Resonance Frequency Spectra Research Articles

NODAL SEPTA AND THE RIGIDITY OF AERIAL SHOOTS OF EQUISETUM HYEMALE

The biomechanical role of septate nodes (points of leaf attachment with transverse diaphragms of tissue) in the otherwise hollow aerial stems of Equisetum hyemale L. is examined by means of multiple resonance frequency spectra. Resonance frequencies were determined for intact shoots, as well as the same shoots through which metal needles were inserted to destroy septa at nodes. The elastic modulus (E) of shoots, before and after surgical manipulation, was calculated. Shoots with perforated septa had E values from 17 to 32% less than intact shoots. During winter months with subfreezing temperatures, shoots with intact nodal septa accumulated water (in the form of ice) in their internodal pith canals. Values of E calculated for a shoot with intact septa and internodal water, and for the same shoot without septa do not differ significantly. Calculations indicate that the mass of internodal water is a significant fraction of the mass sufficient to deflect and buckle shoots. The added mass of internodal water is sufficient to mask the actual elastic modulus of shoots. The data indicate that nodes with septa significantly influence the flexural rigidity of shoots, but that this influence changes as a function of the quantity of water found in pith cavities.

Nodal Septa and the Rigidity of Aerial Shoots of Equisetum hyemale

The biomechanical role of septate nodes (points of leaf attachment with transverse diaphragms of tissue) in the otherwise hollow aerial stems of Equisetum hyemale L. is examined by means of multiple resonance frequency spectra. Resonance frequencies were determined for intact shoots, as well as the same shoots through which metal needles were inserted to destroy septa at nodes. The elastic modulus (E) of shoots, before and after surgical manipulation, was calculated. Shoots with perforated septa had E values from 17 to 32% less than intact shoots. During winter months with subfreezing temperatures, shoots with intact nodal septa accumulated water (in the form of ice) in their internodal pith canals. Values of E calculated for a shoot with intact septa and internodal water, and for the same shoot without septa do not differ significantly. Calculations indicate that the mass of internodal water is a significant fraction of the mass sufficient to deflect and buckle shoots. The added mass of internodal water is sufficient to mask the actual elastic modulus of shoots. The data indicate that nodes with septa significantly influence the flexural rigidity of shoots, but that this influence changes as a function of the quantity of water found in pith cavities.

Flexural Stiffness and Modulus of Elasticity of Flower Stalks from Allium Stalks from Allium sativum as Measured by Multiple Resonance Frequency Spectra

Multiple resonance frequency spectra (MRFS) provide a rapid and repeatable method for determining the flexural stiffness and modulus of elasticity, E, of segments of plant stems and leaves. Each resonance frequency in a spectrum can be used to compute E, and removal of the distal portion of an organ produces characteristic shifts in spectra dependent upon the geometry of an organ. Hence, MRFS can be used to quantitatively determine the extent to which a particular leaf or stem morphology can be modelled according to beam theory. MRFS of flower stalks of Allium sativum L. are presented to illustrate the technique. The fundamental, f1, and higher resonance frequencies, f2 … fn, of stems and the ratios of f2/f1 f3/f1, and f3/f2 increase as stalk length is reduced by clipping. The magnitudes of these shifts conform to those predicted from the MRFS of a linearly tapered beam. Morphometric data confirm this geometry in 21 flower stalks. Based on this model, the average modulus equals 3.71 × 108 ± 0.32 × 108 N/m2, which compares favorably with values of E determined by static loading (3.55 × 108 ± 0.22 × 108 N/m2) and is in general agreement with ultrasonic measurements (3.8 × 108 to 4.4 × 108 N/m2). Data indicate that determinations of E from a single resonance frequency are suspect, since each resonance frequency yields slightly different values for E. Statistical evaluations from all the frequencies within a MRFS are more reliable for determining E and testing the appropriateness of beam theory to evaluate the biomechanical properties of plants.

FLEXURAL STIFFNESS AND MODULUS OF ELASTICITY OF FLOWER STALKS FROM ALLIUM SATIVUM AS MEASURED BY MULTIPLE RESONANCE FREQUENCY SPECTRA

Multiple resonance frequency spectra (MRFS) provide a rapid and repeatable method for determining the flexural stiffness and modulus of elasticity, E, of segments of plant stems and leaves. Each resonance frequency in a spectrum can be used to compute E, and removal of the distal portion of an organ produces characteristic shifts in spectra dependent upon the geometry of an organ. Hence, MRFS can be used to quantitatively determine the extent to which a particular leaf or stem morphology can be modelled according to beam theory. MRFS of flower stalks of Allium sativum L. are presented to illustrate the technique. The fundamental, f1, and higher resonance frequencies, f2 … fn, of stems and the ratios of f2/f1 f3/f1, and f3/f2 increase as stalk length is reduced by clipping. The magnitudes of these shifts conform to those predicted from the MRFS of a linearly tapered beam. Morphometric data confirm this geometry in 21 flower stalks. Based on this model, the average modulus equals 3.71 × 108 ± 0.32 × 108 N/m2, which compares favorably with values of E determined by static loading (3.55 × 108 ± 0.22 × 108 N/m2) and is in general agreement with ultrasonic measurements (3.8 × 108 to 4.4 × 108 N/m2). Data indicate that determinations of E from a single resonance frequency are suspect, since each resonance frequency yields slightly different values for E. Statistical evaluations from all the frequencies within a MRFS are more reliable for determining E and testing the appropriateness of beam theory to evaluate the biomechanical properties of plants.

Analytic formulation and quantitative solutions of the coupled ULf wave problem

In the terrestrial magnetosphere, the inhomogeneous magnetic field and plasma density give rise to a continuous spectrum of field line resonant frequencies. Compressional disturbances with characteristic frequencies lying within the range of the spectrum may couple to transverse oscillations of resonant field lines. The coupling is of particular interest for global compressional modes trapped in the magnetic cavity. These modes decay in time through the coupling, even in the absence of dissipation. The importance of the process is that, through the damping of the global modes, large‐scale motion can drive localized field line resonances. In this study, we investigate the mode coupling and examine the parameter dependence of the damping rate of the global mode. The problem is discussed as an initial value problem in the box model which retains most of the significant physics yet remains mathematically tractable. To treat the coupling, we use the analogy of Landau damping in a homogeneous plasma. From the Laplace transform approach, we obtain the complex frequencies of the compressional wave by finding the singularities of the associated Green's function. Once the complex frequency has been found numerically, we obtain the corresponding waveforms in the box. Many observed wave properties can then be obtained. The calculations agree well with other simulation work and correspond to results obtained for the reflection of radio waves from the ionosphere and for plasma heating by absorption of radiation.

Apparatus for measuring elastic constants of single crystals by a resonance technique up to 1825 K

By holding the rectangular parallelepiped specimen between long, thin alumina buffer rods, we can detect the resonance vibration of a specimen even at temperatures above 1800 K. This new technique, in combination with the theory for the calculation of the resonance frequency spectrum of a rectangular parallelepiped specimen, enables us to determine the high-temperature elastic properties of single-crystal materials. The first application of this new device was to determine the elastic stiffness constants of single-crystal corundum up to 1825 K.

General one-dimensional treatment of the layered piezoelectric resonator with two electrodes

A general transfer matrix description of arbitrarily oriented layered piezoelectric structures is presented. Except for the restriction to two electrodes, it is the most general one-dimensional treatment possible. The description is derived as an exact solution of the fundamental differential equations and the boundary conditions at the terminating surfaces and at the electrical port. It allows the calculation of the electrical admittance appearing between the electrodes for any frequency, as well as the determination of the entire resonance frequency spectrum using only simple matrix multiplications. It covers the general case of multimode excitations and its coupling results. Thus it is not restricted to a single displacement direction and can be used for the rigorous analysis of layered structures containing, e.g., doubly rotated Y-cut quartz crystals.

Chemical shift imaging: a review.

Chemical shift is the phenomenon that is seen when an isotope possessing a nuclear magnetic dipole moment resonates at a spectrum of resonance frequencies in a given magnetic field. These resonance frequencies, or chemical shifts, depend on the chemical environments of particular nuclei. Mapping the spatial distribution of nuclei associated with a particular chemical shift (e.g., hydrogen nuclei associated with water molecules or with lipid groups) is called chemical shift imaging. Several techniques of proton chemical shift imaging that have been applied in vivo are presented, and their clinical findings are reported and summarized. Acquiring high-resolution spectra for large numbers of volume elements in two or three dimensions may be prohibitive because of time constraints, but other methods of imaging lipid of water distributions (i.e., selective excitation, selective saturation, or variations in conventional magnetic resonance imaging pulse sequences) can provide chemical shift information. These techniques require less time, but they lack spectral information. Since fat deposition seen by chemical shift imaging may not be demonstrated by conventional magnetic resonance imaging, certain applications of chemical shift imaging, such as in the determination of fatty liver disease, have greater diagnostic utility than conventional magnetic resonance imaging. Furthermore, edge artifacts caused by chemical shift effects can be eliminated by certain selective methods of data acquisition employed in chemical shift imaging.

Portable emergency ventilators. 2. Sensitivity to environment.

Three compact ventilators (Oxylog, Maxaman and Pneupac 2), commercially available in Sweden, were subjected to tests concerning sensitivity to environmental stress. The ventilators functioned very well at temperatures above 0 degree C. The Oxylog apparatus was very sensitive to subzero temperatures. It also had a spectrum of resonance frequencies when subjected to vibration testing that restricts its use outside the sheltered hospital environment. The Maxaman and Pneupac 2 in the modified version withstood the tests in a reliable way. The shock tests performed had no negative effects on any of the ventilators or their functions.

Field Characteristics of an Alvarez-Type Linac Structure Having Chain-Like Electrode Array

A chain-like electrode configuration in an Alvarez-type linac cavity was studied by models. The structure has been devised to get a moderate shunt impedance together with simplicity of operation, in ion velocity region of more than a few percent of that of light by incorporating focusing scheme by high frequency quadrupolar fields into an TM-010 accelerating field of an Alvarez linac. It has a chain-like electrode array instead of drift tubes containing quadrupole lenses for ordinary linacs. The chain-like electrode structure generates along its central axis, high frequency acceleration and focusing fields alternately, separating the acceleration and focusing functions in space. The separation discriminates this structure from spatially uniform acceleration and focusing scheme of the RFQs devised by Kapchinsky and Teplyakov. It gives beam acceleration effects different from those by conventional linacs and reveals possibility of getting a high acceleration efficiency. Resonant frequency spectrum was found relatively simple by measurements on high frequency models. Separation of unwanted modes from the TM-010 acceleration mode is large; a few 10 MHz. at least. Tilt of the acceleration field is not very sensitive to perturbation in gap capacitance for the TM-010 mode.

On systems having an infinitely dense discrete spectrum of resonance frequencies

The infinitely dense spectrum of resonance frequencies arising froma periodic, but non-harmonic excitation, is presented. A physical reasoning for why systems may operate under such conditions is given based on the notions of an allowed value of amplitude of vibrations in a defined time interval of application of the excitation. The phenomenon is illustrated by a periodically moving force on one-dimensional systems.

The origin of spurious resonances in composite resonators

Three-dimensional models have been developed to explain the characteristics of composite resonators. Simple disc or rectangular plate models predict resonance frequencies that are in excellent agreement with the results of experimental measurement. In particular, agreement with the relatively complicated spurious resonance frequency spectra is remarkable, whereas a standard one-dimensional model lacks this feature. The geometry of the resonator is found to be directly responsible for the spurious resonances as well as the principal resonances. It is suggested that a way of eliminating or at least controlling the unwanted modes can be found since the origin of the spurious frequencies is now understood.

Electromagnetic and acoustic resonance scattering theory

The excitation of the eigenfrequencies of finite radar or sonar targets, of inhomogeneities in elastic materials, of geological strata or of the entire earth by the impact of propagating waves (of electromagnetic or acoustic nature, or of ultrasonic, elastic, or seismic character, respectively) manifests itself in the appearance of poles in the resulting wave amplitudes, as described by the Resonance Scattering Theory (RST). In the complex frequency plane, these poles relate to the ringing of the scattering resonances. In the complex mode number plane, corresponding poles are connected with circumferential or creeping waves. An analytic relation between these two descriptions is indicated here, and a number of examples from the above-mentioned fields will be discussed. We introduce the concepts of ‘ Acoustic Spectroscopy’ and of ‘ Radar Spectroscopy’, respectively, by exhibiting the target's resonance frequency spectrum in a form familiar from atomic spectroscopy, in order to study the shifting and splitting of resonances ‘levels’ under changes of target shape, and to provide us with possible solutions for the ‘inverse problem’ (i.e., determination of target properties from echo properties - here, resonant echoes).

A study of the chlorine nuclear quadrupole resonance frequency spectrum in potassium hexachloro-osmate by Fourier transform methods

A study of the chlorine nuclear quadrupole resonance spectrum of K2OsCl6 in the vicinity of the structural phase transition using Fourier transform techniques is reported. At high temperatures a single symmetric line spectrum is observed as expected from the high temperature cubic antifluorite structure. Below Tc = 45 K the two symmetric line spectrum characteristic of a tetragonal distortion is seen. At intermediate temperatures, 45 < T < 150 K the spectrum consists of a single asymmetric line. A detailed analysis reveals that for the single crystal sample the asymmetric line is composed of two symmetric components, a main line, and a weak satellite shifted −1.5 kHz relative to the main line. This feature is unaffected by changes in temperature near Tc. It is attributed to the influence of interstitial impurities on neighbouring chlorine ions. For the powder sample, the asymmetry is qualitatively different. A detailed analysis shows that the line is a superposition of three components. In addition to the two components present in the single crystal, a third, broad component develops as the temperature approaches Tc. This feature of the spectrum is the cluster induced order-disorder manifestation of the local dynamics. The most probable reason that this third component is not observed in the single crystal spectrum is because it is too broad due to a difference in the detailed dynamics of the two samples.

Resonant modes of optical cavities with phase-conjugate mirrors

The lowest-order self-consistent Gaussian transverse modes are derived, also the resonant frequencies of an optical resonator formed by conventional paraxial optical components plus a phase-conjugate mirror (PCM) on one end. The conventional optical elements are described by an over-all ABCD matrix. Cavities with purely real elements (no aperturing) have a continuous set of self-reproducing Gaussian modes described by a semicircular locus in the 1/q plane for one round trip; all Gaussian beams are self-reproducing after two round trips. Complex ABCD matrices, such as are produced by Gaussian aperturing in the cavity, lead to unique self-consistent perturbation-stable Gaussian modes. The resonant frequency spectrum of a PCM cavity consists of a central resonance at the driving frequency omega(0) of the PCM element, independent of the cavity length L, plus half-axial sidebands spaced by Deltaomega(ax) = 2pi(c/4L), with phase and amplitude constraints on each pair of upper and lower sidebands.

Experimental study of flexural vibrations in thick beams

The resonant frequency spectrum for flexural vibrations in thick rectangular beams has been analyzed in terms of the elastic parameters of the beam material. An apparatus for the precise measurement of such resonant frequencies up to the tenth or higher modes in the range ∼0.3 to ∼20 kHz is described together with results for sample aluminum beams. By comparing the measured frequency spectrum with that calculated from a first-order theoretical treatment it has been found possible to derive both the elongational modulus and Poisson’s ratio from such a measurement, thereby completely characterizing the elastic response of an isotropic material.

The dynamic elastic behaviour of a fibre-reinforced composite sheet. II. The transfer matrix calculation of the resonant frequencies and vibration shapes

For pt.I see ibid., vol.8, no.15, p.1733 (1975). A simple finite-element technique employing transfer matrix calculations is used to calculate the spectrum of flexural and torsional resonant frequencies of specimens of material of orthotropic symmetry. The calculations incorporate Lekhnitskii's theory (1963) for static torsion-flexure coupling and the Timoshenko beam corrections (1937) for flexure. Vibration shapes and nodal contours are also calculated and displayed by computer. The non-crossing rule for the coupled oscillations is verified experimentally.

Mössbauer spectroscopy

A brief account of the M?ssbauer effect and its applications is given. The most popular types of spectrometer are described and their deficiencies considered in some detail. The problems of the reduction of data are dealt with, and the problems of obtaining spectra at low temperatures. A final section considers the choice of counters for transmission and backscattering methods. between the nucleus and the atomic electrons, called the hyperfine interactions. The strength and nature of these interactions depend strongly on the electronic, chemical and magnetic state of the atom. Thus a spectrum of the nuclear resonant frequencies can give valuable information about the atom and its surroundings. The hyperfine interactions can be understood by reference to figure 1, which is drawn for the case of 57Fe. On the extreme

Nuclear Anomalous Dispersion inFe57by the Method of Total Reflection

The recoil-free coherent resonant scattering of the 14.4-keV ${\mathrm{Fe}}^{57}$ gamma rays has been investigated by employing the techniques of the M\"ossbauer effect together with those of total reflection. Of particular interest are the observed large interference effects attributed to the coherent superposition of the several resonant nuclear contributions and the nonresonant electronic contribution to the scattering amplitude in the forward direction. Gamma rays from a 300-mCi ${\mathrm{Co}}^{57}$ source, diffused into the thin edge of a stainless steel plate, were reflected at small glancing angle $\ensuremath{\theta}$ by an optically flat ${\mathrm{Fe}}^{57}$ mirror through a narrow slit into a NaI scintillation detector. The resonant frequency spectrum of the ${\mathrm{Fe}}^{57}$ nuclei in the mirror was scanned by varying the source velocity $v$. Values of the absolute reflectivity $R(\ensuremath{\theta}, v)$ were obtained by comparison of the direct and reflected measured intensities. In an auxiliary experiment $R(v)$ was measured with an external magnetic field applied to the mirror. The results of these measurements were compared with computerprogrammed calculations based on the classical optical theory of total reflection. Appropriately averaged quantum-mechanical expressions were introduced for the coherent resonant nuclear scattering amplitude in the forward direction. Separate computations were made for each polarization state of the incident radiation; these were averaged to give $R(\ensuremath{\theta}, v)$ appropriate for an unpolarized source and a polarization-insensitive detector. Suitable integrations were performed to take into account the frequency spread and angular width of the incident radiation. For $\ensuremath{\theta}=4$ mrad, $R(v)$, computed with the six resonances of normal ferromagnetic ${\mathrm{Fe}}^{57}$, agreed in shape and magnitude with the observed reflectivity, when the resonance width was assumed to be four times the natural width. For $\ensuremath{\theta}=2$ mrad, where the gamma-ray penetration depth is small, anomalies in the magnetic and chemical environment of the ${\mathrm{Fe}}^{57}$ nuclei near the mirror surface required the introduction of additional resonances for FeO and for nonmagnetic Fe.

Transverse oscillations in travelling strings

The behaviour of transverse standing waves is examined for a uniform string which is pulled over two smooth supports under constant speed and tension. A harmonic spectrum of resonance frequencies is found which, for small ratios of the speed of travel to the propagation velocity of transverse waves, are only slightly lower than those of a string with clamped ends. The frequency response to a simple harmonic disturbance and the envelope of the oscillations are similar to those of a clamped string, but the phase of oscillation varies from point to point so that the instantaneous configuration of the string is not a sine curve. The conclusions remain valid in the presence of damping.