Resonant Frequency Analysis Research Articles

An Approach for Decentralized Mode Estimation Based on the Random Decrement Method

Structural health monitoring methods based on modal properties have been proven to be well suited for infrastructure objects, e.g. bridges, buildings or wind turbines. The considerable size of these structures leads to long distances between the sensors and the signal processing units and a large number of sensors. To save cabling effort and lower the amount of data which has to be transmitted, the structural analysis may be decentralized with a network of smart sensors. In this paper, a strategy for decentralized signal analysis with the Random Decrement method is discussed. This method allows for the estimation of auto- and cross-correlation functions simply from triggered averaging of time histories. These serve as a basis for the modal decomposition by operational modal analysis methods. While the Random Decrement signatures can be processed in a decentralized way on the small microcontrollers commonly used, e.g. in wireless sensing applications, the deeper analysis of resonance frequencies and mode shapes is done by a central unit. After a short introduction into the theory of the Random Decrement method, its application in decentralized data acquisition is illustrated with a numerical example. Afterwards, a simple experimental structure exposed to actual wind loads is instrumented and the decentralized signal processing strategy is tested with the acquired data. A first algorithm for the modal decomposition of the estimated correlation functions is implemented and tested.

Estimation and veering analysis of nonlinear resonant frequencies of cracked plates

In this paper, veering phenomena in the nonlinear vibration frequencies of a cantilevered cracked plate are investigated, and an efficient method for estimating these frequencies is proposed. Of particular interest is the vibration response in parameter regions where the natural frequency loci show veerings. For a representative finite element model, it is shown that the veerings due to crack length variation involve the switching of mode shapes and modal interactions. The nonlinearity caused by the crack closing effect is then introduced, and its effect on the vibration response near the veerings is discussed. The nonlinear forced response analysis is carried out using a hybrid frequency/time domain method, which is based on the method of harmonic balance. The nonlinear vibration response near loci veerings and crossings due to the variation of crack length is investigated in detail. Finally, a novel method for estimating the nonlinear resonant frequency is introduced by generalizing the concept of bilinear frequency approximation, and the method is validated with the results of nonlinear forced response analysis for several veering regions.

The Dynamic Behaviour of Chiral, Fixed-Free, Single-Walled Carbon Nanotube-Based Nanomechanical Mass Sensors Due to Atomic Vacancies

The dynamic analysis of single-walled carbon nanotubes (SWCNTs) with chiralities has been performed using an atomistic finite element method. SWCNTs with different chiral angles are considered for the resonant frequency analysis. The cantilever carbon nanotube (CNT) is modelled by considering it as a space frame structure similar to three-dimensional beams and point masses. The beam element elastic properties are calculated by considering the mechanical characteristics of covalent bonds between the carbon atoms in the hexagonal lattice. The mass of each beam element is assumed as a point mass at nodes coinciding with carbon atoms. This atomistic simulation approach is used to visualize the effect of defects such as atomic vacancies in the CNT on the resonant frequency. The variation of the atomic vacancy is performed along the length and the response is obtained for different chiralities. It is observed that there is a reduction in the simulated natural frequency due to the atomic vacancy. This has a significant effect on dynamic behaviour when the defect is nearer to the fixed end. The change in resonant frequency of such a defective CNT is observed when it is used as a mass sensor. The resonant frequency is also evaluated for various chiralities and numbers of defects. The simulation results indicate that the existence of defects mostly affects the resonant frequency (bending rigidity) of the SWCNT as the number of defects increases. It is quite evident from the simulation results that the effect of atomic vacancies is a maximum when they are situated nearest to the fixed end and the effect diminishes at a mass addition of 10 —2 fg.

Vibrational testing of trabecular bone architectures using rapid prototype models

The purpose of this study was to investigate if standard analysis of the vibrational characteristics of trabecular architectures can be used to detect changes in the mechanical properties due to progressive bone loss. A cored trabecular specimen from a human lumbar vertebra was μCT scanned and a three-dimensional, virtual model in stereolithography (STL) format was generated. Uniform bone loss was simulated using a surface erosion algorithm. Rapid prototype (RP) replicas were manufactured from these virtualised models with 0%, 16% and 42% bone loss. Vibrational behaviour of the RP replicas was evaluated by performing a dynamic compression test through a frequency range using an electro-dynamic shaker. The acceleration and dynamic force responses were recorded and fast Fourier transform (FFT) analyses were performed to determine the response spectrum. Standard resonant frequency analysis and damping factor calculations were performed. The RP replicas were subsequently tested in compression beyond failure to determine their strength and modulus. It was found that the reductions in resonant frequency with increasing bone loss corresponded well with reductions in apparent stiffness and strength. This suggests that structural dynamics has the potential to be an alternative diagnostic technique for osteoporosis, although significant challenges must be overcome to determine the effect of the skin/soft tissue interface, the cortex and variabilities associated with in vivo testing.

Spatial Sensitivity of Capacitors in Distributed Resonators and Its Application to Fine and Wide Frequency Tuning Digital Controlled Oscillators

Analysis of resonance frequency in shorted transmission lines with inserted capacitor has been made. The analysis shows a resonance frequency dependence on capacitance position on a shorted transmission line. Two analysis methods are presented to predict the resonance frequency and understand how the inserted capacitor affects the resonance frequency of the shorted transmission line. Using this knowledge we propose a new structure for digital controlled oscillators utilizing the capacitance's sensitivity dependence on position of the shorted transmission line to increase the frequency resolution. A 9GHz transmission line based digital controlled oscillator was designed and fabricated as a proof of concept. Measured results show that more than 100 times frequency step resolution increase is possible utilizing the same tuning capacitor size located at different points on the transmission line.

Uncertainty Modeling and Analysis of Natural Resonant Frequency and Transconductance Parameters in Microresonators Design

The correspondence presents a method of analyzing uncertainty in microelectromechanical systems (MEMS). A specific example is presented using comb microresonators. The equation governing the resonant frequency and the transconductance values was analyzed. The mathematical formulation of the convex model was derived. The major finding is that convex models can be used as an uncertainty analysis tool in MEMS design applications.

Application of Taguchi robust design method to SAW mass sensing device

It is essential that measurement systems provide an accurate and robust performance over a wide range of input conditions. This paper adopts Taguchi's signal-to-noise ratio (SNR) analysis to develop a robust design for the Rayleigh surface acoustic wave (SAW) gas sensing device operated in a conventional delay-line configuration. The goal of the present Taguchi design activity is to increase the sensitivity of this sensor while simultaneously reducing its variability. A time- and cost-efficient finite-element analysis method is used to investigate the effects on the sensor's response output of variations in the carbon dioxide (CO2) gas deposited mass. The simulation results for the resonant frequency and wave mode analysis are all shown to be in good agreement with the values predicted theoretically.

Resonant frequency analysis of fixed-free single-walled carbon nanotube-based mass sensor

Carbon nanotubes (CNTs) have good mechanical properties and unique structural, electronic, thermal, and optical characteristics. Fixed-free single-walled carbon nanotubes (SWCNTs) have attracted intense interest in recent years due to their suitability for a wide range of applications, such as field emission and vacuum microelectronic devices, nano-sensors and nano-actuators, etc. This paper investigates the resonant frequency and mode shapes of a SWCNT analytically and via continuum mechanics-based finite element method (FEM) simulations using a beam-bending model. Additionally, this study explores the resonant frequency shift of the fixed-free SWCNT caused by the addition of a nano-scale particle to the beam tip in order to explore the suitability of the SWCNT as a mass detector device. The simulation results for the resonant frequency are compared to the theoretical solutions and published experimental data. It is shown that the FEM simulation results are in good agreement with the theoretical and experimental data and hence the current modeling approach is suitable as a coupled-field design tool for the development of SWCNT-based NEMS applications.

Analytical and finite element method design of quartz tuning fork resonators and experimental test of samples manufactured using photolithography 2: comprehensive analysis of resonance frequencies using Sezawa's approximations

Resonance frequency of a quartz tuning fork crystal for use in chips of code division multiple access, personal communication system, and a global system for mobile communication was comprehensively analyzed by an analytical method, Sezawa's approximations and the finite element method. A comparison was also made in a more detailed and comprehensive manner among resonance frequencies calculated by the Sezawa's approximations. From the finite element method analysis results, actual tuning fork crystals were fabricated using mass-production capable positive (subtractive) photolithography, selective etching and subsequent positive (subtractive) photoresist spray coating method. A target resonance frequency of 32.768 kHz + 544 Hz was aimed at and a general scheme of commercially available 32.768 kHz tuning fork resonators was also followed in designing tuning fork geometry, tine electrode pattern and thickness. Comprehensive comparison was made among the modeled and experimentally measured resonance frequencies and the discrepancy explained and discussed. Finite element method analysis results quite closely agreed with the experimentally measured resonance frequencies (32.676–32.933 kHz) of the fabricated tuning fork samples measured at a vacuum level of 10 −5 Torr. The difference between modeling and experimentally measured resonance frequency is attributed to the error in exactly manufacturing tuning fork tine width by photolithography. However, the tuning fork design using finite element method modeling must be modified comprehensively to optimize various design parameters affecting both the resonance frequency and other crystal parameters, most importantly crystal impedance (series resistance).

Frequency Domain Analysis for Extending Time Domain Reflectometry Water Content Measurement in Highly Saline Soils

Water content and electrical conductivity of soils are routinely determined using time‐domain reflectometry (TDR) based on analysis of signal travel time and attenuation along embedded probes. In soils with appreciable salinity, time domain analysis becomes progressively inaccurate due to signal attenuation to the point of failure. Our objectives were to test whether dielectric permittivity, which is inextricable using TDR travel time analysis (TTA) in saline soils could be extracted using frequency domain techniques applied to waveforms from shorter TDR probes that reduce signal attenuation. The methodology was tested using coaxial cells and three‐wire TDR probes in sand and silt loam soil under a wide range of saturated solution soil electrical conductivities. Three different interpretation techniques were compared; conventional TTA, scatter function fitting (SFF), and resonant frequency analysis (RFA). Using a range of probe lengths (2, 3, 6, 10, and 15 cm) soil bulk dielectric permittivity estimates were obtained using all three techniques in solution electrical conductivities up to 48 dS m−1 Both SFF and RFA produced similar permittivity estimates, which generally increased with increasing solution electrical conductivity. Network analyzer permittivity measurements (0.5–1.5 GHz) were greater than estimates using TTA, which were both greater than values from SFF and RFA in a saturated silt loam soil. Although dependent upon dielectric permittivity and electrical conductivity, frequency domain analysis results indicate a 3‐cm probe is optimal for maintaining a interpretable scatter function in the TDR frequency band while providing maximum extension of dielectric determination under lossy conditions in saturated soils.

Measurement of local elastic properties of injection moulded polymer structures by analysis of flexural resonant frequencies. Applications in POM, PA66, filled PA 66

The polymer processing conditions used in injection moulding strongly influence mechanical properties of materials in the solid state. This investigation presents an experimental method for measuring the local Young’s modulus and its application to polyoxymethylene (POM), polyamide 66 and glass fibre-filled polyamide 66 test pieces. An inverse method allowing local longitudinal Young’s moduli to be estimated from local natural flexural frequencies has been evaluated. The results obtained reveal a large variation in the local Young’s modulus over the thickness of an injection moulded piece, in particular in the outer skin zone. The influence of the various operational parameters has been evaluated.

ACOUSTIC MEASUREMENT OF AVOCADO FIRMNESS DURING LOW TEMPERATURE STORAGE: EFFECT OF STORAGE TEMPERATURE

ACOUSTIC MEASUREMENT OF AVOCADO FIRMNESS DURING LOW TEMPERATURE STORAGE: EFFECT OF STORAGE TEMPERATURE

Resonant frequency analysis of reentrant resonant cavity applicator by using FEM and FD-TD method

A reentrant resonant cavity applicator is analyzed as a generalized eigenvalue problem by using the finite element method (FEM) with edge elements. The subspace iteration method is used to solve for selected eigenvalues. The resonant frequencies obtained are in good agreement with both the measured values and with the ones obtained using the finite-difference time-domain (FD-TD) method. Computation time and the amount of memory required are also discussed.

Measuring the mechanical stiffness of an eggshell using resonant frequency analysis

1. A new method was introduced for the measurement of mechanical eggshell characteristics based on the analysis of the vibration response of a chicken egg excited with a non-destructive impact. Four major topics were examined. 2. The 3 dimensional vibration pattern of an intact chicken egg was described for the spherical vibration with the lowest resonant frequency. 3. The resonant frequency of this basic vibration mode and the total egg mass were used to calculate a dynamic stiffness value of the eggshell based on a mathematical mass-spring model. 4. A correlation analysis between this dynamic stiffness value and several common egg and eggshell variable was calculated. Pearson correlation coefficients between the dynamic stiffness and static stiffness, eggshell thickness at the equator, eggshell width and shape index were all significantly different from zero and were 0.71, 0.60, 0.43 and 0.51, respectively. 5. Graphical analysis of the static vs the dynamic eggshell stiffness indicated that eggs with thick shells (>360 mum) had a higher static stiffness value than the dynamic stiffness measurement, whereas the static stiffness of eggs with thin shells (>300 mum) was lower than the dynamic stiffness. 6. The new vibration test method is a promising alternative for evaluating mechanical eggshell properties because of its non-destructive nature and brief measuring time.

Influence of the resonant frequency on the control of knock in diesel engines

This paper presents an alternative approach to investigating the origin and the development process of knock vibrations that occur in an indirect injection (IDI) diesel engine. In contrast to the conventional analysis of the pressure rise rate, this study focuses on the analysis of instantaneous resonant frequencies at different moments during combustion. The smoothed pseudo-Wigner-Ville distribution (SPWVD) and Hilbert transform methods are applied to estimate the resonant frequency under different conditions representing various knock intensities. Two important factors are found significantly to influence knock development. Finally, design strategies and preferable fuel injection patterns are suggested for reducing knock intensity.

Treating late-time instability of hybrid finite-element/finite-difference time-domain method

The hybrid finite element/finite-difference time-domain (FETD/FDTD) method previously proposed to handle arbitrarily shaped dielectric objects is employed to investigate electromagnetic problems of high Q systems for which the transient response over a very long duration is necessary. To begin with, the paper demonstrates that this hybrid method may suffer from late-time instability and spurious DC modes. Then an approach which combines the temporal filtering and frequency shifting techniques is presented to overcome sequentially and, respectively, the two drawbacks. Its accuracy is validated by the favorable comparison with several different methods for the analysis of resonant frequencies and and factors of the various modes in an isolated dielectric resonator. Finally, the present method is applied to calculate the scattering parameters on the microstrip line due to the presence of the cylindrical dielectric resonator.

Torsional Micromirror Array Design for Optical Binary Switching and Amplitude Modulation Applications

AbstractA torsional micromirror was designed and fabricated using a three-level, polysilicon, surface micromachined, microelectromechanical systems (MEMS) process. The torsional micromirrors have highly-reflective, gold-coated polysilicon optical surfaces. Electrostatically induced in-plane and outof-plane vertical deflections on the order of 2.75 νm were achieved. The modeling phase focused on the microdynamical behavior of the torsional micromirror. The IntelliCAD® finite element analysis program was used to generate a plot of the micromirror's deflection (d) versus applied direct current voltage (V). The data was least-squares fitted to the well-established V μ d3/2 relationship. A resonant frequency analysis predicted an approximate switching speed of 6 νsec. The relative reliability (number of operational cycles) of the torsional micromirror design was measured to exceed 2 million flexure events. The potential for using torsional micromirrors as binary optical switches and amplitude modulators is addressed.

Implementation of micromirror arrays as optical binary switches and amplitude modulators

Five types of micromirror arrays were designed and fabricated using a three-level, polysilicon, surface micromachined, microelectromechanical systems (MEMS) process. The electrostatically deflectable micromirror designs included arrays of simple cantilever beams, torsion beams, tethered (piston-style) beams, circular membranes and oval membranes. The smallest micromirror element was the simple cantilever beam, measuring 50 μm square. The largest micromirror element was the oval membrane; it possessed an active optical surface that was 320 μm by 920 μm. Each of the remaining micromirror designs have gold-coated polysilicon optical surfaces with geometries between these two limits. Electrostatically induced vertical deflections on the order of 2.75 μm were achieved. The torsion beam micromirror design exhibits both in-plane and out-of-plane deflection. The other micromirror designs only manifest in-plane deflections. The modeling phase focused on the microdynamical behavior of the torsion beam micromirror. The IntelliCAD® finite element analysis program was used to generate a plot of the micromirror’s deflection (d) versus applied direct current voltage (V). The data was least-squares fitted to the well-established V∝d3/2 relationship. A resonant frequency analysis predicted an approximate switching speed of 6 μsec. The reliability (number of operational cycles) of each micromirror design, when operated with a rectified 60 Hz alternating current (ac) signal, was measured to exceed more than 1 million flexure events. Experimental evidence supporting the potential for using micromirrors as binary optical switches and amplitude modulators was also addressed.

Effect of salmon calcitonin on femoral bone quality in adult ovariectomized ewes.

The aim of this study was to evaluate the effect of intermittent calcitonin on femoral bone quality in adult ewes from the time of ovariectomy. Six months after the start of the experiment, bone density measurements and mechanical testing (torsion and resonant frequency analysis of the diaphysis and compression of an excised trabecular bone cylinder from the femoral neck) were performed in sham-control and ovariectomized (OVX) ewes treated with placebo or salmon calcitonin (50 or 100 units, 3 times/week). Crystallinity of bone was evaluated by measuring X-ray diffraction line broadening. After OVX, a nonsignificant bone loss was found at all measured sites in the femur (-3 to -9%) together with a decreased biomechanical competence in the trabecular bone (compressive strain -28%, P < 0.05). Treatment with salmon calcitonin, 50 or 100 IU subcutaneously three times a week from the time of ovariectomy, resulted in a significant dose-dependent preservation of bone strength in the trabecular bone of the femoral neck compared with OVX. No adverse effects of calcitonin were observed on bone crystal composition as assessed by diffractiometry. We conclude that in adult ewes intermittent calcitonin treatment from the time of OVX was associated with a significant preservation of cancellous bone strength and strain in trabecular bone of the femoral neck, without affecting crystalline properties of bone.

Rigorous analysis of radiation properties of lossy patch resonators on complex anisotropic media and lossy ground metallization

An extended spectral-domain immittance approach for the rigorous analysis of resonant frequencies and radiation characteristics of microstrip resonators is presented. The dyadic Green's function in the spectral domain is modified to include a complex anisotropic substrate with both permeability and permittivity tensors, lossy ground metallization, and a lossy conducting patch of conventional or superconducting material. Closed-form expressions for the transverse propagation constants and related immittances of TE and TM waves in the spectral domain lead to a CPU-time efficient algorithm that is operational on standard workstations. Numerical results show how the radiation characteristics are affected by losses as well as uniaxial and biaxial anisotropies.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>