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At least 73 records · Page 4

Magnetoelastic sensing apparatus and method for remote pressure query of an environment

A pressure sensing apparatus for operative arrangement within an environment, having: a sensor comprising a hermetically-sealed receptacle, at least one side of which has an flexible membrane to which a magnetically hard element is attached. Enclosed within the receptacle is a magnetostrictive element that vibrates in response to a time-varying magnetic field. Also included is a receiver to measure a plurality of successive values for magneto-elastic emission intensity of the sensor taken over an operating range of successive interrogation frequencies to identify a resonant frequency value for the sensor. Additional features include: (a) the magnetically hard element may be adhered to an inner or outer side of, or embedded within, the membrane; (b) the magnetostrictive element can include one or more of a variety of different pre-formed, hardened regions; (c) the magneto-elastic emission may be a primarily acoustic or electromagnetic emission; and (d) in the event the time-varying magnetic field is emitted as a single pulse or series of pulses, the receiver unit can detect a transitory time-response of the emission intensity of each pulse (detected after a threshold amplitude value for the transitory time-response is observed). A Fourier transform of the time-response can yield results in the frequency domain. Also, an associated method of sensing pressure of an environment is included that uses a sensor having a magnetostrictive element to identify a magneto-elastic resonant frequency value therefore. Using the magneto-elastic resonant frequency value identified, a value for the pressure of the environment can be identified.

Grimes, Craig A.↗

High-frequency resonant-tunneling oscillators

Advances in high-frequency resonant-tunneling-diode (RTD) oscillators are described. Oscillations up to a frequency of 420 GHz have been achieved in the GaAs/AlAs system. Recent results obtained with In0.53Ga0.47As/AlAs and InAs/AlSb RTDs show a greatly increased power density and indicate the potential for fundamental oscillations up to about 1 THz. These results are consistent with a lumped-element equivalent circuit model of the RTD. The model shows that the maximum oscillation frequency of the GaAs/AlAs RTDs is limited primarily by series resistance, and that the power density is limited by low peak-to-valley current ratio.

Brown, E. R.↗

Fabrication of an Absorber-Coupled MKID Detector

Absorber-coupled microwave kinetic inductance detector (MKID) arrays were developed for submillimeter and far-infrared astronomy. These sensors comprise arrays of lambda/2 stepped microwave impedance resonators patterned on a 1.5-mm-thick silicon membrane, which is optimized for optical coupling. The detector elements are supported on a 380-mm-thick micro-machined silicon wafer. The resonators consist of parallel plate aluminum transmission lines coupled to low-impedance Nb microstrip traces of variable length, which set the resonant frequency of each resonator. This allows for multiplexed microwave readout and, consequently, good spatial discrimination between pixels in the array. The transmission lines simultaneously act to absorb optical power and employ an appropriate surface impedance and effective filling fraction. The fabrication techniques demonstrate high-fabrication yield of MKID arrays on large, single-crystal membranes and sub-micron front-to-back alignment of the micro strip circuit. An MKID is a detector that operates upon the principle that a superconducting material s kinetic inductance and surface resistance will change in response to being exposed to radiation with a power density sufficient to break its Cooper pairs. When integrated as part of a resonant circuit, the change in surface impedance will result in a shift in its resonance frequency and a decrease of its quality factor. In this approach, incident power creates quasiparticles inside a superconducting resonator, which is configured to match the impedance of free space in order to absorb the radiation being detected. For this reason MKIDs are attractive for use in large-format focal plane arrays, because they are easily multiplexed in the frequency domain and their fabrication is straightforward. The fabrication process can be summarized in seven steps: (1) Alignment marks are lithographically patterned and etched all the way through a silicon on insulator (SOI) wafer, which consists of a thin silicon membrane bonded to a thick silicon handle wafer. (2) The metal microwave circuitry on the front of the membrane is patterned and etched. (3) The wafer is then temporarily bonded with wafer wax to a Pyrex wafer, with the SOI side abutting the Pyrex. (4) The silicon handle component of the SOI wafer is subsequently etched away so as to expose the membrane backside. (5) The wafer is flipped over, and metal microwave circuitry is patterned and etched on the membrane backside. Furthermore, cuts in the membrane are made so as to define the individual detector array chips. (6) Silicon frames are micromachined and glued to the silicon membrane. (7) The membranes, which are now attached to the frames, are released from the Pyrex wafer via dissolution of the wafer wax in acetone.

Brown, Ari↗

Radio Frequency Mass Gauging of Propellants

A combined experimental and computer simulation effort was conducted to measure radio frequency (RF) tank resonance modes in a dewar partially filled with liquid oxygen, and compare the measurements with numerical simulations. The goal of the effort was to demonstrate that computer simulations of a tank's electromagnetic eigenmodes can be used to accurately predict ground-based measurements, thereby providing a computational tool for predicting tank modes in a low-gravity environment. Matching the measured resonant frequencies of several tank modes with computer simulations can be used to gauge the amount of liquid in a tank, thus providing a possible method to gauge cryogenic propellant tanks in low-gravity. Using a handheld RF spectrum analyzer and a small antenna in a 46 liter capacity dewar for experimental measurements, we have verified that the four lowest transverse magnetic eigenmodes can be accurately predicted as a function of liquid oxygen fill level using computer simulations. The input to the computer simulations consisted of tank dimensions, and the dielectric constant of the fluid. Without using any adjustable parameters, the calculated and measured frequencies agree such that the liquid oxygen fill level was gauged to within 2 percent full scale uncertainty. These results demonstrate the utility of using electromagnetic simulations to form the basis of an RF mass gauging technology with the power to simulate tank resonance frequencies from arbitrary fluid configurations.

Zimmerli, Gregory A.↗

EPR Imaging at a Few Megahertz Using SQUID Detectors

An apparatus being developed for electron paramagnetic resonance (EPR) imaging operates in the resonance-frequency range of about 1 to 2 MHz well below the microwave frequencies used in conventional EPR. Until now, in order to obtain sufficient signal-to-noise radios (SNRs) in conventional EPR, it has been necessary to place both detectors and objects to be imaged inside resonant microwave cavities. EPR imaging has much in common with magnetic resonance imaging (MRI), which is described briefly in the immediately preceding article. In EPR imaging as in MRI, one applies a magnetic pulse to make magnetic moments (in this case, of electrons) precess in an applied magnetic field having a known gradient. The magnetic moments precess at a resonance frequency proportional to the strength of the local magnetic field. One detects the decaying resonance-frequency magnetic- field component associated with the precession. Position is encoded by use of the known relationship between the resonance frequency and the position dependence of the magnetic field. EPR imaging has recently been recognized as an important tool for non-invasive, in vivo imaging of free radicals and reduction/oxidization metabolism. However, for in vivo EPR imaging of humans and large animals, the conventional approach is not suitable because (1) it is difficult to design and construct resonant cavities large enough and having the required shapes; (2) motion, including respiration and heartbeat, can alter the resonance frequency; and (3) most microwave energy is absorbed in the first few centimeters of tissue depth, thereby potentially endangering the subject and making it impossible to obtain adequate signal strength for imaging at greater depth. To obtain greater penetration depth, prevent injury to the subject, and avoid the difficulties associated with resonant cavities, it is necessary to use lower resonance frequencies. An additional advantage of using lower resonance frequencies is that one can use weaker applied magnetic fields: For example, for a resonance frequency of 1.4 MHz, one needs a magnetic flux density of 0.5 Gauss approximately the flux density of the natural magnetic field of the Earth.

Hahn, Inseob↗

Controller for Driving a Piezoelectric Actuator at Resonance

A digital control system based partly on an extremum-seeking control algorithm tracks the changing resonance frequency of a piezoelectric actuator or an electrically similar electromechanical device that is driven by a sinusoidal excitation signal and is required to be maintained at or near resonance in the presence of uncertain, changing external loads and disturbances. Somewhat more specifically, on the basis of measurements of the performance of the actuator, this system repeatedly estimates the resonance frequency and alters the excitation frequency as needed to keep it at or near the resonance frequency. In the original application for which this controller was developed, the piezoelectric actuator is part of an ultrasonic/sonic drill/corer. Going beyond this application, the underlying principles of design and operation are generally applicable to tracking changing resonance frequencies of heavily perturbed harmonic oscillators. Resonance-frequency-tracking analog electronic circuits are commercially available, but are not adequate for the present purpose for several reasons: The input/output characteristics of analog circuits tend to drift, often necessitating recalibration, especially whenever the same controller is used in driving a different resonator. In the case of an actuator in a system that has multiple modes characterized by different resonance frequencies, an analog controller can tune erroneously to one of the higher-frequency modes. The lack of programmability of analog controllers is problematic when faults occur, and is especially problematic for preventing tuning to a higher-frequency mode. In contrast, a digital controller can be programmed to restrict itself to a specified frequency range and to maintain stability even when the affected resonator is driven at high power and subjected to uncertain disturbances and variable loads. The present digital control system (see figure) is implemented by means of an algorithm that comprises three main subalgorithms: a hill-climbing control algorithm, an estimation-based extremum-seeking control (ESC) algorithm, and a supervisory algorithm. The hill-climbing algorithm is useful for coarse tracking to find and remain within the vicinity of the resonance. The ESC algorithm is not capable of coarse resonance tracking, but is capable of fine resonance tracking once the estimates of parameters generated by the hill-climbing algorithm have converged sufficiently. On the basis of the parameter-estimation errors, the supervisory algorithm switches operation to whichever of the other two algorithms performs best at a given time.

Aldrich, Jack↗

Using Whispering-Gallery-Mode Resonators for Refractometry

A method of determining the refractive and absorptive properties of optically transparent materials involves a combination of theoretical and experimental analysis of electromagnetic responses of whispering-gallery-mode (WGM) resonator disks made of those materials. The method was conceived especially for use in studying transparent photorefractive materials, for which purpose this method affords unprecedented levels of sensitivity and accuracy. The method is expected to be particularly useful for measuring temporally varying refractive and absorptive properties of photorefractive materials at infrared wavelengths. Still more particularly, the method is expected to be useful for measuring drifts in these properties that are so slow that, heretofore, the properties were assumed to be constant. The basic idea of the method is to attempt to infer values of the photorefractive properties of a material by seeking to match (1) theoretical predictions of the spectral responses (or selected features thereof) of a WGM of known dimensions made of the material with (2) the actual spectral responses (or selected features thereof). Spectral features that are useful for this purpose include resonance frequencies, free spectral ranges (differences between resonance frequencies of adjacently numbered modes), and resonance quality factors (Q values). The method has been demonstrated in several experiments, one of which was performed on a WGM resonator made from a disk of LiNbO3 doped with 5 percent of MgO. The free spectral range of the resonator was approximately equal to 3.42 GHz at wavelengths in the vicinity of 780 nm, the smallest full width at half maximum of a mode was approximately equal to 50 MHz, and the thickness of the resonator in the area of mode localization was 30 microns. In the experiment, laser power of 9 mW was coupled into the resonator with an efficiency of 75 percent, and the laser was scanned over a frequency band 9 GHz wide at a nominal wavelength of approximately equal to 780 nm. Resonance frequencies were measured as functions of time during several hours of exposure to the laser light. The results of these measurements, plotted in the figure, show a pronounced collective frequency drift of the resonator modes. The size of the drift has been estimated to correspond to a change of 8.5 x 10(exp -5) in the effective ordinary index of refraction of the resonator material.

Matsko, Andrey↗

Banded Structures in Electron Pitch Angle Diffusion Coefficients from Resonant Wave Particle Interactions

Electron pitch angle (D (alpha)) and momentum (D(pp)) diffusion coefficients have been calculated due to resonant interactions with electrostatic electron cyclotron harmonic (ECH) and whistler mode chorus waves. Calculations have been performed at two spatial locations L = 4.6 and 6.8 for electron energies 10 keV. Landau (n = 0) resonance and cyclotron harmonic resonances n = +/-1, +/-2,...+/-5 have been included in the calculations. It is found that diffusion coefficient versus pitch angle (alpha) profiles show large dips and oscillations or banded structures. The structures are more pronounced for ECH and lower band chorus (LBC) and particularly at location 4.6. Calculations of diffusion coefficients have also been performed for individual resonances. It is noticed that the main contribution of ECH waves in pitch angle diffusion coefficient is due to resonances n = +1 and n = +2. A major contribution to momentum diffusion coefficients appears from n = +2. However, the banded structures in D alpha and Dpp coefficients appear only in the profile of diffusion coefficients for n = +2. The contribution of other resonances to diffusion coefficients is found to be, in general, quite small or even negligible. For LBC and upper band chorus waves, the banded structures appear only in Landau resonance. The Dpp diffusion coefficient for ECH waves is one to two orders smaller than D alpha coefficients. For chorus waves, Dpp coefficients are about an order of magnitude smaller than D alpha coefficients for the case n does not = 0. In case of Landau resonance, the values of Dpp coefficient are generally larger than the values of D alpha coefficients particularly at lower energies. As an aid to the interpretation of results, we have also determined the resonant frequencies. For ECH waves, resonant frequencies have been estimated for wave normal angle 89 deg and harmonic resonances n = +1, +2, and +3, whereas for whistler mode waves, the frequencies have been calculated for angle 10 deg and Landau resonance. Further, in ECH waves, the banded structures appear for electron energies (is) greater than1 keV, and for whistler mode chorus waves, structures appear for energies greater than 2 keV at L = 4.6 and above 200 eV for L = 6.8. The results obtained in the present work will be helpful in the study of diffusion curves and will have important consequences for diffuse aurora and pancake distributions.

diffusion↗

Acoustic positioning and orientation prediction

A method is described for use with an acoustic positioner, which enables a determination of the equilibrium position and orientation which an object assumes in a zero gravity environment, as well as restoring forces and torques of an object in an acoustic standing wave field. An acoustic standing wave field is established in the chamber, and the object is held at several different positions near the expected equilibrium position. While the object is held at each position, the center resonant frequency of the chamber is determined, by noting which frequency results in the greatest pressure of the acoustic field. The object position which results in the lowest center resonant frequency is the equilibrium position. The orientation of a nonspherical object is similarly determined, by holding the object in a plurality of different orientations at its equilibrium position, and noting the center resonant frequency for each orientation. The orientation which results in the lowest center resonant frequency is the equilibrium orientation. Where the acoustic frequency is constant, but the chamber length is variable, the equilibrium position or orientation is that which results in the greatest chamber length at the center resonant frequency.

Barmatz, Martin B.↗

Radio-Frequency Tank Eigenmode Sensor for Propellant Quantity Gauging

Although there are several methods for determining liquid level in a tank, there are no proven methods to quickly gauge the amount of propellant in a tank while it is in low gravity or under low-settling thrust conditions where propellant sloshing is an issue. Having the ability to quickly and accurately gauge propellant tanks in low-gravity is an enabling technology that would allow a spacecraft crew or mission control to always know the amount of propellant onboard, thus increasing the chances for a successful mission. The Radio Frequency Mass Gauge (RFMG) technique measures the electromagnetic eigenmodes, or natural resonant frequencies, of a tank containing a dielectric fluid. The essential hardware components consist of an RF network analyzer that measures the reflected power from an antenna probe mounted internal to the tank. At a resonant frequency, there is a drop in the reflected power, and these inverted peaks in the reflected power spectrum are identified as the tank eigenmode frequencies using a peak-detection software algorithm. This information is passed to a pattern-matching algorithm, which compares the measured eigenmode frequencies with a database of simulated eigenmode frequencies at various fill levels. A best match between the simulated and measured frequency values occurs at some fill level, which is then reported as the gauged fill level. The database of simulated eigenmode frequencies is created by using RF simulation software to calculate the tank eigenmodes at various fill levels. The input to the simulations consists of a fairly high-fidelity tank model with proper dimensions and including internal tank hardware, the dielectric properties of the fluid, and a defined liquid/vapor interface. Because of small discrepancies between the model and actual hardware, the measured empty tank spectra and simulations are used to create a set of correction factors for each mode (typically in the range of 0.999 1.001), which effectively accounts for the small discrepancies. These correction factors are multiplied to the modes at all fill levels. By comparing several measured modes with the simulations, it is possible to accurately gauge the amount of propellant in the tank. An advantage of the RFMG approach of applying computer simulations and a pattern-matching algorithm is that the Although there are several methods for determining liquid level in a tank, there are no proven methods to quickly gauge the amount of propellant in a tank while it is in low gravity or under low-settling thrust conditions where propellant sloshing is an issue. Having the ability to quickly and accurately gauge propellant tanks in low-gravity is an enabling technology that would allow a spacecraft crew or mission control to always know the amount of propellant onboard, thus increasing the chances for a successful mission. The Radio Frequency Mass Gauge (RFMG) technique measures the electromagnetic eigenmodes, or natural resonant frequencies, of a tank containing a dielectric fluid. The essential hardware components consist of an RF network analyzer that measures the reflected power from an antenna probe mounted internal to the tank. At a resonant frequency, there is a drop in the reflected power, and these inverted peaks in the reflected power spectrum are identified as the tank eigenmode frequencies using a peak-detection software algorithm. This information is passed to a pattern-matching algorithm, which compares the measured eigenmode frequencies with a database of simulated eigenmode frequencies at various fill levels. A best match between the simulated and measured frequency values occurs at some fill level, which is then reported as the gauged fill level. The database of simulated eigenmode frequencies is created by using RF simulation software to calculate the tank eigenmodes at various fill levels. The input to the simulations consists of a fairly high-fidelity tank model with proper dimensions and including internal tank harare, the dielectric properties of the fluid, and a defined liquid/vapor interface. Because of small discrepancies between the model and actual hardware, the measured empty tank spectra and simulations are used to create a set of correction factors for each mode (typically in the range of 0.999 1.001), which effectively accounts for the small discrepancies. These correction factors are multiplied to the modes at all fill levels. By comparing several measured modes with the simulations, it is possible to accurately gauge the amount of propellant in the tank. An advantage of the RFMG approach of applying computer simulations and a pattern-matching algorithm is that the

Zimmerli, Gregory A.↗

Characterization of the Dynamic Material Properties of Magnetostrictive Terfenol-D

A major limitation in use of electromagnetic and/or magnetomechanical models for design of Terfenol-D actuators is the lack of reliable material property data for Terfenol-D. In particular data on the performance of Terfenol-D as employed in a transducer, operating under real world dynamic conditions is needed. To provide this information, Terfenol-D rod properties need to be measured under as run prestressed and magnetically biased states. Using a Terfenol-D actuator, the following properties can be measured and/or calculated: mechanical quality factor, speed of sound in the material, the resonant frequency, the anti-resonant frequency, two magnetic permeabilities (one at constant stress and one at constant strain), two Young's moduli (one at constant amplitude applied magnetic field and one at constant amplitude magnetic flux density in the material), the magnetomechanical coupling, and the axial strain coefficient. The development of the material properties measurements and calculations is based on the model of low signal, linear, magnetostriction from Clark, the linear transduction equations for a transducer from Hunt, and a one degree of freedom mechanical model of the transducer. The electrical impedance and admittance mobility loops are used to determine the resonant, anti-resonant, and half power point frequencies. The rest of the material properties indicated above can then be calculated using these frequencies, acceleration from an accelerometer mounted on the actuator arm, and readily measurable transducer and Terfenol-D rod parameters.

Calkins, Frederick T.↗

Effect of thermal cycling on stress in metallic films on ceramic substrates

The hydrogen maser is the most stable frequency standard currently available for averaging intervals of hours to weeks. A major contributor to maser frequency variations is the maser's microwave resonant cavity: by means of the cavity pulling effect, a change in the cavity's resonance frequency produces a proportional change in the maser's output frequency. To minimize variations in the cavity's dimensions, and thus in its resonance frequency, maser cavities are often constructed of a low-expansivity glass-ceramic material coated on its surface with a conductive metallic film. It was previously shown that silver films like those used in SAO maser cavities develop tensile stress when cooled to room temperature after being fired onto the cavity, and that the stress in such films relaxes with time at a rate proportional to the level of stress. Stress relaxation in maser cavity coatings can alter the shape, and hence the resonance frequency, of the cavity, resulting in a slow variation in the maser's output frequency. The possibility was investigated of reversing the initial tensile stress by precooling the coated cavity material. It was hypothesized that cooling the material well below its normal working temperature and then warming it to its normal temperature would result in a lower tensile stress or even a compressive stress. Under such a condition stress relaxation, and thus any consequent frequency drifts, might be reduced or reversed.

Mattison, Edward M.↗

Spectral Analysis of Vibrational Harmonic Motion by use of a Continuous-Wave CO2 Doppler Lidar

Vibrational motion of a harmonic oscillator was investigated using a focused continuous wave CO2 Doppler lidar at 9.1 microns wavelength. A continuum of frequencies along with many discrete, equally spaced, resonant frequency modes was observed. The frequency modes are similar in structure to the oscillatory longitudinal modes of a laser cavity and arise because of interference of the natural resonant frequency of the oscillator with specific frequencies within the continuum. The spectra revealed departures from linear motion for vigorous vibrations of the oscillator. Each consecutive resonant frequency mode occurred for a movement of the oscillator much less than the wavelength of incident lidar radiation.

Jarzembski, Maurice A.↗

Active control of the forced and transient response of a finite beam

Structural vibrations from a point force are modelled on a finite beam. This research explores the theoretical limit on controlling beam vibrations utilizing another point source as an active controller. Three different types of excitation are considered, harmonic, random, and transient. For harmonic excitation, control over the entire beam length is possible only when the excitation frequency is near a resonant frequency of the beam. Control over a subregion may be obtained even between resonant frequencies at the cost of increasing the vibration outside of the control region. For random excitation, integrating the expected value of the displacement squared over the required interval, is shown to yield the identical cost function as obtained by integrating the cost function for harmonic excitation over all excitation frequencies. As a result, it is always possible to reduce the cost function for random excitation whether controlling the entire beam or just a subregion, without ever increasing the vibration outside the region in which control is desired. The last type of excitation considered is a single, transient pulse. The form of the controller is specified as either one or two delayed pulses, thus constraining the controller to be casual. The best possible control is examined while varying the region of control and the controller location. It is found that control is always possible using either one or two control pulses.

Post, John T.↗

Calculation of low frequency vibrational resonances of submerged structures

Numerical techniques for calculating the low frequency vibrational resonances of submerged structures are reviewed. Both finite element and boundary element approaches for calculating fully-coupled added mass matrices for use in NASTRAN analysis are described and illustrated. The finite element approach is implemented using existing capability in NASTRAN. The boundary element approach uses the NASHUA structural-acoustics program to compute the added mass matrix. The two procedures are compared to each other for the case of a submerged cylindrical shell with flat end closures. It is concluded that both procedures are capable of computing accurate submerged resonances and that the more elegant boundary element procedure is easier to use but may be more expensive computationally.

Everstine, Gordon C.↗

Active Control of the Forced and Transient Response of a Finite Beam

When studying structural vibrations resulting from a concentrated source, many structures may be modelled as a finite beam excited by a point source. The theoretical limit on cancelling the resulting beam vibrations by utilizing another point source as an active controller is explored. Three different types of excitation are considered, harmonic, random, and transient. In each case, a cost function is defined and minimized for numerous parameter variations. For the case of harmonic excitation, the cost function is obtained by integrating the mean squared displacement over a region of the beam in which control is desired. A controller is then found to minimize this cost function in the control interval. The control interval and controller location are continuously varied for several frequencies of excitation. The results show that control over the entire beam length is possible only when the excitation frequency is near a resonant frequency of the beam, but control over a subregion may be obtained even between resonant frequencies at the cost of increasing the vibration outside of the control region. For random excitation, the cost function is realized by integrating the expected value of the displacement squared over the interval of the beam in which control is desired. This is shown to yield the identical cost function as obtained by integrating the cost function for harmonic excitation over all excitation frequencies. As a result, it is always possible to reduce the cost function for random excitation whether controlling the entire beam or just a subregion, without ever increasing the vibration outside the region in which control is desired. The last type of excitation considered is a single, transient pulse. A cost function representative of the beam vibration is obtained by integrating the transient displacement squared over a region of the beam and over all time. The form of the controller is chosen a priori as either one or two delayed pulses. Delays constrain the controller to be causal. The best possible control is then examined while varying the region of control and the controller location. It is found that control is always possible using either one or two control pulses. The two pulse controller gives better performance than a single pulse controller, but finding the optimal delay time for the additional controllers increases as the square of the number of control pulses.

Post, John Theodore↗

Acoustic Mechanical Feed-Throughs for Producing Work Across a Structure

An apparatus that passes vibrational energy across a mechanical structure lacking a perforation. The disclosed apparatus and method provide the ability to transfer work (rotary or linear motion) across pressure or thermal barriers or in a sterile environment without generating contaminants; the presence of reflectors in the solid barrier to enhance the efficiency of the energy/power transmission, and the ability to produce a bi-directional driving mechanism using a plurality of different mode resonances, such as a fundamental frequency resonance and a higher frequency resonance. In some instances, a plane within the mechanical structure lacking a perforation is a nodal plane of the vibrational energy field.

Sherril, Stewart↗