoelectric patches connected to the proposed self-tuning multi-resonant shunts.

Excitation and propagation of torsional T(0,1) mode for guided wave testing of pipeline integrity

Guided wave testing is one of non-destructive testing techniques for pipeline inspection using low-frequency ultrasonic waves. Guided wave testing uses a set of equally placed piezoelectric transducers around a pipe, and the number of transducers in the array is a key factor for suppressing higher order flexural modes. This paper presents an effective approach for the excitation and propagation of torsional T(0,1) wave mode for detecting defects in a steel pipe by using finite element numerical simulations and experimental studies. From the numerical and experimental results, the optimised design for transducer arrangement is investigated. The relationship between defect type, dimension and transducer arrangement is also investigated. To validate the finite element modelling, the numerical results are then compared to the experimental data. Finally, the sensitivity of reflected signal from defects to two types of transducer array design is evaluated, and circumferential displacement along the pipe is investigated by using polar plots at different axial positions.

Reducing dissipation in piezoelectric flexural microplate resonators in liquid environments

While piezoelectric microplates are emerging as a promising MEMS liquid-based sensing platform, often acoustic radiation losses limit device performance. This paper presents a new analysis of microplate acoustic radiation losses through the use of traditional analytical models for the fundamental mode and a new finite element model that is used to analyze trends affecting Q for both the fundamental and higher order flexural modes. Results from these models are compared with experimental measurements of frequency and Q measured using both electrical characterization and the laser Doppler vibrometer for multiple modes of the microplate in water as compared to air and vacuum. Finally, a microplate mode with a high initial Q of around 150 in air and that demonstrates an increase in Q going from air to water is presented as a strong candidate for use in droplet based sensing applications.

Evidence for structural damping in a high-stress silicon nitride nanobeam and its implications for quantum optomechanics

We resolve the thermal motion of a high-stress silicon nitride nanobeam at frequencies far below its fundamental flexural resonance (3.4 MHz) using cavity-enhanced optical interferometry. Over two decades, the displacement spectrum is well-modeled by that of a damped harmonic oscillator driven by a 1/f thermal force, suggesting that the loss angle of the beam material is frequency-independent. The inferred loss angle at 3.4 MHz, ϕ=4.5⋅10−6, agrees well with the quality factor (Q) of the fundamental beam mode (ϕ=Q−1). In conjunction with Q measurements made on higher order flexural modes, and accounting for the mode dependence of stress-induced loss dilution, we find that the intrinsic (undiluted) loss angle of the beam changes by less than a factor of 2 between 50 kHz and 50 MHz. We discuss the impact of such “structural damping” on experiments in quantum optomechanics, in which the thermal force acting on a mechanical oscillator coupled to an optical cavity is overwhelmed by radiation pressure shot noise. As an illustration, we show that structural damping reduces the bandwidth of ponderomotive squeezing.

Excitation and reception of single torsional wave T(0,1) mode in pipes using face-shear d24 piezoelectric ring array

Excitation of single fundamental torsional wave T(0, 1) mode is of practical importance in inspecting or monitoring the structural integrity of pipelines, as T(0, 1) wave is the only non-dispersive mode in pipe-like structures. This work presents a piezoelectric ring array to excite and receive single T(0, 1) mode which is made up of a series of equally-spaced face-shear d24 PZT elements around the pipe. Firstly, we proposed that single T(0, 1) mode can be excited by the piezoelectric ring, when the number of d24 PZT elements is slightly greater than n, where F(n, 2) is the highest circumferential order flexural torsional mode within the frequency bandwidth of the drive signal. Then this proposed principle was confirmed by finite element simulations. Later, experimental testing was conducted on a 100 mm outer diameter, 3 mm thick aluminum pipe. Results show that the ring of 24 face-shear d24 PZT elements can suppress all the non-axisymmetric flexural modes at the excitation frequency of 150 kHz so that single T(0, 1) mode is generated. Moreover, such a piezoelectric ring transducer can also filter flexural modes and receive the T(0, 1) mode only at 150 kHz. Note that here the highest circumferential order flexural torsional mode within the frequency bandwidth is F(20, 2), so the experimental results are in good agreement with the proposed principle. The presented ring of face-shear d24 PZT elements is very suitable for severing as the T(0, 1) wave transducer in structural health monitoring system, as it is cost-effective and no external load is required for operation.

Tuning Nonlinear Mechanical Mode Coupling in GaAs Nanowires Using Cross-Section Morphology Control.

We investigate the nonlinear mechanical properties of GaAs nanowires with anisotropic cross-section. Fundamental and second order flexural modes are studied using laser interferometry with good agreement found between experiment and theory describing the nonlinear response under mechanical excitation. In particular, we demonstrate that the sign of the nonlinear coupling between orthogonal modes is dependent on the cross-section aspect ratio. The findings are of interest for applications such as amplitude to frequency conversion and vectorial force sensing.

Device for filamentous fungi growth monitoring using the multimodal frequency response of cantilevers

Filamentous fungi cause opportunistic infections in hospital patients. A fast assay to detect viable spores is of great interest. We present a device that is capable of monitoring fungi growth in real time via the dynamic operation of cantilevers in an array. The ability to detect minute frequency shifts for higher order flexural resonance modes is demonstrated using hydrogel functionalised cantilevers. The use of higher order resonance modes sees the sensor dependent mass responsivity enhanced by a factor of 13 in comparison to measurements utilizing the fundamental resonance mode only. As a proof of principle measurement, Aspergillus niger growth is monitored using the first two flexural resonance modes. The detection of single spore growth within 10 h is reported for the first time. The ability to detect and monitor the growth of single spores, within a small time frame, is advantageous in both clinical and industrial settings.

High-Bandwidth AFM Probes for Imaging in Air and Fluid

Due to the high mechanical bandwidth of an integrated diffraction-grating-based force sensor, interdigitated AFM probes enable probing the nanomechanical properties of the sample by measuring fast varying tip-sample interaction forces while operating in tapping mode. To explain the mechanical frequency response obtained from finite-element analysis, we developed an analytical model that incorporates the higher order flexural modes of a cantilever. To enable flexibility necessary to use the probes in different imaging environments, a step is introduced into the batch fabrication where high-stress nitride is used. This step allows the probe to be used in various optical conditions such as different laser wavelengths (in the light-lever configuration), incident angles, and ambient refractive indices (such as air and water). We demonstrate that the probe can operate in both air and fluid and measure fast varying tip-sample interactions by imaging a sputtered gold film in both conditions.

A novel dual stator-ring rotary ultrasonic motor

In this work, a novel dual stator-ring rotary ultrasonic motor is proposed, designed, fabricated and characterized for raising driving torque of the rotary ultrasonic motor operating in the flexural vibration mode. It uses four bending mode Langevin transducers, which are evenly distributed between its two identical stator rings, to excite the ninth order flexural mode traveling waves in the two stator-rings and drive its two rotors. Driving bars assembled at the center of the Langevin transducers are employed to excite two ninth order flexural standing waves spatially and temporally orthogonal to each other in each stator-ring, and form the traveling wave. Results of vibration measurement are used to confirm the operating principle, and the finite element method is used to design the motor size in order that the motor can operate in resonance. The appearance size of the motor is 80mm×80mm×53mm, stator outer diameter is 60mm, and operating frequency is around 39kHz. The major mechanical and thermal characteristics of the motor have been measured. At the room temperature and 250V0-p operating voltage, its stalling torque is 1.6Nm, no-load speed is 120rpm, and output power reaches the maximum (=5.5W) with a driving torque of 0.9Nm and speed of 54rpm. At ambient temperature of 100°C, the motor still has stalling torque of 0.9Nm and no-load speed of 79rpm for a operating voltage of 250V0-p, which means that this motor can operate in relatively high temperature environment.

Low frequency broadband monopole transducer based on trilaminar bender bar structures

A transducer which is produced by a skeleton and four Trilaminar bender bar vibration elements is presented in the paper. Four vibration elements formed a square array are excited by the same signal to realize monopole radiation. The influence of the skeleton is taken into account: flexural mode of vibration of the skeleton is used to extend the bandwidth. The transmitting voltage response of a modeling result shows that there are two peaks existed close to 1.8 kHz, which correspond to the 2nd order flexural mode of the Trilaminar bender bar and the 1st order flexural mode of the skeleton. The -3dB operational frequency range from 16.6kHz to 20.2kHz. The directivity patterns reflect that transducer can realize a monopole radiation in the horizontal plane before 13kHz.

Excitation mechanisms and dispersion characteristics of guided waves in multilayered cylindrical solid media

This paper first reviews a method of simulating the propagation characteristics of guided waves in multilayered coaxial cylindrical elastic solid media. Secondly, this method is used to investigate the properties of the guided waves for the ultrasonic long-range non-destructive evaluation techniques for rockbolts. To do so, the special case of non-leaky guided modes in open waveguides is considered. The method explains how the complex dispersion function is converted into a real function: hence the bisection technique can be employed to search for all the real roots. The model is used to (i) characterize the low dispersion range and anomalous dispersion of normal and Stoneley modes and (ii) analyze the excitation mechanisms of guided waves from axisymmetric and non-axisymmetric acoustic sources. The results are used to select suitable excitation frequency ranges associated with dominant modes with large amplitudes, low dispersion, and distinguishable propagation velocities to reduce signal distortion. The results suggest the lowest order flexural mode, excited by a radial force source, has potential to be used in practice. Also, the highly dispersive Stoneley mode propagating along a cylindrical interface is defined and distinguished from the normal mode using two properties, velocity high-frequency asymptotes and amplitude distributions along the radial direction.

Effect of Photoresist Coating on the Reusable Resonant Cantilever Sensors for Assessing Exposure to Airborne Nanoparticles

Abstract Silicon cantilever resonators were designed and fabricated in various shapes and dimensions to be used in an airborne nanoparticle (NP) sensing application. For a repeatedly usable sensor, the cantilever surface was covered by a sacrificial layer of photoresist prior to the airborne NP sampling. Using the electrostatic precipitation method, airborne NPs were sampled on the cantilever. Within a lift-off process of wet cleaning, the photoresist layer was removed together with the trapped NPs. The resonant frequency and the quality factor ( Q -factor) of the fundamental and higher order flexural modes of the silicon cantilevers were characterized for different thickness given by viscosity of the photoresist layer. It was found that the proposed recycling technique was most effective when a thin photoresist film was used. By using higher order resonant modes, Q -factors of more than 1000 in air were maintained even after the photoresist coating.

Investigation of the relationship between the vibration patterns of the skull and bone-conducted sound

Analytic and numerical models are used to evaluate acoustic energy converted into bone conducted sound that reaches the middle and inner ear. Sound impinging upon the skull, from an outside source, is channeled into surface waves on the outside of the skull. These waves have components in both the solid bone and the background medium of air, travel at much slower speeds than longitudinal sound speed for bone and have wavelengths smaller than those of an acoustic signal existing solely in bone or in the cranial cavity. Frequencies, at which an integer number plus one half of surface wave wavelengths fit around the circumference of the sphere, cause resonant vibrations. The added one half is due to phase matching surface waves at the poles. The relatively slow sound and short wavelengths mean resonance frequencies for the skull are lower than if the acoustic energy were confined to standing waves within the cranial cavity wherein wavelengths are longer. At acoustic frequencies skull vibrations are analogous to lowest order flexural modes of a fluid-loaded elastic sphere. Numerical models suggest bone's conducted sounds are confined to the skull surface with wave speeds much lower than speed of sound for boney or soft tissue.

Angled long tip to tuning fork probes for atomic force microscopy in various environments

We expand the range of applications of a tuning fork probe (TFP) in frequency-modulation atomic force microscopy (FM-AFM) by attaching a long metal tip at a certain angle. By the combined flexure of the metal tip and the tuning fork prong, this TFP can change the direction of the detectable force by switching the resonance frequency, which has not been realized with conventional TFPs with short tips. The oscillatory behavior of the tip apex of the TFP is predicted by computer simulations and is experimentally confirmed with scanning electron microscope. FM-AFM operations using this TFP are performed in various environments, i.e., in ultrahigh vacuum, air, and water. FM-AFM images obtained at an atomic step of highly oriented pyrolytic graphite in air show a clear difference depending on the excitation frequency. It is also revealed that the higher order flexural modes of this TFP are advantageous for FM-AFM in water due to the reduction in the degree of hydrodynamic damping.

Nanoscale charging hysteresis measurement by multifrequency electrostatic force spectroscopy

We report a scanning probe technique that can be used to measure charging of localized states on conducting or partially insulating substrates at room temperature under ambient conditions. Electrostatic interactions in the presence of a charged particle between the tip and the sample is monitored by the second order flexural mode, while the fundamental mode is used for stabilizing the tip-sample separation. Cycling the bias voltage between two limits, it is possible to observe hysteresis of the second order mode amplitude due to charging. Results are presented on silicon nitride films containing silicon nanocrystals.