Measurement Of Eigenfrequencies Research Articles

Eigenfrequency analysis using fiber optic sensors and low-cost accelerometers for structural damage detection

Structural Health Monitoring (SHM) is crucial for infrastructure safety and integrity. Arduino-based sensors are gaining popularity in low-cost SHM structures. Distributed fiber optic systems (DFOS), such as Distributed Acoustic Sensing (DAS), are employed for accurate SHM despite their high costs, computational demands, and energy consumption. The primary objectives of this work are to compare the accuracy of an accelerometer named LARA (Low-cost Adaptable Reliable Accelerometer (LARA)) that utilizes both Arduino and Raspberry Pi technologies with a DAS system in detecting structural damage and to explore the potential advantages of combining LARA and DAS to create an effective SHM tool. This study is the first to enhance the design of LARA. Subsequently, LARA and DAS were used in a laboratory setting to analyze eigenfrequency changes in a beam model with induced localized damage. Finally, this study evaluated the precision and reliability of LARA and its potential role as a trigger for DAS in detecting localized damage. The findings show that both LARA and DAS can identify changes in the eigenfrequencies of damaged structures with deviations as small as 3.68 %. Consequently, LARA demonstrated its potential as a trigger for DAS, significantly reducing the computational demands while enriching the analysis. This approach offers highly accurate eigenfrequency measurements and enhances the analytical capabilities of DAS by identifying the primary axes of the detected eigenfrequencies.

Penning-trap eigenfrequency measurements with optical radiofrequency detectors

We use an electric-dipole laser-driven transition to precisely measure the cyclotron-frequency ratios of the pairs Ca+42−Ca+40, Ca+44−Ca+40, and Ca+48−Ca+40 in a 7-tesla Penning trap. A single laser-cooled (T≈1 mK) ion serves, together with photon-counting and photon-imaging units, as a radiofrequency detector covering a broadband frequency spectrum, in the present case from kHz to a few MHz. Such detectors (Ca+40,42,44,48) allow measuring extremely small forces increasing the sensitivity in Penning-trap mass spectrometry. The direct determination of the ions' amplitudes makes a cyclotron-frequency measurement process more robust against inhomogeneities of the magnetic field and/or deviations of the electric quadrupole field due to mechanical imperfections of the trap. Published by the American Physical Society 2024

Biologically Inspired Girder Structure for the Synchrotron Radiation Facility PETRA IV

Lightweight structures are widely used across different industry sectors. However, they get easily excited by external influences, such as vibrations. Undesired high vibration amplitudes can be avoided by shifting the structural eigenfrequencies, which can be achieved adapting the structural design considering optimisation procedures and structures primarily inspired by diatoms. This procedures has been applied to the development process of a girder structure installed in a synchrotron radiation facility to support heavy magnets and other components. The objective was to design a 2.9 m long girder structure with high eigenfrequencies, a high stiffness and a low mass. Based on a topology optimisation result, a parametric beam–shell model including biologically inspired structures (e.g., Voronoi combs, ribs, and soft and organic-looking transitions) was built up. The subsequent cross-sectional optimisation using evolutionary strategic optimisation revealed an optimum girder structure, which was successfully manufactured using the casting technology. Eigenfrequency measurements validated the numerical models. Future changes in the specifications can be implemented in the bio-inspired development process to obtain adapted girder structures.

A method for generating finite element models of wood boards from X-ray computed tomography scans

A method is presented for reconstructing the geometry, the pith, the knots and the local fibre orientations in timber boards, based on X-ray computed tomography scans. The local fibre deviations around knots were found by a new algorithm, based on image analysis. The experimental data comprised tomography scans, eigenfrequency measurements and four-point bending tests of 20 Norway spruce boards. 3D and 1D finite element models of the pure bending zone of the bending tests were created, accounting for the exact board geometry and the reconstructed fibre deviations. A purely density based, a purely eigenfrequency based, and a mixed constitutive law were compared. Model estimations showed a high coefficient of determination (R2) for global modulus of elasticity (MoE) (R2⩽0.93), local MoE (R2⩽0.87), bending strength (R2⩽0.83), and the location of initial failure. Constitutive laws accounting for eigenfrequency showed the most accurate results. In the future, adapting the method for logs could enable analyses of boards before sawing.

Numerical Analysis and Experimental Verification of Eigenfrequencies of Overhead ACSR Conductor

<span lang="EN-GB">This contribution deals with the modal analysis of ACSR conductor using the finite element method (FEM) and experimental measurements of eigenfrequencies. In numerical experiments for the modelling of the conductor the material properties of the chosen conductor cross-section are homogenized by the </span><span lang="EN-US">Representative</span><span lang="EN-GB"> Volume Element (RVE) method. The spatial modal analysis of the power line is carried out by means of our new 3D FGM beam finite element and by standard beam finite element of the commercial software ANSYS. Experimental measurements are also carried out for verification of the numerical calculation accuracy.</span>

Experimental and Numerical Modal Analysis of the Carbon Composite Plate Damaged by Cut

The given paper is closely connected with the experimental and numerical modal analysis of the carbon composite plate damaged by cut. In relation to the tested carbon composite, modal analysis was performed by help of special measuring device Pulse 12. The mentioned device was supplied by company BrĂźel & Kjear and the experimental measurements were carried out using damaged and undamaged plate sample which were prepared from the mentioned material hereinbefore. The investigated and analyzed plates of carbon composite were made of six layers of carbon fibres and they were arranged under the angle 90º (it is like fabric material made off carbon fibres). The layers arranged in the given way were joined by epoxide resin MGS 285. The experimental measurement of eigenfrequencies of carbon composite plates was carried out using the undamaged and damaged sample with proportions 78 mm x 78 mm while ten measurements were performed for each one specified site of the sample. In relation to the damaged plate sample, there was cut in length of 20 mm in the centre border. The finite element method in the software system ADINA v.8.6.2 was used for numerical analysis of the eigenfrequencies.

Eigenfrequency characterization and tuning of Ti-6Al-4V ultrasonic horn at high temperatures for glass molding

Glass molding assisted by ultrasonic vibration is a promising yet challenging technique for microoptics fabrication. During glass molding localized high temperatures (300–600 °C) often result in transformed eigenfrequencies of the ultrasonic horn, and hence decreased electroacoustic efficiencies of the ultrasonic system. This study proposes a systematic methodology to optimally tune the objective eigenfrequency of the horn at elevated temperatures. Theoretical and numerical analyses are first performed to characterize the thermally disturbed modal characteristics of the horn. Numerical results indicate that the longitudinal eigenfrequency of the horn decreases significantly with the increasing molding temperature Tm. To compensate for this eigenfrequency decrease, numerical size optimization is then conducted and a two-segment cylindrical horn with an optimized tool (68.62 mm in length) is obtained. In situ eigenfrequency measurements of the optimized horn are further implemented at varying molding temperatures. Experimental results suggest that the tuned eigenfrequencies of the optimized Ti-6Al-4V horn are within the prescribed frequency-tracking range (35 ± 0.5 kHz) over a wide range of molding temperatures (226–641 °C). Thus, by merely pre-adjusting the theoretical eigenlength of the horn, a well-tuned and adaptable high-temperature ultrasonic vibration system can be effectively developed. In addition to glass molding, the proposed methodology applies to design and optimization of ultrasonic horns for diverse thermally involved processes.

Experimental and numerical investigation of PUR foam under dynamic loading

AbstractVarious factors may subject buildings to shock which continues in their structure and is perceived by the people living in them as noticeable vibrations or noise. In this context, polyurethane (PUR) foams, which have been developed to isolate vibrations, have shown to be very effective in practical use. However, whereas static properties of open‐cell structures have already been determined numerically in good agreement to experimental results, cf. [1], there are hardly any investigations on the dynamical properties characterizing acoustic damping.In order to validate experimental measurements of eigenfrequencies for different PUR foam specimen we present here a strategy to reproduce the foam behavior numerically. In doing so, PUR foams are modeled using a three dimensional Voronoi‐tessellation technique. The resulting Voronoi cells correspond to open pores and are scaled in such a way that the volume ratio between the pores and material matches the given PUR foam. For finite element analysis the connections between the cells are modeled as beam elements, the beam shape follows Bezièr curves. The generated model is analyzed with a finite element software and the dynamical parameters are determined. The numerical results are compared to our experimental data. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Comparison of Modal Analysis Using FEM and Eigenfrequency Measurements

In ultrasonic testing the vibration spectrum must be understood and the measured frequency peaks should match specific sample characteristics. In this paper, the experimental data are compared with results obtained using modal analysis based on Finite Element Method and the vibration was also calculated using classical Euler-Bernoulli approach, which is very simple but somewhat limited. The specimen geometry as well as the material of choice are both very simple to predict, model and measure - i.e. round cross section metal rod. In this case the FEM gives slightly better result that the simplified analytical calculation.

Some problems of nanomechanics

The paper presents a selection of simulation results obtained for nanosized objects in continuum and structural mechanics. Eigenfrequency measurements as a tool to study nanostructures composed of a multitude of like nanoelements are discussed. The structures under consideration are ordered arrays of nanoobjects (nanocrystals, nanoshells) fixed on an elastic substrate. It is shown that from the eigenfrequency spectrum of this type of mechanical systems one can determine several eigenfrequencies of a single nanoobject. Also considered in the paper is accounting for surface stress and associated modification of effective properties of nanomaterials.

Recent developments in the dynamic analysis of water turbines

This article gives an overview of the current methods for life cycle analysis with special emphasis on dynamic load analysis. Recent developments in CFD simulations of time-dependent phenomena are presented, such as the von Kármán vortex shedding at stay vanes in a Kaplan turbine and the part load vortex in the draft tube of a Francis turbine and a pump turbine. A major topic of this article is the unsteady pressure field in a pump turbine, which is caused by the interaction of guide vanes and runner blades. CFD results of the pressure pulsations and their validation through comparison with measurement data are presented. It is shown how the predicted time-dependent pressure load is transferred as input to the structural analysis of the runner. For the analysis of the response of the runner to the dynamic load knowledge of the natural frequencies of the structure is required including the influence of the surrounding water on the natural frequencies. New results of the prediction of the natural frequencies of a Francis runner including the added mass effect due to the surrounding water are presented. For Pelton runners the state-of-the-art of measurement of eigenfrequencies and detuning are discussed along with the potential improvements due to the new simulation methods.

Coupled horizontal and vertical bending vibrations of a stationary shaft with two cracks

This paper investigates the coupled bending vibrations of a stationary shaft with two cracks. It is known from the literature that, when a crack exists in a shaft, the bending, torsional, and longitudinal vibrations are coupled. This study focuses on the horizontal and vertical planes of a cracked shaft, whose bending vibrations are caused by a vertical excitation, in the clamped end of the model. When the crack orientations are not symmetrical to the vertical plane, a response in the horizontal plane is observed due to the presence of the cracks. The crack orientation is defined by the rotational angle of the crack, a parameter which affects the horizontal response. When more cracks appear in a shaft, then the coupling becomes stronger or weaker depending on the relative crack orientations. It is shown that a double peak appears in the vibration spectrum of a cracked or multi-cracked shaft. Modeling the crack in the traditional manner, as a spring, yields analytical results for the horizontal response as a function of the rotational angle and the depths of the two cracks. A 2×2 compliance matrix, containing two non-diagonal terms (those responsible for the coupling) serves to model the crack. Using the Euler–Bernoulli beam theory, the equations for the natural frequencies and the coupled response of the shaft are defined. The experimental coupled response and eigenfrequency measurements for the corresponding planes are presented. The double peak was also experimentally observed.

Detection of Damage to Frame Structures from Changes in Eigenfrequencies

Based on its effect on the normal modes of a structure, a method for damage detection is proposed. The method uses frequency measurements before and after damage to locate the damage and estimate its severity in shear buildings. Numerical simulation is performed of a 10-story shear building, with different cases including complete eigenfrequency measurements, incomplete frequency measurements, and differing measurement noise levels. The method is further evaluated by vibration tests of two frame models. Numerical simulation and experimental verification clearly show that, for shear buildings, damage severity and locations can be accurately inferred using the present method.

Vibration of beams with multiple open cracks subjected to axial force

A new method is proposed to obtain the eigenfrequencies and mode shapes of beams containing multiple cracks and subjected to axial force. Cracks are assumed to introduce local flexibility changes and are modeled as rotational springs. The method uses one set of end conditions as initial parameters for determining the mode shape functions. Satisfying the continuity and jump conditions at crack locations, mode shape functions of the remaining parts are determined. Other set of boundary conditions yields a second-order determinant that needs to be solved for its roots. As the static case is approached, the roots of the characteristic equation give the buckling load of the structure. The proposed method is compared against the results predicted by finite element analysis. Good agreement is observed between the proposed approach and finite element results. A parametric study is conducted in order to investigate the effect of cracks and axial force levels on the eigenfrequencies. Both simply supported and cantilever beam-columns are considered. It is found that eigenfrequencies are strongly affected by crack locations, severities and axial force levels. Simple modifications to account for flexible intermediate supports are presented as well. The proposed method can efficiently be used in detecting crack locations, severities and axial forces in beam-columns. Furthermore it can be used to predict the critical load of damaged structures based on eigenfrequency measurements.

Structural identification of a steel frame from dynamic test-data

Structural identification via modal analysis in structural mechanics is gaining popularity in recent years, despite conceptual difficulties connected with its use. This paper is devoted to illustrate both the capabilities and the indeterminacy characterizing structural identification problems even in quite simple instances, as well as the cautions that should be accordingly adopted. In particular, we discuss an application of an identification technique of variational type, based on the measurement of eigenfrequencies and mode shapes, to a steel frame with friction joints under various assembling conditions. Experience has suggested, so as to restrict the indeterminacy frequently affecting identification issues, having resort to all the a priori acknowledged information on the system, to the symmetry and presence of structural elements with equal stiffness, to mention one example, and mindfully selecting the parameters to be identified. In addition, considering that the identification techniques have a local character and correspond to the updating of a preliminary model of the structure, it is important that the analytical model on the first attempt should be adequately accurate. Secondly, it has proved determinant to cross the results of the dynamic identification with tests of other typology, for instance, static tests, so as to fully understand the structural behavior and avoid the indeterminacy due to the nonuniqueness of the inverse problem.

Crack identification in frame structures

In this paper the problem of crack depth and position identification in frame structures is examined, using eigenfrequency measurements. It has been established that a crack has an important effect on the dynamic behavior of a structure. This effect depends mainly on the crack size and position. The basic idea is to present in contour graph form the dependency of the first two structural eigenfrequencies on crack depth and location, using the finite element method. To identify the location and depth of a crack in a frame structure, one only needs to determine the intersecting point of the superposed contours that correspond to the measured eigenfrequency variations caused by the crack presence. A number of beam and frame examples are included in the present paper to verify the applicability of this combined computational-graphical or experimental-graphical method.

Low-$\ell$p-mode solar eigenfrequency measurements from the Birmingham Network

We present here the results of observations of oscillations of the Sun over a period of eight years from 1981

Eigenvibrations of the Earth observed at Trieste

Summary Earth oscillations which followed the Chilean earthquake of 1960, May 22, have been clearly recorded by a sensitive tiltmeter situated in the Grotta Gigante near Trieste. An analysis of 85 hours of the N-S record has resolved the frequency spectrum in the frequency range 0.02 cycles per minute to 0.20 cycles per minute into a series of discrete peaks, most of which are highly significant at the 95 per cent confidence level. Comparison with other recent observations of free oscillations, as well as with theoretical values, leads to the identification of a complete sequence of 23 fundamental torsional eigenfrequencies (2 ≤ 1 ≤ 24); on removal of the main semidiurnal tides there is an indication that the four lowest fundamental spheroidal modes were also recorded. The tiltmeter and the method of analysis are described. For the 15 torsional modes with 10 ≤ 1 ≤ 24, application of a statistical t-test to squared deviations between the observed periods and theoretical periods for Earth models with (a) J. B. shear velocities and Bullen B densities, and (b) Gutenberg shear velocities and Bullen A densities, indicates that the latter model gives significantly better agreement with the Trieste data. The reported measurements of eigenfrequencies allow an important comparison with earlier measurements made at stations on the American continent.