Correct Frequency Research Articles

Why are large conformational changes well described by harmonic normal modes?

Low-frequency normal modes generated by elastic network models tend to correlate strongly with large conformational changes of proteins, despite their reliance on the harmonic approximation, which is only valid in close proximity of the native structure. We consider 12 variants of the torsional network model (TNM), an elastic network model in torsion angle space, that adopt different sets of torsion angles as degrees of freedom and reproduce with similar quality the thermal fluctuations of proteins but present drastic differences in their agreement with conformational changes. We show that these differences are related to the extent of the deviations from the harmonic approximation, assessed through an anharmonic energy function whose harmonic approximation coincides with the TNM. Our results indicate that mode anharmonicity is more strongly related to its collectivity, i.e., the number of atoms displaced by the mode, than to its amplitude; low-frequency modes can remain harmonic even at large amplitudes, provided they are sufficiently collective. Finally, we assess the potential benefits of different strategies to minimize the impact of anharmonicity. The reduction of the number of degrees of freedom or their regularization by a torsional harmonic potential significantly improves the collectivity and harmonicity of normal modes and the agreement with conformational changes. In contrast, the correction of normal mode frequencies to partially account for anharmonicity does not yield substantial benefits. The TNM program is freely available at https://github.com/ugobas/tnm.

Absolute choline tissue concentration mapping for prostate cancer localization and characterization using 3D 1 H MRSI without water-signal suppression.

PurposeUntil now, 1H MRSI of the prostate has been performed with suppression of the large water signal to avoid distortions of metabolite signals. However, this signal can be used for absolute quantification and spectral corrections. We investigated the feasibility of water‐unsuppressed MRSI in patients with prostate cancer for water signal–mediated spectral quality improvement and determination of absolute tissue levels of choline.MethodsEight prostate cancer patients scheduled for radical prostatectomy underwent multi‐parametric MRI at 3 T, including 3D water‐unsuppressed semi‐LASER MRSI. A postprocessing algorithm was developed to remove the water signal and its artifacts and use the extracted water signal as intravoxel reference for phase and frequency correction of metabolite signals and for absolute metabolite quantification.ResultsWater‐unsuppressed MRSI with dedicated postprocessing produced water signal and artifact‐free MR spectra throughout the prostate. In all patients, the absolute choline tissue concentration was significantly higher in tumorous than in benign tissue areas (mean ± SD: 7.2 ± 1.4 vs 3.8 ± 0.7 mM), facilitating tumor localization by choline mapping. Tumor tissue levels of choline correlated better with the commonly used (choline + spermine + creatine)/citrate ratio (r = 0.78 ± 0.1) than that of citrate (r = 0.21 ± 0.06). The highest maximum choline concentrations occurred in high‐risk cancer foci.ConclusionThis report presents the first successful water‐unsuppressed MRSI of the whole prostate. The water signal enabled amelioration of spectral quality and absolute metabolite quantification. In this way, choline tissue levels were identified as tumor biomarker. Choline mapping may serve as a tool in prostate cancer localization and risk scoring in multi‐parametric MRI for diagnosis and biopsy procedures.

Analytical computation of quasinormal modes of slowly rotating black holes in dynamical Chern-Simons gravity

Using gravitational wave observations to search for deviations from general relativity (GR) in the strong-gravity regime has become an important research direction. One aspect of the strong gravity modifications to GR is parity violation. Chern Simons (CS) gravity is one of the most frequently studied parity-violating models of strong gravity. CS gravity is indistinguishable from GR for all conformally flat space-times and for space-times that possess a maximally symmetric two-dimensional subspace. Also, it is known that the Kerr black hole is not a solution for CS gravity. At the same time, the only rotating solution available in the literature for dynamical CS (DCS) gravity is the slow-rotating case most accurately known to quadratic order in spin. In this work, for the slow-rotating case (accurate to first order in spin), we derive the linear perturbation equations governing the metric and the DCS field accurate to linear order in spin and quadratic order in the CS coupling parameter ($\ensuremath{\alpha}$) and obtain the quasinormal mode (QNM) frequencies. After confirming the recent results of Wagle et al. arXiv:2103.09913, we find an additional contribution to the eigenfrequency correction at the leading perturbative order of ${\ensuremath{\alpha}}^{2}$. Unlike Wagle et al., we also find corrections to frequencies in the polar sector. We compute these extra corrections by evaluating the expectation values of the perturbative potential on unperturbed QNM wave functions along a contour deformed into the complex-$r$ plane. For $\ensuremath{\alpha}=0.1{M}^{2}$, we obtain the ratio of the imaginary parts of the DCS correction to the GR correction in the first QNM frequency (in the polar sector) to be 0.263 implying significant change. For the (2, 2) mode, the DCS corrections make imaginary part of the first QNM of the fundamental mode less negative, thereby decreasing the decay rate. Our results, along with future gravitational wave observations, can be used as a test for DCS gravity and to further constrain the CS coupling parameters.

Spatial Frequency Domain Imaging System Calibration, Correction and Application for Pear Surface Damage Detection.

Spatial frequency domain imaging (SFDI) is a non-contact wide-field optical imaging technique for optical property detection. This study aimed to establish an SFDI system and investigate the effects of system calibration, error analysis and correction on the measurement of optical properties. Optical parameter characteristic measurements of normal pears with three different damage types were performed using the calibrated system. The obtained absorption coefficient μa and the reduced scattering coefficient μ’s were used for discriminating pears with different surface damage using a linear discriminant analysis model. The results showed that at 527 nm and 675 nm, the pears’ quadruple classification (normal, bruised, scratched and abraded) accuracy using the SFDI technique was 92.5% and 83.8%, respectively, which has an advantage compared with the conventional planar light classification results of 82.5% and 77.5%. The three-way classification (normal, minor damage and serious damage) SFDI technique was as high as 100% and 98.8% at 527 nm and 675 nm, respectively, while the classification accuracy of conventional planar light was 93.8% and 93.8%, respectively. The results of this study indicated that SFDI has the potential to detect different damage types in fruit and that the SFDI technique has a promising future in agricultural product quality inspection in further research.

Improved prospective frequency correction for macromolecule-suppressed GABA editing with metabolite cycling at 3T.

To combine metabolite cycling with J-difference editing (MC MEGA) to allow for prospective frequency correction at each transient without additional acquisitions and compare it to water-suppressed MEGA-PRESS (WS MEGA) editing with intermittent prospective frequency correction. Macromolecule-suppressed gamma aminobutyric acid (GABA)-edited experiments were performed in a phantom and in the occipital lobe (OCC) (n = 12) and medial prefrontal cortex (mPFC) (n = 8) of the human brain. Water frequency consistency and average offset over acquisition time were compared. GABA multiplet patterns, signal intensities, and choline subtraction artifacts were evaluated. In vivo GABA concentrations were compared and related to frequency offset in the OCC. MC MEGA was more stable with 21% and 32% smaller water frequency SDs in the OCC and mPFC, respectively. MC MEGA also had 39% and 40% smaller average frequency offsets in the OCC and mPFC, respectively. Phantom GABA multiplet patterns and signal intensities were similar. In vivo GABA concentrations were smaller in MC MEGA than in WS MEGA, with median (interquartile range) of 2.52 (0.27) and 2.29 (0.19) institutional units (i.u.), respectively in the OCC scans without prior DTI, and 0.99 (0.3) and 1.72 (0.5), respectively in the mPFC. OCC WS MEGA GABA concentrations, but not MC MEGA GABA concentrations were moderately correlated with frequency offset. mPFC WS MEGA spectra contained significantly more subtraction artifacts than MC MEGA spectra. MC MEGA is feasible and allows for prospective frequency correction at every transient. MC MEGA GABA concentrations were not biased by frequency offsets and contained less subtraction artifacts compared to WS MEGA.

Accuracy of the predicting for creep-fatigue cyclic life based on parameters in a characteristic cycle

The purposes of the present work are to evaluate the prediction accuracy of characteristic cycle on creep-fatigue life prediction and to analyze the advantages and disadvantages of various models in tensile strain-dwell tests. The parameters of the first cycle, the 10% life, the half-life, and the characteristic cycle that we proposed (a turning point between the initial rapid softening and subsequent slight softening/hardening) are employed to linear-damage-summation (LDS) and energy-life prediction models based on the creep-fatigue data of directionally-solidified Nickel-based superalloy, DZ445, at 900 °C. It is found that the characteristic cycle parameters with clear physical significance have the highest life prediction accuracy. Moreover, the optimal critical value of fatigue and creep damage (the coordinate of the creep-fatigue envelope intersection) in the LDS is also determined. The prediction accuracy of creep damage based on the time-fraction, the simple ductility-exhaustion, and the strain-energy- density-exhaustion models is sequentially improved in the LDS rule. In the energy-life model, the life prediction accuracy based on damage mechanism and frequency correction is higher than the value without any correction. This investigation provides a new method of the parameter-selection for the creep-fatigue life prediction, which is accurate and convenient. It provides the theoretical-guidance for creep-fatigue life prediction in both laboratory experiment and actual components.

Seventh-order wavefront modulation with a gravity-neutral optofluidic deformable phase plate

A 63-electrode optofluidic refractive wavefront modulator enabling spatial frequency correction up to the seventh radial Zernike order, the highest spatial order ever achieved with a refractive dynamic wavefront modulator, is presented. The modulator is designed so that aberration correction performance is nearly identical in both horizontal and vertical orientations, virtually eliminating the gravity-induced parasitic surface deformations typical for optofluidic devices. With 55 of its electrodes located within the 1-cm clear pupil, the modulator offers the versatility of continuous face-sheet deformable mirrors within a compact, high efficiency, and transmissive device. Using a fluidic interfacing method based on wafer-level 3D micro-structuring of glass, the modulator is only 0.86-mm-thick, facilitating the cascading of multiple modulators within close proximity. We demonstrate a bi-directional stroke of more than 13 λ, and replications of Zernike mode shapes up to the seventh radial order with high fidelity, representing a significant leap in the performance of ultra-miniaturized refractive wavefront modulators.

Correction and quantification of MTF in scanning laser microscopy.

Observations using conventional microscopy often lack information related to the fine structures of an object, such as intensity and phase, because of limitations in the lens aperture. In this study, the intensity and phase information are appropriately converted into an electrical signal using laser scanning and photodetectors. Intensity and phase are completely separated, and the missing information is restored based on the frequency of the electrical signal. Using this method, the original intensity and phase information of the object to be observed can be correctly restored. Therefore, we propose a novel method to calculate the degree of intensity and phase modulation by calculating the direct and alternating current components obtained from the output of the sum and difference of the two photodetectors. The degree of spatial frequency modulation is corrected according to the electrical signal frequency to detect transparent or unstained cells. We first performed laser scanning of an object. Then, signals were detected using two photodetectors placed in the far-field, separated by the optical axis as the boundary. The output signals of the photodetectors were processed and the intensity and phase were unambiguously separated, thus allowing the visualization of the phase information of the transparent bodies and unstained cells. Spatial frequency correction was performed to correct the modulation. Our method successfully separated the information related to the intensity and optical path difference (OPD). In future work, by accurately correcting the intensity and OPD, it will be possible to separate the absorption rate from the ratio of the irradiation light intensity to the observed intensity and to separate the OPD into the refractive index and the thickness information. This method allows the accurate determination of these parameters in a noninvasive manner.

Theory of spin-Hall magnetoresistance in the ac terahertz regime

In bilayers consisting of a normal metal (N) with spin-orbit coupling and a ferromagnet (F), the combination of the spin-Hall effect, the spin-transfer torque, and the inverse spin-Hall effect gives a small correction to the in-plane conductivity of N, which is referred to as spin-Hall magnetoresistance (SMR). We here present a theory of the SMR and the associated off-diagonal conductivity corrections for frequencies up to the terahertz regime. We show that the SMR signal has pronounced singularities at the spin-wave frequencies of F, which identifies it as a potential tool for all-electric spectroscopy of magnon modes. A systematic change of the magnitude of the SMR at lower frequencies is associated with the onset of a longitudinal magnonic contribution to spin transport across the F-N interface.

Design and simulations of the HEBT spiral buncher cavities for the high current injector at IUAC

The high energy beam transport (HEBT) section of the high current injector (HCI) accelerator requires two spiral buncher (SB) cavities to match the input Twiss parameters at the entrance of the superconducting super buncher (SSB) cavity by providing the longitudinal phase matching between drift tube linac (DTL) and SSB. The spiral type open-ended quarter-wave (λ/4) resonators were chosen for their high shunt impedance, mechanical, and vibrational stability. The 48.5 MHz frequency of cavities was chosen for its broad acceptance of time width. TRACE 3D codes were simulated to determine the bunching voltage for the spiral buncher cavities. The locations of HEBT spiral bunchers have been fixed in such a way that the ion beam can be transported from DTL to SSB with negligible growth in longitudinal beam emittance within the framework of first-order linear beam optics. The cavity parameters were optimized to get the significantly high shunt impedance and quality factor to achieve the desired electric field level at the minimum input power. The inner and outer radii of the drift tubes were honed to get the uniform electric field profile along the beam direction while βλ/2 was kept constant during the refinement. The HEBT SB cavities require ~2 kW of input power to produce ~160 kV across two RF gaps. The simulated quality factor and shunt impedance for two identical HEBT SB cavities are ~8300 and ~13.5 MΩ, respectively. The cylindrical type chamber will be fabricated of copper-plated mild-steel (MS) while other components including end plates, spiral, stem, and flanges were fabricated of pure OFHC copper due to excellent electrical as well as thermal conductivity. The cavity frequency can be easily coarse tuned by varying the length of the spiral. The distinguishing feature of the design is to tailor the cavity frequency by ±250 kHz by varying the diameter of the drift tubes and stem, even after fabrication. A cylindrical type frequency tuner of diameter 90 mm and thickness 10 mm has been designed which is capable of providing the additional frequency correction of ± 250 kHz in the travel distance of ~200 mm. The details of longitudinal beam optics, ion-optical and electrical design, simulations, and mechanical design are discussed in this article.

Tuned nonlinear spring-inerter-damper vibration absorber for beam vibration reduction based on the exact nonlinear dynamics model

Nonlinear vibration absorbers have been extensively investigated for passive vibration control, motion isolation, and synchronous energy harvesting. This paper studies the exact nonlinear dynamics of a simply-supported beam carrying a nonlinear spring-inerter-damper energy absorber for primary resonance vibration reduction. The nonlinear governing equations of the system are derived from the energy method by considering the midplane stretching, structural discontinuity, and nonlinear boundary conditions at the spring-inerter-damper location of the beam and directly solved using the method of multiple scales. The nonlinear frequency correction factor, frequency response function, peak nonlinear frequency response, and bifurcation frequency are obtained and investigated for various system parameters. The influence of the location, spring stiffness, inertial mass, and damping of the nonlinear vibration absorber on the beam dynamics, including natural frequency, mode shape, and nonlinear frequency response, are studied. The stiffness and mass of the nonlinear vibration absorber are optimally tuned to minimize the peak nonlinear frequency response of the beam. The results show that ignoring the nonlinear boundary conditions at the spring-inerter-damper location could lead to serious underestimation of the nonlinear frequency responses. The nonlinear stiffness of the vibration absorber enhances the system nonlinearity but has no contribution to the peak nonlinear frequency response of the beam. Increasing the damping of the vibration absorber could effectively mitigate the beam vibration. When the nominal frequency of the absorber is tuned to be close to the natural frequency of the beam, the beam vibration is mostly reduced.

Non-uniform electric field in cantilevered piezoelectric energy harvesters: An improved distributed parameter electromechanical model

In the existing electromechanical model for cantilevered piezoelectric energy harvesters, the electric field in the piezoelectric layer is generally considered as a uniform field. In the present study, it is found and described in detail that the oversimplified uniform electric field assumption could lead to critical issues regarding the fundamental of piezoelectricity. Further, inspired by the electric field distribution obtained using the exact solutions for plane problems, a non-uniform electric field is proposed. Accordingly, an improved distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters including both unimorph and bimorph configurations is established, in which the bending stiffness term involved in the electromechanical governing equations is explicitly corrected, and the aforementioned critical issues are perfectly addressed. The present proposed non-uniform electric field is then validated by comparing the static analysis results of the present model with finite element results and the results obtained using exact solutions for plane problems. Dynamic analysis of the present model is also conducted, and the electromechanical characteristic corrections for the traditional distributed parameter model adopting uniform electric field assumption is carried out including bending stiffness correction, resonant frequency correction, voltage output correction and power output correction.

Correction of calculated dynamic scheme of unmanned aerial vehicle based on results of ground modal tests

The problem of correcting of the calculated dynamic scheme of an unmanned aerial vehicle (UAV) based on the results of ground modal tests is considered. The provisions that allow achieving satisfactory results when the UAV calculated dynamic scheme correcting are formulated. Correction criteria are considered. Features of the calculated dynamic scheme correction in the study of the flutter and the aeroelastic stability of the UAV with the automatic control system (ACS) are presented. It is noted that along with the provisions that are universal for dynamical aeroelasticity tasks related to the correction of natural frequencies, forms, and coefficients of structural damping of the UAV on the results of ground modal tests, in the study of aeroelastic stability of the UAV with the ACS is also crucial to correct the transfer function of the UAV body from section, in which the rudder rotation axes are located, up to the cross-section, where ACS sensors are installed. This is because the UAV body is directly part of the UAV stabilization loop and significantly affects to its stability reserves. An example of correcting of the UAV calculated dynamic scheme is given.

A study on the change of characteristics and frequency correction method of OCXO by temperature sensor position

A study on the change of characteristics and frequency correction method of OCXO by temperature sensor position

On the Frequency Carrier Offset and Symbol Timing Estimation for CCSDS 131.2-B-1 High Data-Rate Telemetry Receivers.

In recent years there have been significant developments in satellite transmitter technology to follow the rapid innovation of sensors on-board new satellites. The CCSDS 131.2-B-1 standard for telemetry downlink, released in 2012, is part of the next generation of standards that aims to support the increased data-rate caused by these improvements in resolution. As a result of its relative novelty, this standard currently lacks in-depth analysis by researchers, but it is also strongly supported by the European Space Agency (ESA) for future missions. For these reasons, it seems important to evaluate how major receiver sub-components, such as timing recovery and carrier frequency correction, can be designed and implemented in new receivers that support this standard. The timing error detectors (TED) and frequency error detectors (FED) were therefore studied on the specific peculiarities of CCSDS 131.2-B-1 in its usual environment of Low Earth Orbit (LEO). Estimators have been evaluated highlighting performances, trade-offs and peculiarities of each one with respect to corresponding architectural choices. Finally, a receiver architecture derived from the paper considerations is proposed in the aim of supporting very different mission scenarios. Specifically, the realized architecture employs a parallel feedforward estimator for the timing recovery section and a novel multi-algorithm feedback frequency correction loop to efficiently cover both low symbol rates (5 Mbaud) and high data-rates (up to 500 Mbaud). This solution represents a good trade-off to support these scenarios in a very compact footprint by pushing the clock frequency to the FPGA limit. The FPGA resources occupation on a Zynq Ultrascale+ RFSoC XCZU28DR FPGA is 5202 LUT, 4851 FF, 5 BRAM, and 21 DSP for the timing recovery part, while the frequency recovery section occupies 1723 LUT, 1511 FF, 2.5 BRAM and 32 DSP.

A non-linear model for elastic hysteresis in the time domain: Implementation for multiple degrees of freedom

A model that captures the weak frequency sensitivity of elastic hysteretic damping is proposed for the time-domain simulation of structures with multiple degrees of freedom (MDOF) under free or forced vibration. The model is based on a recently proposed modification to the conventional single degree of freedom (SDOF) viscous damping model, utilising a correction factor computed based on the local instantaneous response to adjust the damping coefficient such that the dissipated energy remains insensitive to the frequency characteristics of the motion. The model compares favourably to the well-established viscous (incl. Collar’s frequency correction), Rayleigh and Reid MDOF models, is applicable to any type of loading and, unlike other classes of damping models, such as Rayleigh, modal, Bouc-Wen, Biot, and Collar/Neumark, does not require extensive calibration, knowledge of the past history of motion, or a priori knowledge of the excitation characteristics and frequency.

Profile-based intensity and frequency corrections for single-snapshot spatial frequency domain imaging.

We have proposed the profile-based intensity and frequency corrections for single-snapshot spatial frequency domain (SFD) imaging to mitigate surface profile effects on the measured intensity and spatial frequency in extracting the optical properties. In the scheme, the spatially modulated frequency of the projected sinusoidal pattern is adaptively adjusted according to the sample surface profile, reducing distortions of the modulation amplitude in the single-snapshot demodulation and errors in the optical property extraction. The profile effects on both the measured intensities of light incident onto and reflected from the sample are then compensated using Minnaert's correction to obtain the true diffuse reflectance of the sample. We have validated the method by phantom experiments using a highly sensitive SFD imaging system based on the single-pixel photon-counting detection and assessed error reductions in extracting the absorption and reduced scattering coefficients by an average of 40% and 10%, respectively. Further, an in vivo topography experiment of the opisthenar vessels has demonstrated its clinical feasibility.

Water-suppression cycling 3-T cardiac 1 H-MRS detects altered creatine and choline in patients with aortic or mitral stenosis.

Cardiac proton spectroscopy (1H‐MRS) is widely used to quantify lipids. Other metabolites (e.g. creatine and choline) are clinically relevant but more challenging to quantify because of their low concentrations (approximately 10 mmol/L) and because of cardiac motion. To quantify cardiac creatine and choline, we added water‐suppression cycling (WSC) to two single‐voxel spectroscopy sequences (STEAM and PRESS). WSC introduces controlled residual water signals that alternate between positive and negative phases from transient to transient, enabling robust phase and frequency correction. Moreover, a particular weighted sum of transients eliminates residual water signals without baseline distortion. We compared WSC and the vendor's standard ‘WET’ water suppression in phantoms. Next, we tested repeatability in 10 volunteers (seven males, three females; age 29.3 ± 4.0 years; body mass index [BMI] 23.7 ± 4.1 kg/m2). Fat fraction, creatine concentration and choline concentration when quantified by STEAM‐WET were 0.30% ± 0.11%, 29.6 ± 7.0 μmol/g and 7.9 ± 6.7 μmol/g, respectively; and when quantified by PRESS‐WSC they were 0.30% ± 0.15%, 31.5 ± 3.1 μmol/g and 8.3 ± 4.4 μmol/g, respectively. Compared with STEAM‐WET, PRESS‐WSC gave spectra whose fitting quality expressed by Cramér‐Rao lower bounds improved by 26% for creatine and 32% for choline. Repeatability of metabolite concentration measurements improved by 72% for creatine and 40% for choline. We also compared STEAM‐WET and PRESS‐WSC in 13 patients with severe symptomatic aortic or mitral stenosis indicated for valve replacement surgery (10 males, three females; age 75.9 ± 6.3 years; BMI 27.4 ± 4.3 kg/m2). Spectra were of analysable quality in eight patients for STEAM‐WET, and in nine for PRESS‐WSC. We observed comparable lipid concentrations with those in healthy volunteers, significantly reduced creatine concentrations, and a trend towards decreased choline concentrations. We conclude that PRESS‐WSC offers improved performance and reproducibility for the quantification of cardiac lipids, creatine and choline concentrations in healthy volunteers at 3 T. It also offers improved performance compared with STEAM‐WET for detecting altered creatine and choline concentrations in patients with valve disease.

Modeling the α- and β-resorcinol phase boundary via combination of density functional theory and density functional tight-binding.

The ability to predict not only what organic crystal structures might occur but also the thermodynamic conditions under which they are the most stable would be extremely useful for discovering and designing new organic materials. The present study takes a step in that direction by predicting the temperature- and pressure-dependent phase boundary between the α and β polymorphs of resorcinol using density functional theory (DFT) and the quasi-harmonic approximation. To circumvent the major computational bottleneck associated with computing a well-converged phonon density of states via the supercell approach, a recently developed approximation is employed, which combines a supercell phonon density of states from dispersion-corrected third-order density functional tight binding [DFTB3-D3(BJ)] with frequency corrections derived from a smaller B86bPBE-XDM functional DFT phonon calculation on the crystallographic unit cell. This mixed DFT/DFTB quasi-harmonic approach predicts the lattice constants and unit cell volumes to within 1%-2% at lower pressures. It predicts the thermodynamic phase boundary in almost perfect agreement with the experiment, although this excellent agreement does reflect fortuitous cancellation of errors between the enthalpy and entropy of transition.

Asymptotic analysis of radial vibration of thin piezoelectric disks

AbstractThe one‐dimensional radial vibration model of piezoelectric disks has been widely used to determine the relevant material coefficients from admittance measurements. However, the one‐dimensional model assumes infinitely thin disks, and therefore cannot predict their axial displacements. We extend the one‐dimensional model by performing an asymptotic analysis of the axisymmetric radial vibration of thin disks. The asymptotic expansions include the asymptotic axial displacement and the second‐order corrections to the admittance and the radial displacement in the one‐dimensional model. We verify the asymptotic expansions and the one‐dimensional model with the Chebyshev tau method. In the one‐dimensional model, the frequencies of the maximum admittance in the first and second radial modes are accurate to 1% for Pz27 disks with thickness‐to‐diameter ratios of 0.15 and 0.065, respectively. For a general piezoelectric disk in the forced vibration, the error of in the one‐dimensional model can be estimated from the second‐order correction of the asymptotic resonance frequency in the free vibration.