Flexural Vibration Modes Research Articles

A Touch Interface Exploiting Time-Frequency Classification Using Zak Transform for Source Localization on Solids

We propose a new approach to the development of a touch interface using surface-mounted sensors which allows one to convert a hard surface into a touch pad. This is achieved by using location template matching (LTM), a source localization algorithm that is robust to dispersion and multipath. In this interdisciplinary research, we employ mechanical vibration theories that model wave propagation of the flexural modes of vibration generated by an impact on the surface. We then verify that the amplitude variance across time for each propagating mode frequency is unique to each location on a surface. We show that the Zak transform allows us to faithfully track these amplitude variations and we exploit the uniqueness of this variance as a time-frequency classifier which in turn allows us to localize a finger tap in the context of a human-computer interface. The performance of the proposed algorithm is compared with existing LTM approaches on real surfaces.

Simulation and vibrational analysis of thermal oscillations of single-walled carbon nanotubes

The first four flexural thermal vibrational modes of single-walled carbon nanotubes (SWCNTs) of various lengths and radii were studied using atomistic molecular dynamics within the framework of the Brenner interatomic potential and Fourier analysis. These simulations provide clear evidence for the failure of simplistic analytic models to accurately extract resonance frequencies as the ratio $R/L$ between the tube radius and the length increases. They are in excellent agreement with the Timoshenko beam model, which includes the effect of both rotary inertia and of shearing deformation. In addition, our results partially resolve Yakobson's paradox and provide an upper cutoff estimate for the effective SWCNT thickness.

Control of floor vibration and noise using multiple tuned mass dampers

The floor impact noise that occurs between upper and lower households in residential houses has been known as one of major causes that adversely affects residential environments and can lead to serious social troubles in a residential community. In order to alleviate this problem of floor impact noise and to improve the residential conditions, regulations are applied in many countries to reduce the floor impact noise. The floor impact noise can be divided into two categories - light weight floor impact noise and heavy weight floor impact noise - depending on the standard impact sources and the frequency range where the noise is dominant. The light weight floor impact noise generated in the high frequency ranges can be easily reduced by resilient material used in a conventional floating slab system, whereas the heavy weight floor impact noise induced by flexural vibration modes in the relatively lower frequency ranges is difficult to reduce using the traditional methodologies such as a floating slab system or increasing the thickness of slab. In this study, a new method is presented to effectively reduce the heavy weight floor impact noise induced by the vibration of slab using the multi tuned mass dampers (MTMDs). A substructure modal synthesis technique based on the FEM model is utilized to develop an analytical model of the slab coupled with MTMDs. Further, the acoustic power and acceleration responses are analyzed to evaluate the performance of the MTMDs in reducing floor impact noise. Numerical analysis is carried out to investigate the effect of the MTMD on the vibration and noise control of the simply supported slab

554 二枚の共振平板の間に生成される移動空間を利用した送風機構

Air blower using travelling space generated between two resonantly-driven plates, which are excited at an eigenfrequency of flexural vibration mode has been developed. This air blower is suitable for a cool down device of compact electrical devices, because of a thin configuration. The advantage of this transportation machine is that the energy efficiency, because of the resonance driving. Firstly we experimentally verified the generation mechanism of travelling space by use of small device and indicated possibility as a small air blower.

Ferroelectric Thin Film Diaphragm Resonators for Bio-Detection

In this paper, we have investigated a piezoelectric resonator biosensor based on ferroelectric thin film diaphragm. The diaphragm structure utilizing a flexural vibration mode has been adopted to replace the microcantilever structure in a biosensor. It is an acoustic wave device which can be immobilized with a bio-molecular recognition layer on its surface. Like a microcantilever sensor, the resonance frequency of the diaphragm sensor shifts when the bio-molecular recognition layer reacts with the target species. But a diaphragm sensor has more robust structure comparing with a microcantilever sensor. The responses of the diaphragm biosensor have been simulated using a commercial FEM software package, ANSYS. The prototype devices were fabricated by a conventional method and a MEMS process, respectively. The performance of the sensor was tested and reported.

Design and Characteristics of Bar Type Piezoelectric Micropump

Micropump is very useful component in micro/nano fluidics and bioMEMS applications. Using the flexural vibration mode of PZT bar, a piezopump is successfully made. The PZT bar is polarized along the thickness direction. The proposed structure for the piezo-pump consists of the input and output ports the piezoelectric ceramic actuator, the actuator support, and the diaphragm. The traveling flexural wave along the bar is obtained by dividing two standing waves which are temporally and spatially phase shifted by 90 degrees from each other. Fluid is drawn into a forming chamber, eventually the forming chamber closes trapping the fluid therein. Components of piezopump were made, assembled, and tested to validate the concepts of the proposed pump and confirm the simulation results.

Nonlinear Modal Interactions in Clamped-Clamped Mechanical Resonators

A theoretical and experimental investigation is presented on the intermodal coupling between the flexural vibration modes of a single clamped-clamped beam. Nonlinear coupling allows an arbitrary flexural mode to be used as a self-detector for the amplitude of another mode, presenting a method to measure the energy stored in a specific resonance mode. The observed complex nonlinear dynamics are quantitatively captured by a model based on coupling of the modes via the beam extension; the same mechanism is responsible for the well-known Duffing nonlinearity in clamped-clamped beams.

Squeeze-film damping characteristics of cantilever microresonators for higher modes of flexural vibration

Squeeze-film characteristics of electrostatically actuated microcantilevers observed under large DC load coupled with small AC component are presented for the first three flexural modes of vibration of the resonator operating in different ambient pressure conditions. A semi-analytical model of an electrostatically actuated microcantilever beam is developed taking into account the dependency of the effective viscosity on variable gap spacing through the variable Knudsen number. The quality factors of the system are also obtained numerically using the coupled field FE analysis software ANSYS. A comparison of the results up to the pull-in instability shows excellent agreement for damping characteristics obtained by both the semi-analytical and FE methods. The effects of large DC bias voltages on quality factor and resonance frequency are found to differ considerably for the different flexural modes of vibration of the resonator. Under rarefied flow conditions, variations in ambient pressure significantly influence the squeeze film damping characteristics for the entire range of DC polarization. A comparison between compressible and incompressible flow models predicts notable difference in the squeeze-film characteristics. Keywords: MEMS, Electrostatic actuation, Squeeze-film damping, Rarefied flow, Resonant sensor.

A micro-machined piezoelectric flexural-mode hydrophone with air backing: Benefit of air backing for enhancing sensitivity

A micro-machined underwater acoustic receiver that utilizes the flexural vibration mode of a silicon thin plate and piezoelectric transduction material was investigated. In particular, air was used as the backing material for the hydrophone in order to improve sensitivity in the audible frequency range. To evaluate the effects of air backing on receiving sensitivity, a transduction model incorporating mechanical/electrical/acoustical design parameters was used in designing a piezoelectric micro-machined hydrophone. The sensitivity and displacement responses of the sensor were simulated using the model for air backing and water backing cases, and the benefit of using air backing to enhance sensitivity was confirmed. The micro-machined piezoelectric transducer was fabricated, assembled in the shape of a hydrophone, and tested to ascertain its characteristics as an underwater sensor. These characteristics, such as frequency response and sensitivity, were measured and compared with the simulated results.

An approach based on tool mode control for surface roughness reduction in high-frequency vibration cutting

The presented research work, aimed at deeper understanding of vibrational process during high-frequency vibration cutting, is accomplished by treating cutting tool as an elastic structure which is characterized by several modes of natural vibrations. An approach for surface quality improvement is proposed in this paper by taking into account that quality of machined surface is related to the intensity of tool–tip (cutting edge) vibrations. It is based on the excitation of a particular higher vibration mode of a turning tool, which leads to the reduction of deleterious vibrations in the machine–tool–workpiece system through intensification of internal energy dissipation in the tool material. The combined application of numerical analysis with accurate finite element model as well as different experimental methods during investigation of the vibration turning process allowed to determine that the most favorable is the second flexural vibration mode of the tool in the direction of vertical cutting force component. This mode is excited by means of piezoelectric transducer vibrating in axial tool direction at the corresponding natural frequency, thereby enabling minimization of surface roughness and tool wear.

Noncontact ultrasonic transportation of small objects in a circular trajectory in air by flexural vibrations of a circular disc.

We have developed a noncontact ultrasonic technique for transporting small objects with a linear trajectory over long distances using a bending vibrating plate and a reflector. In this paper, noncontact transportation of small particles around a circular trajectory was investigated. A circular aluminum plate with a piezoelectric ring was employed as a vibrating plate. On the basis of finite element analysis (FEA) calculations, the electrodes of the piezoelectric ring were divided into 24 pieces to generate a flexural vibration mode with one nodal circle and four nodal lines at the resonance frequency of 47.8 kHz. A circular plate having the same dimensions as the vibrating plate was installed parallel to the vibrator. It was used as a reflector to generate an acoustic standing wave in the air between the two plates. The acoustic field between the vibrating plate and reflector was calculated by FEA and the distribution of the acoustic radiation force acting on a small rigid particle was calculated to predict the position of the trapped particle. Using a prototype of the vibrating plate, polystyrene particles with diameters of several millimeters could be trapped at regular intervals along the horizontal nodal line of the standing wave. The sound pressure distribution between the vibrating plate and reflector was measured by a fiber optic probe and the experimental and calculated results showed good agreement. By switching the driving conditions of the divided electrodes in the circumferential direction, the nodal lines of the vibrating plate could be rotated and the trapped particle could be manipulated with a circular trajectory in air.

A cylindrical traveling wave ultrasonic motor using longitudinal and bending composite transducer

A cylindrical type traveling wave ultrasonic motor using longitudinal and bening composite transducer was proposed in this paper. A composite transducer is attached to the cylinder on its outer surface to excite two degenerate flexural vibration modes spatially and temporally orthogonal to each other in the cylinder. In this new design, a single transducer can excite a flexural traveling wave in the cylinder. Two cone type rotors are pressed in contact to the borders of the inner surface of teeth by means of a spring and nut system. The working principle of the motor was analyzed. The resonance frequencies of the two vibration modes of stator were tuned to be close to one another using finite element method. A prototype motor was fabricated and tested. Typical output of the prototype is no-load speed of 281 rpm and maximum torque of 1.2 N m at an exciting voltage of 200 V rms.

Cooling of a Suspended Nanowire by an ac Josephson Current Flow

We consider a nanoelectromechanical Josephson junction, where a suspended nanowire serves as a superconducting weak link, and show that an applied dc bias voltage can result in suppression of the flexural vibrations of the wire. This cooling effect is achieved through the transfer of vibronic energy quanta first to voltage-driven Andreev states and then to extended quasiparticle electronic states. Our analysis, which is performed for a nanowire in the form of a metallic carbon nanotube and in the framework of the density matrix formalism, shows that such self-cooling is possible down to the ground state of the flexural vibration mode of the nanowire.

Noncontact ultrasonic transportation of small objects in a circular trajectory in air by flexural vibrations of a circular disc

We have developed a noncontact ultrasonic technique for transporting small objects with a linear trajectory over long distances using a bending vibrating plate and a reflector. In this paper, noncontact transportation of small particles around a circular trajectory was investigated. A circular aluminum plate with a piezoelectric ring was employed as a vibrating plate. On the basis of finite element analysis (FEA) calculations, the electrodes of the piezoelectric ring were divided into 24 pieces to generate a flexural vibration mode with one nodal circle and four nodal lines at the resonance frequency of 47.8 kHz. A circular plate having the same dimensions as the vibrating plate was installed parallel to the vibrator. It was used as a reflector to generate an acoustic standing wave in the air between the two plates. The acoustic field between the vibrating plate and reflector was calculated by FEA and the distribution of the acoustic radiation force acting on a small rigid particle was calculated to predict the position of the trapped particle. Using a prototype of the vibrating plate, polystyrene particles with diameters of several millimeters could be trapped at regular intervals along the horizontal nodal line of the standing wave. The sound pressure distribution between the vibrating plate and reflector was measured by a fiber optic probe and the experimental and calculated results showed good agreement. By switching the driving conditions of the divided electrodes in the circumferential direction, the nodal lines of the vibrating plate could be rotated and the trapped particle could be manipulated with a circular trajectory in air.

A theory of sound transmission through a clamped curved piezoelectric membrane connected to a negative capacitor

An analytical calculation of the acoustic transmission loss of sound propagating through a thin cylindrically curved piezoelectric membrane, which is rigidly clamped at its straight ends, is presented. The membrane is placed inside an acoustic tube and connected to an active electric shunt circuit that behaves as a negative capacitor. A properly adjusted shunt circuit has a significant impact on the effective elastic stiffness of the piezoelectric membrane and, hence, influences the membrane acoustic reflectivity and transmission loss of sound. Such a setup represents a noise control system based on the principles of the active elasticity control of piezoelectric materials. The non-uniform radial motion of the clamped membrane and its interaction with the acoustic field and the electric shunt circuit are analyzed. The main objective of the calculations, which are based on Donnell’s theory, is the determination of the effects of the membrane clamps on the flexural motion of the membrane and, therefore, effects on the acoustic transmission loss of sound. Approximative formulae for the amplitude of the membrane displacement and the acoustic transmission loss of sound are expressed as well as the resonant frequencies of the uniform mode and flexural vibration modes.

A distributed-mass approach for dynamic analysis of Bernoulli–Euler plane frames

The exact dynamic analysis of plane frames should consider the effect of mass distribution in beam elements, which can be achieved by using the dynamic stiffness method. Solving for the natural frequencies and mode shapes from the dynamic stiffness matrix is a nonlinear eigenproblem. The Wittrick–Williams algorithm is a reliable tool to identify the natural frequencies. A deflated matrix method to determine the mode shapes is presented. The dynamic stiffness matrix may create some null modes in which the joints of beam elements have null deformation. Adding an interior node at the middle of beam elements can eliminate the null modes of flexural vibration, but does not eliminate the null modes of axial vibration. A force equilibrium approach to solve for the null modes of axial vibration is presented. Orthogonal conditions of vibration modes in the Bernoulli–Euler plane frames, which are required in solving the transient response, are theoretically derived. The decoupling process for the vibration modes of the same natural frequency is also presented.

Optimum design of a multilayer beam partially treated with magnetorheologicalfluid

The modal damping characteristics of beams partially treated with magnetorheological(MR) fluid elements are studied using the modal strain energy approach and the finiteelement method. Different configurations of a sandwich beam partially treated with MRfluid are considered, including a beam with a cluster of MR fluid segments and abeam with arbitrarily located MR fluid segments. The significance of the locationof the MR fluid segments on the modal damping factor is investigated underdifferent end conditions. An optimization problem is formulated by combiningfinite element analysis with optimization algorithms based on sequential quadraticprogramming (SQP) and the genetic algorithm (GA) to identify optimal locationsfor MR fluid treatment to achieve maximum modal damping corresponding tothe first five modes of flexural vibration, individually and simultaneously. Thesolutions of the optimization problem revealed that the GA converges to theglobal solutions rapidly compared to the SQP method, which in some modalconfigurations usually entraps in the local optimum. The results suggest thatthe optimal location of the MR fluid treatment is strongly related to the endconditions and also the mode of vibration. Furthermore, partial treatments with MRfluid can significantly alter the deflection modes of the beam. It has also beendemonstrated that optimal locations of the MR fluid segments based on linearcombination of the modal damping factors of the first five modes are identicalto those obtained based on the first mode, irrespective of the end conditions.However, the optimal locations of the MR fluid segments, identified based on thelogarithmic summation of the modal damping factors of the first five modes, wouldyield a more uniform shear energy distribution compared to that attained byconsidering individual modes or a linear summation of the individual modes.

Actuating Mechanism and Design of a Cylindrical Traveling Wave Ultrasonic Motor Using Cantilever Type Composite Transducer

BackgroundUltrasonic motors (USM) are based on the concept of driving the rotor by a mechanical vibration excited on the stator via piezoelectric effect. USM exhibit merits such as simple structure, quick response, quiet operation, self-locking when power off, nonelectromagnetic radiation and higher position accuracy.Principal FindingsA cylindrical type traveling wave ultrasonic motor using cantilever type composite transducer was proposed in this paper. There are two cantilevers on the outside surface of cylinder, four longitudinal PZT ceramics are set between the cantilevers, and four bending PZT ceramics are set on each outside surface of cantilevers. Two degenerate flexural vibration modes spatially and temporally orthogonal to each other in the cylinder are excited by the composite transducer. In this new design, a single transducer can excite a flexural traveling wave in the cylinder. Thus, elliptical motions are achieved on the teeth. The actuating mechanism of proposed motor was analyzed. The stator was designed with FEM. The two vibration modes of stator were degenerated. Transient analysis was developed to gain the vibration characteristic of stator, and results indicate the motion trajectories of nodes on the teeth are nearly ellipses.ConclusionsThe study results verify the feasibility of the proposed design. The wave excited in the cylinder isn't an ideal traveling wave, and the vibration amplitudes are inconsistent. The distortion of traveling wave is generated by the deformation of bending vibration mode of cylinder, which is caused by the coupling effect between the cylinder and transducer. Analysis results also prove that the objective motions of nodes on the teeth are three-dimensional vibrations. But, the vibration in axial direction is minute compared with the vibrations in circumferential and radial direction. The results of this paper can guide the development of this new type of motor.

Wave Propagation in a Homogeneous Transversely Isotropic Thermoelastic Solid Cylinder of Polygonal Cross-sections

The problem of wave propagation in an infinite, homogeneous, transversely isotropic polygonal cross-sectional cylinder is studied using Fourier expansion collocation method, within the framework of linearized, three dimensional theory of thermoelasticity. Three displacement potential functions are introduced, to uncouple the equations of motion and the heat conduction. The frequency equations are obtained for longitudinal and flexural (symmetric and antisymmetric) modes of vibration and are studied numerically for triangular, square, pentagonal and hexagonal cross-sectional Zinc cylinders. To study the convergence, the non-dimensional wave numbers are obtained by Fourier Expansion Collocation Method and Finite Element Method and they are compared. The computed non-dimensional wave numbers are presented in the form of dispersion curves.

Electromechanical Behavior of Interdigitated SiO2 Cantilever Arrays

Bending and first flexural mode vibration behavior of electrostatic actuated nanometer-sized interdigitated cantilever arrays are characterized under vacuum conditions. The “pull-in" effect in dc driving and the “hard spring effect" in ac driving are observed. A mass sensitivity of 20 fg is expected for our devices due to the ultra-small mass of the arm and relative high Q factor. The mass-spring lump model combined with Green's function method is used to fit the dc driving behaviors including the pull-in voltage. For the ac driving case, the polynomial expansion of the capacitive force is used in the model. The successfully fittings of the pull-in voltage and the hard spring effect prove that our simulation method could be used for guiding the geometrical design of cantilever-based sensors.