Resonance Frequency Of Beam Research Articles

High-performance spinning device for DVD-based micromechanical signal transduction

Here we report a high-throughput spinning device for nanometric scale measurements of microstructures with instrumentation details and experimental results. The readout technology implemented in the designed disc-like device is based on a DVD data storage optical pick-up unit (OPU). With a spinning mechanism, this device can simultaneously measure surface topography, mechanical deflections and resonance frequencies of several microfabricated beams at a high speed. In biochemical sensing applications, the OPU can measure bending changes of functionalized microcantilevers, providing a statistically robust and label-free bio-detection analysis of multiple compounds. The signal-to-noise ratio (S/N) is demonstrated from statistical measurements as 1.2 with arginine detection at 750 nM concentration. Practically, the OPU can measure up to 480 individual cantilever sensors per second with nanometer resolution. The opto-mechanical optimization of the device design and settings for biochemical detection are described.

A Simple Analytical Model for the Resonance Frequency of Perforated Beams

In this work, a compact analytical model to evaluate the effect of perforations on the resonance frequencies of MEMS beams is presented. The model is based on a modification of the standard Euler-Bernoulli beam theory. Analytical expressions for an equivalent bending stiffness of the beam are developed and used to compute the expected resonance frequencies. The results are in good agreement with FEM simulations for most practical designs.

Evaluation of a Single-Crystal-Silicon Microelectromechanical Systems Resonator Utilizing a Narrow Gap Process

To investigate a higher frequency microelectromechanical systems (MEMS) resonator, mechanical behaviors and electrical characteristics on a single-crystal-silicon MEMS resonator, utilizing a narrow gap process, have been evaluated. The size reduction for the resonators leads to a decrease in output signal. To overcome this problem, an increase in electromechanical coupling coefficient is required. To investigate the effect of the reduction of the gap between a beam and a driving electrode, two types of 100 kHz MEMS resonator with different gaps have been fabricated and compared. It has been observed that the resonator with a narrow gap (1 µm) has a larger displacement amplitude, as well as a larger phase transition, than that with a 4 µm gap, which suggests that the gap reduction is effective. Then, a 10 MHz MEMS resonator has been fabricated by using the narrow gap process with a focused-ion beam (FIB). The resonant vibration for the fabricated device has been observed at 11.262 MHz. To further improve the resonators, it is suggested that the substrate vibration near the beam resonant frequency should be suppressed and that a smooth surface of the gap should be fabricated.

Evaluation of a Single-Crystal-Silicon Microelectromechanical Systems Resonator Utilizing a Narrow Gap Process

To investigate a higher frequency microelectromechanical systems (MEMS) resonator, mechanical behaviors and electrical characteristics on a single-crystal-silicon MEMS resonator, utilizing a narrow gap process, have been evaluated. The size reduction for the resonators leads to a decrease in output signal. To overcome this problem, an increase in electromechanical coupling coefficient is required. To investigate the effect of the reduction of the gap between a beam and a driving electrode, two types of 100 kHz MEMS resonator with different gaps have been fabricated and compared. It has been observed that the resonator with a narrow gap (1 µm) has a larger displacement amplitude, as well as a larger phase transition, than that with a 4 µm gap, which suggests that the gap reduction is effective. Then, a 10 MHz MEMS resonator has been fabricated by using the narrow gap process with a focused-ion beam (FIB). The resonant vibration for the fabricated device has been observed at 11.262 MHz. To further improve the resonators, it is suggested that the substrate vibration near the beam resonant frequency should be suppressed and that a smooth surface of the gap should be fabricated.

Bidirectional frequency tuning of a piezoelectric energy converter based on a cantilever beam

A piezoelectric energy converter is presented, whose resonance frequency can be tuned by applying mechanical stress to its structure. The converter consists of a piezo-polymer cantilever beam with two additional thin arms, which are used to apply an axial preload to the tip of the beam. The compressive or tensile prestress applied through the arms leads to a shift of the beam's resonance frequency. Experiments with this structure indicate a high potential: the resonance frequency of a harvester to which a compressive preload was applied could be altered from 380 Hz to 292 Hz. In another experiment, a harvester with stiffened arms was tuned from 440 Hz to 460 Hz by applying a tensile preload. In combination with automatic control of the applied force, this type of structure could be used to enhance the performance of energy harvesters in vibrating environments with occasional shifts of the vibrational frequency.

Two-Port Electromechanical Model for Bulk-Piezoelectric Excitation of Surface Micromachined Beam Resonators

A small-signal model that describes the energy exchange between surface micromachined beams and bulk-lead zirconium titanate (PZT) actuators attached to the silicon substrate is presented. The model includes detection of acoustic waves launched from electrostatically actuated structures on the surface of the die, as well as their actuation by bulk waves generated by piezoelectric ceramics. The interaction is modeled via an empirical equivalent circuit, which is substantiated by experiments designed to extract the model parameters. The equivalent model is valid for cases where the beam resonance frequency is much smaller than the thickness mode resonance of the PZT/silicon stack. In this paper, the resonance frequency of the beams ranges between 200 and 300 kHz. As energy transfer between bulk-PZT and electrostatic actuated beam resonators must be reciprocal for small signals, this paper uses the extracted equivalent model to describe the physical sources of error that account for discrepancies in reciprocity.

Modelling and measurements of a composite microcantilever beam for chemical sensing applications

A resonant microcantilever beam gas sensor was designed and fabricated in Carnegie Mellon University using complementary metal oxide semiconductor (CMU-CMOS) technology. The cantilever beam modified with a suitable sorbent coating was demonstrated as a chemical transducer for monitoring hazardous vapours and gases at trace concentrations. The design of the cantilever beam included interdigitated fingers to allow electrostatic actuation of the device and a piezoresistive Wheatstone bridge design to read out the deflection signal. The cantilever beam resonant frequency was modelled using the Euler-Bernoulli beam theory and ANSYS. The beam resonant frequency was measured with an optical laser Doppler vibrometer. Good agreement was obtained among the measured, simulated, and modelled resonant frequencies. A custom sorbent polymer layer was coated on the surface of the cantilever beam to allow its operation as a gas-sensing device. The frequency response as a function of exposure to the nerve agent simulant dimethylmethylphosphonate (DMMP) at different concentrations was measured, which allowed a demonstrated detection at a concentration of 20 ppb or 0.1 mg/m3. The air-polymer partition coefficient K, for DMMP was estimated and compared favourably with the known values for related polymers.

Fixed-fixed flexural vibration testing method of beams for timber guardrails

Resonance frequencies of beams with various types of end supports were examined for flexural vibration. Rectangular beams with dimensions of 300 (L) × 25 (R) × 5 or 10mm (T) were used as the test specimens. Various compressing stresses were applied to the parts around both ends of a test beam and flexural vibration tests were conducted. The measured resonance frequency started to increase from the resonance frequency of a beam with simply supported ends and was stable around the resonance frequency of a beam with fixed ends as the compressing stress increased. The stable resonance frequency was lower than the theoretical value because perfect fixation of a beam to a post was difficult. From these results, the temporal change in resonance frequency itself, rather than the stable resonance frequency, is effective to examine whether a beam has enough strength as a guardrail.

Silicon resonant accelerometer with electronic compensation of input-output cross-talk

A resonant accelerometer manufactured in silicon bulk micromachining with electrothermal excitation and piezoresistive detection is presented. The structure is a seismic mass supported by two parallel flexure hinges as a doubly-sustained cantilever, with a resonating microbeam located between the hinges. The acceleration normal to the chip plane induces an axial stress in the microbeam and, in turn, a proportional change in the microbeam resonant frequency. Beam resonant frequency of around 70 kHz and acceleration sensitivity of 35 Hz/g over the range 0–3 kHz were measured on prototypes, in accordance with analytical calculations and simulations. The microbeam operates unsealed at atmospheric pressure, therefore a comparatively low quality factor results due to air damping. In this condition, the effect of the input-output cross-talk was found to be significant. The cross-talk is analyzed and modeled, and an electronic active compensation is proposed. The compensated sensor was inserted into a phase-locked loop oscillator and tested. Reported experimental results show that the sensor performs in excellent agreement with the theoretical predictions.

A surface-micromachined resonant-beam pressure-sensing structure

The first study on an entirely surface-micromachined resonant-beam pressure sensor is presented. Using a fully surface-micromachined process, an encapsulated beam resonant pressure-sensor structure with a pressure-sensitive diaphragm of 100/spl times/150/spl times/2 /spl mu/m has been fabricated. The resonating beam is fully enclosed inside the reference vacuum cavity formed beneath the diaphragm. The new design enables high pressure sensitivity and a miniature chip size, essential for sensors such as catheter-mounted intravascular blood pressure sensors. The pressure sensitivity is measured at 3.2%/bar with a beam resonance frequency of about 700 kHz.

Design facts in the axial monotron

Upon reexamining the electron beam radio frequency (RF)-field interaction of the monotron, which is the simplest transit-time microwave tube, it is found that a 20% maximum conversion efficiency can be attained at weakly relativistic beam energies (/spl sim/200 keV). It is shown that the conversion efficiency can be cast as a function of three parameters, namely, injection beam energy, resonant frequency, and electric field strength. From this fact, a design procedure of how the optimum operating parameters should be selected is presented. In support of the analytic study, 2.5-D particle-in-cell simulation of a transverse magnetic (TM)/sub 020/, 6.7 GHz axial monotron operating at 10 keV, 70 A beam parameters has given a tube efficiency of 15.4%, while one-dimensional (1-D) analysis assuming a strictly monoenergetic beam has predicted a maximum theoretical efficiency of 18.5% at a beam energy of 10 keV.

Silicon micro/nanomechanical device fabrication based on focused ion beam surface modification and KOH etching

Selective Ga+ ion implantation and milling by focused ion beam exposure and subsequent wet chemical etching is used to fabricate micro/nanomechanical elements in Si. Freestanding elements with a ≈ 30 nm membrane thickness are made by controlled selective underetching between unexposed and exposed areas. Ultrahigh-frequency cantilever beams have been made with resonances in the tens of MHz range. Using a U-shaped beam cross section, mechanical stiffness could be increased 100-fold, which in turn increased the beam resonance frequency to several hundreds of MHz. The direct-write patterning/milling technique was used to fabricate various arbitrary shapes with vertical sidewalls such as submicrometer-sized containers, cups, and other nanomechanical devices.

Optical beam deflector using a piezoelectric bimorph actuator

Abstract This paper describes optical beam deflectors using piezoelectric bimorphs with both ends clamped. In these deflectors, the bimorph must bend so that a mirror affixed onto its central position tilts by applying voltage. The poling configuration which enables the bimorph to generate such a deformation has been analyzed. Deflectors for both one- and two-dimensional operations have been individually fabricated and investigated based on this analytical result. The maximum optical beam deflection and resonance frequency were about 20 mrad and 3.3 kHz, respectively, for a one-dimensional operation deflector. The values were about 16 mrad and 3.0 kHz, respectively, for a two-dimensional operation deflector.

Process Integration for active polysilicon resonant microstructures

Microsensors based on active polysilicon resonant microstructures are attractive because of their wide dynamic range, high sensitivity and frequency shift output. In this paper, we discuss processing issues for integrating electrostatically-driven and -sensed polysilicon microstructures with on-chip nMOS device. Surface-micro-machining using sacrificial spacer layers is used to obtain relased microstructures. A novel feature is the use of rapid thermal annealing (RTA) for strain relief of the ion-implanted, phosphorous-doped polysilicon. Resonance frequencies of cantilever beams indicate a lower-bound Young's modulus of about 90 GPa and an upper-bound compressive residual strain of only 0.002%, indicating that RTA is potentially useful for strain relief.

Vibration Control of Beams by Ball Screw Type Dampers with a Governor

The forced nonlinear vibrations of simple beams supported with two kinds of ball screw type dampers are discussed both numerically and experimentally. The dampers are composed of a ball screw, a flywheel and flyball or perpendicular type governor, and they possess nonlinear characteristics. The beam is replaced by a lumped mass system and the Continuous System Simulation Language is used to simulate the motion of the masses and the damper on a digital computer. The results may be summarized as follows: (1) Two types of dampers are effective for suppressing the amplitude of the beam at the point of attachment of the damper at the first resonance. (2) The linear solution which is obtained by regarding the governor as a flywheel differs from the nonlinear solution in the vicinity of the first resonance frequency of the beam. (3) Each damper approaches the snubber for larger values of moment of inertia J of the flywheel, and acts like a dynamic vibration absorber for smaller values of J.

Flexural waves and deflection mode shapes of periodic and disordered beams

This paper deals with free flexural wave motion and natural deflection mode shapes of simply supported infinite uniform periodic beams consisting of repeating units that are identical finite beams having equal and unequal span lengths. Governing equations for the natural frequencies and that for the wave propagation constant have first been set up in terms of the receptances of the individual beam elements. The equations are then applied to compute the natural frequencies and deflection mode shapes together with the propagation constants for some specific disordered periodic beams that include four-span and eight-span periodic and disordered beams. Relationship between the natural frequencies of the symmetric finite repeating beam units and the bounding frequencies of the propagation and attenuation zones has been studied. The bounding frequencies are always identified with the resonance frequencies of such beams with their extreme ends either simply supported or clamped. The combinations of the natural frequencies, with which the bounding frequencies of the propagation and attenuation zones can be identified, have been pointed out. Studies of the deflection mode shapes of symmetrically and unsymmetrically disordered four-span beams have shown that the characteristic free waves in an infinite periodic system consisting of disordered repeating beams (beams of unequal span lengths) do not always decay at the natural frequencies. The conditions under which the waves at the natural frequencies of the repeating beam units decay have been studied and explained.

Ensemble averages of power flow in randomly excited coupled beams

The transmission of transverse vibrational energy between two coupled beams subjected to random excitation is considered. Extensive numerical results are given for the frequency decomposition of power flow between the beams. The power flow is a function of the three non-dimensional parameters describing frequency, ω/ω 1 , where ω 1 is the fundamental resonance frequency of beam one, length ratio, L 2 / L 1 , and damping or modal overlap ratio. Single frequency and octave band averages are shown for various values of L 2 / L 1 , and means and variances are calculated for the ensemble of systems corresponding to a uniform distribution of 1≤ L 2 / L 1 ≤2. Various approximate results based on modal analysis and on SEA are compared with the exact results.

Ensemble averages of power flow in randomly excited coupled beams

This paper considers the transmission of transverse vibrational energy between two coupled beams subjected to random excitation. Extensive numerical results are given for the frequency decomposition of power flow between the beams. The power flow is a function of the three nondimensional parameters describing frequency, w/w1, where w1 is the fundamental resonance frequency of beam one, length ratio, L2/L1, and damping or modal overlap ratio. Single frequency and octave band averages are shown for various values of L2/L1, and means and variances are calculated for the ensemble of systems corresponding to a uniform distribution of 1 ⩽ L2/L1 ⩽ 2. Various approximate results based on modal analysis and on SEA are compared with the exact results.

Effects of Shear Deformation, Rotary Inertia, and Elasticity of the Support on the Resonance Frequencies of Short Cantilever Beams

The purpose of this paper is to contribute to the assessment of the influence of shear deformation, rotary inertia, and elasticity of the support on the resonance frequencies of short turbomachinery blades. To obtain defined test conditions and to model the stiffest possible root design, the study is made on beams and supports machined from one piece. Experimental results show good agreement with results obtained from the finite element program NASTRAN. An estimate of the combined effects obtained by taking the individual effects multiplicatively, with the effect of the elasticity of the support being computed on the basis of known static influence coefficients of the elastic half space, results in a frequency reduction larger than measured.

A Critical Assessment of the Cantilever Beam Method for the Determination of Dynamic Young's Modulus

Abstract The application of a noncontacting optical transducer for the measurement of flexural resonant frequencies and normal mode shapes of a cantilever beam is described. Results on the resonant frequencies of cantilever beams, gripped at the fixed end by a vise, are compared with the Bernoulli-Euler and Timoshenko beam theories. Although the mode shapes agree well with the theories, there are large discrepancies between the experimental variation of resonant frequency with inverse slenderness ratio and that predicted by the theories. These discrepancies are attributed to imperfect clamping. It is concluded that for accurate Young's modulus calculations from the measured resonant frequencies of cantilever beams, tests must be restricted to long slender beams. For beams which cannot be fabricated to meet this criterion, an empirical method is presented which yields Young's modulus to within ±3 percent on the specimens tested. For increased accuracy the free-free reasonant beam method should be used.