Measured Resonance Frequencies Research Articles

Monitoring of a Low-Order Even Radial Vibrational Circumferential Mode in a Round Hollow Cylinder

This paper presents a nondestructive testing method for assessing the structural integrity of cylindrical elements by monitoring a range of radial vibrational modes, with a specific emphasis on the so-called ovalling mode. The method involves exciting the cylinder with a single vibration source in the radial direction and measuring the response using two vibration sensors positioned diametrically on the cylinder's surface. The ovalling mode was extracted from the frequency response by adding the in-phase signals recorded by the sensors. Experiments conducted on a PVC pipe showed good agreement between the measured resonance frequency of the ovalling mode and its predicted value, calculated using the theory for thin cylindrical shells and Finite Element Method simulations. This research is an investigation into the potential and reliability of this nondestructive technique for detecting corrosion and strength-weakening defects in concrete building elements, steel pillars, and columns. The extent of the strength reduction can be determined by analyzing the change in the resonance frequency of the ovalling mode.

Temperature-Based Long-Term Stabilization of Photoacoustic Gas Sensors Using Machine Learning

In this study, we address the challenge of estimating the resonance frequency of a photoacoustic detector (PAD) gas cell under varying temperature conditions, which is crucial for improving the accuracy of gas concentration measurements. We introduce a novel approach that uses a long short-term memory network and a self-attention mechanism to model resonance frequency shifts based on temperature data. To investigate the impact of the gas mixture temperature on the resonance frequency, we modified the PAD to include an internal temperature sensor. Our experiments involved multiple heating and cooling cycles with varying methane concentrations, resulting in a comprehensive dataset of temperature and resonance frequency measurements. The proposed models were trained and validated on this dataset, and the results demonstrate real-time prediction capabilities with a mean absolute error of less than 1 Hz for frequency shifts exceeding 30 Hz over four-hour periods. This approach allows continuous, real-time tracking of the resonance frequency without interrupting the laser operation, significantly enhancing gas concentration measurements and contributing to the long-term stabilization of the sensor. The results suggest that the proposed approach is effective in managing temperature-induced frequency shifts, making it a valuable tool for improving the accuracy and stability of gas sensors in practical applications.

LC dynamic signal modeling and analysis of resonant frequency measurement error under rapid eye movements interference

Abstract LC resonant wireless passive intraocular pressure (IOP) sensors measure IOPs by mapping them to LC resonance frequencies. However, during the sweeping acquisition process of each LC signal frame, possible rapid eye movement (REM) can interfere with the wireless mutual inductance coupling, leading to the signal distortion and resulting in the error of resonance frequency measuring. Currently, there is a lack of modelling analysis of the errors generated by REM effect, resulting in an absence of guidance for reducing the impact. Therefore, here, we start from the perspective of the signal model and establish the LC dynamic signal model for sweeping acquisition. By means of the limit state analysis and Monte Carlo simulation, we analyze the influence of external REM parameters (including REM range and velocity) and internal parameters of the LC sensing system (including the quality coefficient of LC sensor, diameter, and number of turns of the reader coil, signal sweep acquisition speed and period) on the errors. We demonstrated theoretical relationship between the extreme errors with these parameters and verify it through a computer simulation. Based on the results, we propose to optimize the internal parameters of the LC sensing system to reduce the REMs effect on errors, safeguarding the quality of signal acquisition and improving the measurement accuracy.

Determination of material constants of piezoceramics using genetic algorithm

This study seeks to accurately determine the piezoelectric material constants of piezoceramic disks from the resonant frequencies of the disks using a genetic algorithm programmed according to the principles of plate theory. Mindlin's plate theory is judged to be most suitable for approximating the relationship between the in-plane and out-of-plane resonant frequencies and the material constants of a disk-shaped piezoceramic thick plate, which was programmed into a genetic algorithm in order to obtain all relevant piezoelectric material constants from measured resonant frequencies of sample piezoceramic disks through inverse calculation. To verify the accuracy of the material constants, finite element method was employed to derive the theoretical resonant frequencies along with the corresponding mode shapes, which were then compared with the actual resonant frequencies measured using amplitude-fluctuation electronic speckle pattern interferometry. The comparison shows that the genetic algorithm can successfully determine all desired material constants of piezoceramic disks from the measured resonant frequencies in a single operation, and that the resonant frequency values modeled using the constants more accurately correspond to the experimentally measured frequencies than those derived from material constants obtained using conventional methods.

Dynamic Testing and Finite Element Model Adjustment of the Ancient Wooden Structure Under Traffic Excitation

In situ dynamic testing is conducted to study the dynamic characteristics of the wooden structure of the North House main hall. The velocity response signals on the measurement points are obtained and analyzed using the self-interaction spectral method and stochastic subspace method, yielding natural frequencies, mode shapes, and damping ratios. This study reveals that the natural frequencies and damping ratios are highly consistent between the two methods. Therefore, to eliminate errors, the average of the results from both modal identification methods is taken as the final measured modal parameters of the structure. The natural frequencies of the first and second order in the X direction were 2.097 Hz and 3.845 Hz and in the Y direction were 3.955 Hz and 5.701 Hz. The modal frequency in the Y direction of the structure exceeds that in the X direction. Concurrently, a three-dimensional finite element model was established using ANSYS 2021R1, considering the semi-rigid properties of mortise–tenon connections, and validated based on in situ dynamic testing. The sensitivity analysis indicates adjustments to parameters such as beam–column elastic modulus, tenon–mortise joint stiffness, and roof mass for finite element model refinement. Modal parameter calculations from the corrected finite element model closely approximate the measured modal results, with maximum errors of 9.41% for the first two frequencies, both within 10% of the measured resonant frequencies. The adjusted finite element model closely matches the experimental results, serving as a benchmark model for the wooden structure of North House main hall. The validation confirms the rationality of the benchmark finite element model, providing valuable insights into ancient timber structures along transportation routes.

Characterization of the Power Distribution Network for Commercialized STM32s Using a Resonance Frequency Measurement Method

Power integrity is a critical aspect of microcontroller (MCU) system design. The present tendency of increasing current density and operating frequency, along with decreasing operating voltage, significantly diminishes voltage margins. Given the cost efficiency required for MCU systems, this context places important constraints on the design of the power distribution network (PDN), which directly impacts power supply noise. Therefore, characterizing the PDN is necessary. This paper introduces a cost-effective measurement and modeling method to estimate the die-package resonance frequency of the PDN, a major threat to power integrity. The method, applied to two 32-bit MCUs from STMicroelectronics with varying PDN configurations, enables the identification of the die-package resonance frequency. The results lead to the refinement of the die capacitance model for both cases, with a maximum relative error of less than 7%. The final objective is to implement the measurement system in the die in order to adjust the PDN if necessary.

Development of an Angular Stiffness Sensor to Measure Dental Implant Stability In Vitro.

This investigation aims to develop an angular stiffness sensor intended for measuring dental implant stability in bone. The sensor hardware included a tiny eccentric motor and an accelerometer to measure a flex constant of an implant with its abutment. The sensor software included a mechanics-based model to convert the flex constant to angular stiffness at the implant/abutment junction to indicate the stability. The sensor's accuracy and effectiveness are demonstrated through use of Sawbones slab models that mimic a mandibular premolar section. The models include a Branemark Mk III implant inserted into Sawbones slabs of 5 different densities with a locator abutment. An incremental insertion torque was first recorded while the implant was placed in the Sawbones models. Then benchtop experiments were conducted to measure resonance frequencies and angular stiffness. Results indicated that angular stiffness increased with Sawbones density, showing high correlation with the measured resonance frequency (R=0.977) and the incremental insertion torque (R=0.959). Finally, accuracy of the angular stiffness sensor is calibrated in light of the resonance frequency. Angular stiffness scores 99% and 95% accuracy for Sawbones models mimicking medium cancellous bones with and without a cortical layer, respectively.

Comparison of the Young’s modulus of the lead free solder alloy Sn-Ag3.8-Cu0.7 determined by hot tensile tests, ultrasonic measurements and [formula omitted]-Sn single crystal calculations

Sn-based solders are known for their tendency to form coarse grained microstructures. In combination with the high elastic anisotropy of β-Sn, the overall elastic properties and their interpretation require a careful discussion of the structure–property-relationship as elastic constants are often important input parameters for creep or fatigue models. This study therefore investigates the influence of microstructure and testing method on the Young’s modulus E for the widespread lead free solder alloy Sn-Ag3.8-Cu0.7 (SAC387) using bulk specimens. Due to its already high homologous temperature at room temperature (Thom≈ 0.6 = T/Tm for Tm being the melting temperature), hot tensile tests generally bear the risk of superimposed creep deformation. Mechanical testing becomes even more challenging, since yield strengths are usually low for these alloys. Consequently, in addition to the hot tensile tests executed for the engineering strain rate ϵ̇e=1⋅10−3 s−1, two supplemental methods are used to determine the Young’s modulus comprising of the dynamic resonance frequency measurement and the calculation of the Young’s modulus based on single crystal compliance data of the majority phase β-Sn.Young’s moduli yielded from dynamic resonance frequency measurement and calculations based on single crystal compliance data showed comparable results of (E35 °C≈ 55 GPa, E80 °C≈ 51 GPa and E125 °C≈ 48 GPa). Hot tensile tests showed similar data with the largest deviation at 80 °C, where E80 °C≈ 53 GPa was determined. These absolute values and their temperature dependence can be attributed to the microstructure of the cast specimens which show a general preferred orientation of β-Sn grains close to <110> after analysis via electron backscattered diffraction (EBSD). A comparison with literature data revealed significant differences in the Young’s moduli which are likely to be attributed to differences in the preferred orientation of β-Sn grains.

Fabrication of Wafer-Level Vacuum-Packaged 3C-SiC Resonant Microstructures Grown on &amp;lt;111&amp;gt; and &amp;lt;100&amp;gt; Silicon

In this work, the fabrication of wafer-level vacuum packaged 3C-SiC resonators obtained from layers grown on &lt;100&gt; and &lt;111&gt; silicon is reported. The resonant microstructures are double-clamped beams encapsulated by glass-silicon anodic bonding using titanium-based vacuum gettering. Open-loop resonance frequency measurements are performed on the vacuum-packaged devices showing Q-factor values up to 292,000 for &lt;100&gt; and 331,000 for &lt;111&gt; substrates, with a maximum vacuum level around 10-2 mbar inside the encapsulations with Ti getter.

Red and Green Laser Powder Bed Fusion of Pure Copper in Combination with Chemical Post-Processing for RF Cavity Fabrication

Linear particle accelerators (Linacs) are primarily composed of radio frequency cavities (cavities). Compared to traditional manufacturing, Laser Powder Bed Fusion (L-PBF) holds the potential to fabricate cavities in a single piece, enhancing Linac performance and significantly reducing investment costs. However, the question of whether red or green laser PBF yields superior results for pure copper remains a subject of ongoing debate. Eight 4.2 GHz single-cell cavities (SCs) were manufactured from pure copper using both red and green PBF (SCs R and SCs G). Subsequently, the surface roughness of the SCs was reduced through a chemical post-processing method (Hirtisation) and annealed at 460 °C to maximize their quality factor (Q0). The geometric accuracy of the printed SCs was evaluated using optical methods and resonant frequency (fR) measurements. Surface conductivity was determined by measuring the quality factor (Q0) of the SCs. Laser scanning microscopy was utilized for surface roughness characterization. The impact of annealing was quantified using Energy-Dispersive X-ray Spectroscopy and Electron Backscatter Diffraction to evaluate chemical surface properties and grain size. Both the SCs R and SCs G achieved the necessary geometric accuracy and thus fR precision. The SCs R achieved a 95% Q0 after a material removal of 40 µm. The SCs G achieved an approximately 80% Q0 after maximum material removal of 160 µm. Annealing increased the Q0 by an average of about 5%. The additive manufacturing process is at least equivalent to conventional manufacturing for producing cavities in the low-gradient range. The presented cavities justify the first high-gradient tests.

Measurement of Resonant Frequency of Radio Frequency Converter under Conditions of Significant Electromagnetic Losses

The measurement of resonant frequency in radio wave converter under conditions of high electromagnetic losses presents a formidable challenge. This frequency serves as a crucial parameter directly linked to non-electronic quantities, such as spatial separation thresholds or substance consumption levels. Consequently, accurate measurement of these non-electric variables necessitates precise determination of the transmitter's resonant frequency. However, when electromagnetic losses escalate due to control environment properties, achieving such precision becomes daunting. Common methodologies often hinge on assessing resonant frequency via the transmitter's amplitude-frequency characteristic. However, conventional approaches, typically reliant on electron beam tubes with intricate control mechanisms, falter in accuracy amidst substantial electromagnetic transmission losses. This inadequacy undermines the efficacy of current devices. This paper introduces an unconventional method for resonance frequency measurement and underscores the benefits of the device developed through this novel approach compared to existing ones. The proposed method ensures sustained high measurement accuracy even in the face of significant transmitter electromagnetic losses. Central to this method is the measurement of frequencies ω₁ and ω₂ proximate to the resonant circuit's extreme value at points characterized by identical transmission coefficients. Resonant frequency is then determined as the half-sum of these frequencies during symmetrical frequency modulation. This innovative approach promises to overcome the limitations of traditional resonance frequency measurement methods, offering enhanced precision and reliability in challenging electromagnetic environments.

Application of Generalized S-Transform in the Measurement of Dynamic Elastic Modulus

Resonance is commonly used for in situ measurement of the dynamic elastic modulus to evaluate the strength of concrete samples. Many researchers are also exploring the application of this convenient measurement technology for safety monitoring. Nevertheless, the presence of cracks and variations in curing conditions within samples can impact the resonance frequency range, potentially leading to potential inaccuracies in measurements. In order to improve the measurement accuracy of resonance frequency, this study introduces the Generalized S-Transform (GST) algorithm for measuring the dynamic elastic modulus, which utilizes its high time-frequency resolution to scan the power peak-point in non-stationary and transient excitation signals to determine the resonance frequency. For concrete materials with lower consistency, the experimental results verify the high accuracy of this algorithm in measuring resonance frequency compared with Fast Fourier Transform (FFT). This provides a reference for using the algorithm to measure the dynamic elastic modulus in civil engineering applications, such as buildings and bridges.

Elastic moduli from crystalline micro-mechanical oscillators carved by focused ion beam.

The elastic moduli provide unique insights into the thermodynamics of quantum materials, particularly into the symmetries broken at their phase transition. Here, we present a workflow to carve crystalline resonators via focused ion beam milling from small and oddly shaped crystals unsuitable for traditional measurements of elasticity. The accuracy of this technique is first established in silicon. Next, we showcase the capacity to probe changes in the electronic state with a resolution on the measured resonance frequency as small as 0.01% on YNiO3, a rare-earth perovskite nickelate, in which bulk single crystals have typical length scales of ≈40μm. Here, we observe a sharp 0.2% discontinuity in Young's modulus of an YNiO3 cantilever at a magnetic phase transition. Finally, an additional potential of using free-standing cantilevers as a tool for examining the time-dependence of chemical changes is illustrated by laser-heating YNiO3.

A Novel Dual-Band Omnidirectional Horizontally Polarised Antenna Using Slotted Ground for Wi-Fi Applications

This paper explores an innovative approach to designing a compact, dual-band, omnidirectional, horizontally polarised (OHP) patch antenna with a low profile. The antenna’s ground plane is meticulously etched with radial and arch slots to create open-circuited stubs. This design generates two circulating current loops: one beneath the circular patch and the other on the outer side of the circular patch, comprised of four circular stubs. These current loops operate in unison to produce dual-band resonance and in-phase circulating current on the ground at both resonance frequencies. The antenna’s configuration includes four circular stubs formed by printing sequential radial and bent slots beneath the patch. This arrangement generates an omnidirectional radiation pattern in the azimuth plane at the upper resonance frequency. In addition, four open circular stubs outside the patch are integrated into the ground plane cascaded to the inner four stubs to achieve resonance at the lower frequency. The complete dimensions of the proposed antenna configuration are 0.29λ0 × 0.29λ0 × 0.025λ0, with bandwidths of 2.84% and 2.77% corresponding to measured resonance frequencies of 2.457 and 5.27 GHz, respectively. The measured gains are 1.2 dBi at the lower resonance frequency and 0.8 dBi at the upper resonance frequency. Furthermore, the measured roundness of the radiation pattern remains within 1 dB at the lower frequency band and within 2.8 dB at the upper-frequency band.

Low-thermal-budget electrically active thick polysilicon for CMOS-First MEMS-last integration

Low-thermal-budget, electrically active, and thick polysilicon films are necessary for building a microelectromechanical system (MEMS) on top of a complementary metal oxide semiconductor (CMOS). However, the formation of these polysilicon films is a challenge in this field. Herein, for the first time, the development of in situ phosphorus-doped silicon films deposited under ultrahigh-vacuum conditions (~10−9 Torr) using electron-beam evaporation (UHVEE) is reported. This process results in electrically active, fully crystallized, low-stress, smooth, and thick polysilicon films with low thermal budgets. The crystallographic, mechanical, and electrical properties of phosphorus-doped UHVEE polysilicon films are studied. These films are compared with intrinsic and boron-doped UHVEE silicon films. Raman spectroscopy, X-ray diffraction (XRD), transmission electron microscopy (TEM) and atomic force microscopy (AFM) are used for crystallographic and surface morphological investigations. Wafer curvature, cantilever deflection profile and resonance frequency measurements are employed to study the mechanical properties of the specimens. Moreover, resistivity measurements are conducted to investigate the electrical properties of the films. Highly vertical, high-aspect-ratio micromachining of UHVEE polysilicon has been developed. A comb-drive structure is designed, simulated, fabricated, and characterized as an actuator and inertial sensor comprising 20-μm-thick in situ phosphorus-doped UHVEE films at a temperature less than 500 °C. The results demonstrate for the first time that UHVEE polysilicon uniquely allows the realization of mechanically and electrically functional MEMS devices with low thermal budgets.

A resonance frequency analysis to investigate the impact of implant size on primary and secondary stability.

Recent years have seen a rise in the usage of dental implants to restore lost teeth. The stability of a dental implant is the main factor in determining its success. Implant stability is influenced by various factors. Several approaches have been employed clinically to evaluate stability at different time intervals. One non-invasive way to assess implant stability is by resonance frequency analysis. Utilizing the resonance frequency analysis method, this study seeks to understand how implant length and diameter affect primary and secondary stability. The current prospective study was conducted in the Prosthodontics Department of Institute of Dentistry, CMH Lahore Medical College. The duration of the study was six months. A total of 90 implants of sizes 4.5 x 8.5 mm and 4 x 10mm were placed. Resonance frequency measurements were recorded using Osstell™ AB device for primary stability at implant insertion and at 12 weeks for secondary stability. All the measurements were carried out by only one of the researchers to minimize inter-observer bias. The average primary stability was 70.33±6.60, and the average secondary stability was 71.43±5.44. The data was stratified for age, gender, and implant site, and the mean primary and secondary stability of both sizes didn't show any statistically significant differences. Without forfeiting implant stability, both implant sizes (4 x 10mm and 4.5 x 8.5mm) can be used interchangeably, depending on available space and anatomical constraints.

Resonant cavity method based on RF measurement and simulation for measuring complex permittivity or permeability of RF absorbing materials

Accurate measurement of complex permittivity and/or permeability of radio-frequency (RF) absorbing materials is essential to predict the performances of higher-order-mode damping in damped accelerating cavities or in vacuum chambers. We propose an improved resonant cavity method that can be used as a complement to the widely used Nicolson–Ross–Weir method for measuring the RF characteristics of materials. The conventional resonant cavity method is based on the cavity perturbation theory. However, the measurements are inaccurate when losses in the materials are large. The improved method we propose determines the complex permittivity or permeability of materials from the measured resonant frequencies and Q factors based on eigenmode simulations. Because the reliability on the eigenmode calculation for RF cavities with lossy materials has become sufficiently reliable, determination of complex permittivity and permeability can be achieved using such a simulation software. We demonstrate this method using ferrite HF70 (TDK Corp.), which is useful for RF absorbers in damped accelerating cavities or in vacuum chambers.

On the τf measurement of microwave dielectric ceramics

As a key parameter of microwave dielectric ceramics, the temperature coefficient of resonant frequency (τf) determines the temperature stability of microwave dielectric ceramics and relevant microwave devices. The τf of a microwave dielectric ceramic is typically calculated from the measured resonant frequencies of the system, consisting of the ceramic sample plus other dielectric elements, at two temperatures ∼60 – 70 °C apart. This measurement process assumes that τf is a constant; however, it is generally temperature-dependent based on both theoretical and experimental results. Furthermore, the as-measured τf is actually the τf of the dielectric resonator system, which is different from that of the sample itself. In this paper, these two overlooked problems during τf measurement are discussed in detail, and suggestions are given to avoid their possible misleading consequences and thus ensure the reliability of τf measurements.

Laser-Induced Selective Metallization on Aluminum Nitride for Fine Line Circuits

The technology of laser direct selective metallization on aluminum nitride substrate was investigated for manufacturing fine line circuits. In laser direct structuring, laser activation and electroless copper plating were used. The feasibility was evaluated by analyzing the sieving, contrast, and fine linewidth patterns, and the results showed that the width of the feasible fine reached 100 μm. A near-field communication (NFC) antenna circuit of the width of 400 μm was fabricated on the aluminum nitride substrate. The measured resonance frequency was close to the NFC specification frequency.

Thermal noise calibration of functionalized cantilevers for force microscopy: Effects of the colloidal probe position

Colloidal probes are often used in force microscopy when the geometry of the tip–sample interaction should be well controlled. Their calibration requires an understanding of their mechanical response, which is very sensitive to the details of the force sensor consisting of a cantilever and the attached colloid. We present some analytical models to describe the dynamics of the cantilever and its load positioned anywhere along its length. The thermal noise calibration of such probes is then studied from a practical point of view, leading to correction coefficients that can be applied in standard force microscope calibration routines. Experimental measurements of resonance frequencies and thermal noise profiles of raw and loaded cantilevers demonstrate the validity of the approach.