Predicted Resonance Frequencies Research Articles

Numerical and experimental investigation of delamination severity estimation using local vibration techniques

This paper presents vibration-based methods for detecting and quantifying delaminations in composite structures. Three different delamination sizes were considered numerically and experimentally. Our approach combines and compares finite element method (FEM) numerical analysis and experimental measurements to find the location of structural delaminations and identify their severity. First, we noticed that a low-frequency modal study comparing pristine and damaged plates could not provide local damage information. Hence, a high frequency-modal analysis was performed to obtain the local damage information. The damaged mode shapes corresponding to resonance frequencies that cause significant local vibration (high amplitude) over the damaged regions were calculated numerically. The result shows the capability of damage identification (location and size of structural delaminations) within the high-frequency modal analysis. The numerical results were validated experimentally. The experiments include electromechanical impedance spectroscopy (EMIS) and scanning laser Doppler vibrometer (SLDV) techniques. The EMIS experiment was implemented to predict the resonance frequencies which cause significant local vibration over the delamination regions. The spectra of the electromechanical response resemble the vibration response of the structure and detect the new resonances created by the presence of the delamination. The test plate’s experimental resonance peaks show a good match with the resonance frequencies of the numerical modal analysis. The SLDV experiments measured the local vibration over the investigated scanning areas. The operational vibration shapes corresponding to predicted resonance frequencies were created. These experimental mode shapes may visually measure the delaminations by observing intense local vibration over the delamination zones. Comparing the numerical mode shapes and the operational vibration shapes shows a good match between numerical and experimental results.

On using nonlinear wave interactions in multi-directional seas for energy conversion on the ocean floor

This paper investigates possible utilization of energy in interacting surface waves on the seafloor. Theory suggests that resonant wave interactions in confused open seas can cause energetic downward traveling second-order pressure waves, which during stormy conditions can be large enough to excite seafloor microseisms (Longuet-Higgins, 1950). Our analysis of contemporaneous data from seafloor pressure and velocity sensors from an Ocean Observatories Initiative (OOI) installation in the Northern Pacific and collocated surface-wave hindcasts showed evidence of the theoretically predicted vertical resonances (Longuet-Higgins, 1950). We observed that area-averaged predicted dynamic pressures and particle velocities 200 m below the water surface and their measured counterparts 2.6 km below at the seafloor were well correlated at the predicted resonance frequencies. Our results further revealed occurrence of net vertical power transfer at resonance from surface to seafloor by means of the predicted double-frequency pressure waves. Motivated by these findings, we estimated year-long seafloor power availability at five selected deep-sea locations. Next, we evaluated upper bounds on potentially convertible area averaged yearly-mean power amounts by a small flexible sphere type device at the seafloor. At ∼400 mW m−2 to ∼15 Wm−2, these power levels could assist sensor operations on and from the deep ocean floor.

Effect of Grain Refinement on the Dynamic, Mechanical Properties, and Corrosion Behaviour of Al-Mg Alloy

In this investigation, aluminium Al-2.5% Mg cast alloy was modified by adding 0.5 Ti and 0.1 B wt % modifiers to investigate their impact on the dynamic behaviour, as well as the mechanical and microstructure properties. The dynamic properties were analysed experimentally using a free vibration impact test and predicted using finite element methods. This study used a high-resolution polarised optical microscope to analyse the microstructure of the studied alloys and X-ray Powder Diffraction (XRD) analysis to determine the developed phases. Microstructure and mechanical properties were mostly enhanced as a result of grain refining during solidification and through the metal segregation process. The microstructure analysis of the modified alloy showed a significant improvement in the grain refinement; hence, the grains were 10 times finer than the cast alloy. The modified Al-2.5% Mg/Ti-B alloy demonstrated reduced inter-granular corrosion (IGC) than the Al-2.5% Mg standard cast alloy. By incorporating Ti-B modifiers into the composition of the cast Al-Mg alloy, the ultimate tensile strength (UTS), strain (ε), and hardness values (HV) were increased by 30.5%, 100%, and 18.18%, respectively. The dynamic properties of the modified alloy showed an enhancement in the resonant (fn) and damping ratio (ζ) by 7% and 68%, respectively. The predicted resonance frequencies of the investigated alloys showed results close to the experimental dynamic tests.

The stress and strain analysis double-layer and eight-leaf backward curved impeller disc agitator

The mixing wing’s stress and strain value of the structure in the mixing equipment needs to be studied and discussed. The research is uses the FLUENT module to simulate the flow field state in the rotating operation of the mixing tank, the stress and strain of the mixing blade, and the modal analysis of the predicted resonance frequency. First, Fluent is uses simulate the shape of the flow field inside the stirred tank. Situation of different speeds, the deformation state of the stress, strain and total displacement of the stirring wing assembly is obtained to achieve the ANSYS fluid-solid coupling effect analysis. Finally, predict the modal appearance and failure points of the simulated stirring wing assembly at different resonance frequencies. After analysis, the rotation speed of the stirring wing is increases, it must be subjected to the centrifugal force of fluid distribution, vortex gravitation, and up and down convection agitation. The total displacement and deformation of the rigid structure of the stirring wing can be obtained. The equivalent stress and strain also adopt a progressive linear growth phenomenon.

Deep learning for both broadband prediction of the radiated emission from heatsinks and heatsink optimization

Heatsinks have quasi-antenna behavior in many cases and cause interference both at the system level and at the PCB design level. Therefore, determination or prediction of both resonance frequencies and maximum radiated emission are crucial at any design step. In this paper, as a novelty, in 2–8 GHz band, a model based on deep learning is developed to predict resonance frequencies in parallel plate-fin type heatsinks. Parameters taken into account are the number of fins, the width, length, and height of the heatsinks. 3888 heatsinks with different sizes are modeled to prepare data set and the Grey Wolf Optimizer algorithm (GWO) is utilized to optimize the heatsink parameters. Consequently, while this model obtains outputs for certain inputs, the optimization algorithm procures certain inputs for these outputs. Furthermore, the predicted and optimized results are compared with the simulation and measurement results. The proposed model successfully works according to the measurement and the proposed model results since R2 values are 0.96, 0.98, 0.97, and 0.99 for f1,f2,REmax1, and REmax2, respectively. The results are good agreement and R-squared values of resonances (f1,f2) and the maximum radiated emissions (REmax1,REmax2) are quite acceptable considering the sophisticate of the proposed model.

Prediction of resonant frequencies of a dual-wavelength plasmonic perfect absorber as a sensor by resistor–inductor–capacitor circuit models

A plasmonic perfect absorber (PPA) based on a metal–insulator–metal–insulator–metal structure has been designed for refractive index sensing of glucose solutions (analyte). Then resistor–inductor–capacitor equivalent circuit models based on dimensions, the position of the components, and materials used in the structure have been developed to predict resonance frequencies of the absorber. Simulation results show that in the perpendicular incidence of a plane wave of light within 5 to 9 μm wavelengths, for the analyte placed over sensor surface with a refractive index of n = 1.312; the output absorption spectrum of the device has two resonance peaks, respectively, on λ1 = 6441.01 nm and λ2 = 7909.74 nm wavelengths. When the refractive index of analyte increases to n = 1.384, both resonant peaks are red shifted. Sensitivities (S = Δλ / Δn) of the first and second resonance peaks have been obtained as S1 = 1287.083 nm / RIU and S2 = 1142.5 nm / RIU, respectively.

Validation of CFD analysis of acoustic effects in pump-turbine runners

Rotor-stator interaction is the main cause of harmonic pressure pulsations and resulting dynamic stresses in pump-turbine runners in normal operation. Considering the guide vane passing excitation frequency and the channel length of pump-turbine runners, it shows that compressible effects in the runner channels need to be taken into account for pump-turbines in the medium to high head range. This affects the choice of blade number combinations, the assessment of pressure pulsations and resulting dynamic stresses in components. The compressible effects are primarily linked to the propagation of pressure waves at a finite speed of sound in water. A lower effective wave propagation velocity is sometimes considered to reduce complex fluid-structure interaction effects into simpler pure acoustic problems. In state of the art computational fluid dynamics (CFD) software, using compressible fluid properties allows to reproduce compressibility effects and to combine them with physically accurate transient rotor-stator modelling by sliding interface techniques. The relative motion of the guide vane cascade and the runner is resulting in a periodic variation of the outer channel ends geometry and is also the source of excitation; both effects are thus included in the model which could not be achieved by modal analysis using finite elements. This paper presents the assessment of the prediction capabilities of CFD simulations using commercial software against an experiment carried out on a pump-turbine reduced scale model using air at ambient conditions as a working medium. Using air allows separating the acoustic problem from fluid-structure interaction effects that are not covered in this comparison, and that are intrinsically hard to transpose from model to prototype. The analysis of results focusses on the predicted resonance frequency; its dependency on time step size and number of inner coefficient loops is shown as well as the influence of different model extent and spatial discretization.

FE-BE computation of electromagnetic noise of a permanent-magnetic excited synchronous ma-chine considering dynamic rotor eccentricity

Electromagnetic noise in Electrical Machines (EMs) occurs due to vibrations caused by magnetic forces acting onto rotor and stator surface. This is the dominant source for the considered permanent-magnetic excited synchronous machine in this paper. The radiated electromagnetic noise is sequentially calculated by a Finite Element (FE) and Boundary Element (BE) computation. An electromagnetic FE model is created to determine magnetic forces. Structure-borne sound and rotor dynamics are calculated using a structural dynamic FE model for the EM housing and the rotor. In order to predict resonance frequencies and amplitudes as reliable as possible, it is important to know the direction-dependent stiffness of the laminated rotor stacks and mechanical joints as well as their structural damping. Thereby, the properties of the laminated stack can be determined experimentally by a shear and dilatation test. Mechanical joint properties can be modelled by Thin-Layer Elements (TLEs) and the overall damping by the model of constant hysteretic damping. The radiated sound power is determined by a direct BE computation. The influence of dynamic rotor eccentricity on radiated sound power is examined for a run-up of the EM. All FE models are verified by data from experimental modal analysis.

Size-dependent effects of surface stress on resonance behavior of microcantilever-based sensors

The mass and surface stress loadings in microcantilever-based sensors, caused by surface adsorption of target analytes/biomolecules, change their resonance behavior. Despite numerous efforts, the mechanisms of surface stress impact on the resonance behavior of microcantilevers are not fully understood. This results in substantial discrepancies between theoretically predicted and experimentally measured resonance frequency shifts in wide microcantilevers with aspect ratios (width-to-thickness) larger than 10, commonly found in chemical and biological sensing applications. This also impedes the proper decoupling of the effects of mass and surface stress loading and hinders the development of accurate microcantilever-based sensors. In this work, we attempt to decrease the discrepancy found between theoretical models and experiments by introducing a new mechanism that correlates the nonlinear geometric effects associated with surface stress-induced variation of microcantilever biaxial curvature to its frequency and modal responses, with a correlation intensity that strongly depends on the microcantilever aspect ratio. A new comprehensive analytical model combining the new mechanism with currently available theoretical models is proposed and used to study the resonance behavior of microcantilevers with different deformations and sizes. Using the new model, it is shown that in wide microcantilevers, the theoretically predicted resonance frequency shifts agree with experimental and finite element simulations results within 30% whereas the predictions by other currently available theoretical models are off by more than one order of magnitude. The new model is also used to investigate the modal response of microcantilevers where it anticipates the bending-extensional mode coupling associated with the flexural vibration modes of microcantilevers with a coupling strength that depends on the microcantilever curvature. The presented model is expected to provide a new tool to decouple the effects of mass and surface stress loadings on the resonance behavior of microcantilevers used in chemical and biological sensors.

Modes of vibration of a sheng reed

The sheng is an Asian mouth organ consisting of a number of bamboo pipes enclosed in a wind chamber with brass free reeds at the end of each pipe inside the chamber. The reed in each pipe typically includes a small wax tuning weight near the free end of the reed tongue. The determination of modes of vibration of these reeds, especially how the tuning weight changes those modes of vibration, is the topic of this paper. Recent research has investigated the acoustics of sheng pipes and compared the measured impedance of sheng pipes augmented with pipe resonators with a theoretical model. This research employs finite element analysis software to construct a theoretical model of sheng reeds and compare that model with measured vibrational analysis data gathered with a laser vibrometer. The primary emphasis is on how well the predicted resonance frequencies compare with measured resonance frequencies of the reed as indicated in a response curve. Also compared are the predicted nodal and antinodal positions alon...

Resonance Frequency Calculation of Long-Neck Cylindrical Acoustic Resonators

This paper presents a general model to predict resonance frequencies for long-neck cylindrical acoustic resonators. The predicted resonance frequencies by the proposed model are compared with those measured and calculated by Panton and Millers model. It is found that the model developed in this paper can give more accurate resonance frequencies for both the first and higher modes, while the Panton and Millers model can only accurately predict the first-order frequency, and up to 4% error is observed in the predicted higher-order resonance frequencies, mainly induced by the lumped-mass simplification.

Study on Moonpool Resonance Effect on Motion of Modern Compact Drillship

A drillship is a representative floating offshore installation. The boom in oil and gas field development has dramatically increased the demands for drillships. Drillships have a moonpool in the center area of the ship for the purpose of drilling. This moonpool has an effect on the seakeeping performance of a drillship in the vicinity of the resonance frequency. Because of the moonpool, drillships act in different resonance modes, called the sloshing mode and piston mode. The objective of this study was to find the moonpool effect on the motion of a drillship through the motion analysis of a currently operating modern compact drillship. The predicted resonance frequencies based on Molin's theoretical formula, Fukuda's empirical formula, and BEM-based numerical analysis are compared. The accuracy of the predictions using the theoretical and empirical formulas is compared with the numerical analysis and evaluated. In the case of the piston mode, the difference between the resonance frequency from theoretical formula and the resonance frequency from the numerical analysis is analyzed. The resonance frequency formula for more a complex moonpool geometry such as a moonpool with a cofferdam is necessarily emphasized.

Numerical simulation of drop oscillation in AC electrowetting

In this paper, a “macroscopic-scale” numerical method for drop oscillation in AC electrowetting is presented. The method is based on a high-fidelity moving mesh interface tracking (MMIT) approach and a “microscopic model” for the moving contact line. The contact line model developed by Ren et al. [Phys Fluids, 2010, 22: 102103] is used in the simulation. To determine the slip length in this model, we propose a calibration procedure using the experimental data of drop spreading in DC electrowetting. In the simulation, the frequency of input AC voltage varies in a certain range while the root-mean-square value remains fixed. The numerical simulation is validated against the experiment and it shows that the predicted resonance frequencies for different oscillation modes agree reasonably well with the experiment. The origins of discrepancy between simulation and experiment are analyzed in the paper. Further investigation is also conducted by including the contact angle hysteresis into the contact line model to account for the “stick-slip” behavior. A noticeable improvement on the prediction of resonance frequencies is achieved by using the hysteresis model.

Models of cylindrical bubble pulsation

Three models are considered for describing the dynamics of a pulsating cylindrical bubble. A linear solution is derived for a cylindrical bubble in an infinite compressible liquid. The solution accounts for losses due to viscosity, heat conduction, and acoustic radiation. It reveals that radiation is the dominant loss mechanism, and that it is 22 times greater than for a spherical bubble of the same radius. The predicted resonance frequency provides a basis of comparison for limiting forms of other models. The second model considered is a commonly used equation in Rayleigh-Plesset form that requires an incompressible liquid to be finite in extent in order for bubble pulsation to occur. The radial extent of the liquid becomes a fitting parameter, and it is found that considerably different values of the parameter are required for modeling inertial motion versus acoustical oscillations. The third model was developed by V. K. Kedrinskii [Hydrodynamics of Explosion (Springer, New York, 2005), pp. 23-26] in the form of the Gilmore equation for compressible liquids of infinite extent. While the correct resonance frequency and loss factor are not recovered from this model in the linear approximation, it provides reasonable agreement with observations of inertial motion.

Flexural resonance vibrations of piezoelectric ceramic tubes in Besocke-style scanners

Flexural resonance vibrations of piezoelectric ceramic tubes in Besocke-style scanners with nanometer resolution are studied by using an electro-mechanical coupling Timoshenko beam model. Meanwhile, the effects of friction, the first moment, and moment of inertia induced by mass loads are considered. The predicted resonance frequencies of the ceramic tubes are sensitive to not only the mechanical parameters of the scanners, but also the friction acting on the attached shaking ball and corresponding bending moment on the tubes. The theoretical results are in excellent agreement with the related experimental measurements. This model and corresponding results are applicable for optimizing the structures and performances of the scanners.

Resonance magnetoelectric effects in disk-ring (piezoelectric - magnetostrictive) composite structure

The magnetoelectric effects in piezoelectric-disk/magnetostrictive-ring (PE-disk/MS-ring) structure at electromechanical resonance (EMR), where the magnetostrictive and piezoelectric phase are coupled through normal stresses, are modeled. The predicted resonance frequency and the frequency dependence of the magnetoelectric (ME) voltage coefficient are in good agreement with the data for the PZT (Pb(Zr0.52Ti0.48)O3) –disk/CFO(CoFe2O4) -ring. The improved interfacial mechanical coupling through normal stresses is responsible for the enhanced magnetoelectric properties of the disk-ring structure. It is suggested that proper frequency and stronger ME effect in the disk-ring structure can be obtained by optimizing the structure. The ME effect in the disk-ring structure shows promising application in transducers for magnetoelectric energy conversion.

Finite element model updating of vibrating structures under free–free boundary conditions for modal damping prediction

A method to predict resonance frequencies and modal loss factors of bare and damped samples, using constrained layer damping treatment, under free–free boundary conditions is proposed. In a first phase, measurements of the frequency response functions of these two specimens are performed. In a second phase, a finite element model of the undamped sample is developed. The novelty lies in the consistent modelling of the suspension with spring–damper elements defined with stiffness and damping coefficients with fixed values over the whole considered frequency range. By updating these, the agreement between experiments and simulation is further improved. In a third phase, a finite element model of the damped sample, with constrained layer damping material, is realized. A good agreement with experimental results is obtained thanks to an optimization algorithm used to determine the material parameters of the viscoelastic layer at various frequency. A comparison with experimental results, from a Dynamic Mechanical Analysis, confirms the consistency of the results from the optimization process.

Design of monofilar and bifilar Archimedean spiral resonators for metamaterial applications

Archimedean spiral resonators as the unit inclusion for a metamaterial structure is studied. These inclusions are very compact, which make them a good candidate for practical metamaterial applications. Equivalent circuit models and analytical design formulas are derived for monofilar and bifilar spiral resonators. The circuit parameters and resonance frequencies are directly predicted by the geometry of the spiral and dielectric substrate/resonator configuration. Numerical simulations on both bulk and planar designs show that the predicted resonance frequencies are accurate enough for a preliminary design. Finally, complementary spiral structures, that is, spiral-shaped apertures in the ground plane, are considered. Loading two transmission lines with a complementary monofilar and a complementary bifilar spiral resonator, two planar band rejection structures are built. Measured results for two prototypes present a good accuracy.

Modeling and design of composite free–free beam piezoelectric resonators

A model is presented and experimentally validated for the design of asymmetrically layered piezoelectric free–free beam micromechanical resonators. The thin film resonators are composed of quad-symmetric torsional anchors connected to the nodal points of a free–free beam vibrating in its fundamental bending mode. The model provides analytical approximations for the resonance frequencies of the composite anchors and the free–free beam. Since dissipation in these devices is minimized when the mechanical impedances of the coupled structures are matched at resonance, i.e. when bending beam and torsional anchor resonance frequencies are equal, the model may be used to design resonators with optimized mechanical quality factors. The model is shown to successfully predict resonance frequencies in agreement with the results of finite element analysis and experimental results obtained for multi-layered lead zirconate titanate (PZT) piezoelectric microresonators with first natural frequencies in the range of 448 kHz to 1.1 MHz. The model is also validated as a tool for optimizing resonator quality factor.

Oscillatory limited compressible fluid flow induced by the radial motion of a thick-walled piezoelectric tube.

A simple oscillatory, slightly compressible, fluid flow model in a thick-walled piezoelectric tube used in a drop-on-demand inkjet print head is developed from the point of view of fluid-structure interaction to take account of pressure wave propagation and pressure loading opposing wall motion. A frequency sweep is performed computationally using the model revealing the first acoustic fluid-structure resonance frequency and the influence of fluid viscosity. The validity of the model, with given information on the speed of sound in a fluid, is evaluated by comparing the theoretically predicted resonance frequency to the experimentally measured resonance frequency. In addition, the intrinsic speed of sound can be easily computed using the measured acoustic resonance frequency and this computed speed of sound agrees closely with speeds of sound reported in the literature.