Frequency Sensitivity Analysis Research Articles

On sensitivity analysis of the fundamental frequency of cracked fiber metal laminated (FML) beams using experimental survey and finite element method

PurposeIn this research, the free vibration sensitivity analysis of cracked fiber metal laminated (FML) beams is investigated numerically and experimentally. The effects of single and double cracks on the frequency of the cantilever beams are simulated using the finite element method (FEM) and compared to the experimental results.Design/methodology/approachIn FEM analysis, the crack defect is simulated by the contour integral technique without considering the crack growth. The specimens are fabricated with an aluminum sheet, woven carbon fiber and epoxy resin. The FML specimens are constructed by bonding five layers as [carbon fiber-epoxy/Al/carbon fiber-epoxy/Al/carbon fiber-epoxy]. First, the location and length of cracks are considered input factors for the frequency sensitivity analysis. Then, the design of the experiment is produced in the cases of single and double cracks to compute the frequency of the beams in the first and second modes using the FEM. The mechanical shaker is used to determine the natural frequency of the specimens. In addition, the predicted response values of the frequency for the beam are used to compare with the experimental results.FindingsConsequently, the results of the sensitivity analysis demonstrate that the location and length of the crack have significant effects on the modes.Originality/valueEffective interaction diagrams are introduced to investigate crack detection for input factors, including the location and length of cracks in the cases of single and double cracks.

Design sensitivity analysis of modal frequencies of elastic structures submerged in an infinite fluid domain

SummaryThis paper presents a numerical approach for the design sensitivity analysis of modal frequencies of elastic structures submerged in an unbounded heavy fluid domain. Because the feedback of sound pressure onto the fluid‐loaded structures has to be taken into account in this case, a fully coupled scheme which combines the structural finite element method (FEM) and the acoustic boundary element method (BEM) is employed in the numerical simulation. The resulting nonlinear eigenvalue problem created by the coupled finite element and boundary element (FE‐BE) method is converted into a generalized eigenvalue problem (GEP) of reduced dimension by using a contour integral method. The design sensitivity formulation for non‐repeated eigenvalues is derived based on an adjoint method which uses both the left and right eigenvectors, and a small GEP is formed to calculate the gradients of repeated eigenvalues. The Burton‐Miller formulation is employed to shift the fictitious eigenfrequencies and their derivatives, and the parameter setting which is beneficial to the filtering of fictitious eigenfrequencies is investigated. Numerical examples are given to verify the accuracy and effectiveness of the developed method.

Dynamic Electrical Circuit Modeling of a Proton Exchange Membrane Electrolyzer for Frequency Stability, Resiliency, and Sensitivity Analysis in a Power Grid

Dynamic Electrical Circuit Modeling of a Proton Exchange Membrane Electrolyzer for Frequency Stability, Resiliency, and Sensitivity Analysis in a Power Grid

Frequency Sensitivity Analysis of Coil-IDE Resonance Topology Circuit and Its Humidity Sensor Applications

In this paper, the frequency sensitivity of Coil-IDE (interdigital electrode) sensor in different integrated topology is studied. In particular, the expression of resonance frequency of the Coil-IDE sensor both in series and parallel topological structure is derived. The sensitivity of frequency to IDE capacitance was analyzed, and two new results can be found: (i) Due to the existence of coil winding capacitance and grounding capacitance, Coil-IDE topology circuit has been changed which cause the Coil-IDE parallel topology structure has the higher frequency sensitivity than series; (ii) Not only the topology structure but also the parameters such as coil inductance and IDE capacitance have the regulatory effect on the frequency sensitivity. After analysis, an experiment of Coil-IDE humidity sensor was applied to verify the presented results. The parallel frequency of the Coil-IDE parallel structure has the higher sensitivity was confirmed. The error of the proposed formula predicting the regulatory effect of parameters on frequency sensitivity was discussed. The error is as low as 7.57%, which shows the beneficial to the integrated design of Coil-IDE sensor both in topological structure and parameters.

Free Vibration of Rectangular Composite Cantilever Plate and Its Application in Material Degradation Assessment

Many composite cantilever plate-like structures have found engineering applications in different industries. For attaining a meaningful assessment of the plate vibration characteristics, it is important to have efficient and effective methods for determining the natural frequencies/mode shapes of composite cantilever plates. In this paper, a method formulated on the basis of the Ritz method and a simple first-order shear deformation theory (SFSDT) is presented to analyze the free vibration of thin as well as thick rectangular composite cantilever plates for determining their natural frequencies. In the SFSDT, the total deflection is the sum of two deflection components, namely, bending and through-thickness shear-deformation-induced deflections. The successful application of the Ritz method together with the SFSDT for the free vibration analysis of thick composite plates relies on the selection of two independent sets of characteristic functions for the bending and through-thickness shear-deformation-induced deflections, respectively, to satisfy the requirements for the displacement and force conditions at the fixed edge of the plate. The novelty of the proposed method is that two independent sets of characteristic functions, namely, polynomials and trigonometric functions, which satisfy the displacement and force conditions at the fixed edge have been identified and used in the variational method to construct the eigenvalue problem for extracting the modal characteristics (natural frequencies and mode shapes) of the plate. It has been shown that the uses of the selected characteristic functions can produce excellent natural frequencies for both thin and thick composite cantilever plates. Some existing theoretical and experimental natural frequencies of thin as well as thick composite plates have been used to demonstrate the accuracy of the proposed method in predicting natural frequencies. The significant effects of through-thickness shear deformation on the natural frequencies of composite cantilever plates are studied to show the merit of the present method. Finally, for illustrating the application of the proposed method in free vibration analysis, a novel procedure established on the basis of the sensitivity analysis of natural frequencies is presented to assess the material degradation of composite cantilever plates. The numerical examples have shown that fewer than 10 iterations are required in the identification process to produce a good estimation of the current value for each material constant.

RF design and frequency sensitivity analysis of a 1500 MHz passive third harmonic superconducting cavity for the SILF

To reduce Touschek scattering in the beam and extend the lifetime of the beam in the Shenzhen Innovation Light-source Facility (a fourth-generation light source), a 1500 MHz passive third harmonic system will be used. The present work is devoted to the RF design and frequency sensitivity analysis of the 1500 MHz passive third harmonic superconducting cavity, optimizing the RF parameters of the cavity, and giving a frequency scheme for the cavity in fabrication. The reliability of the cavity during operation is taken as the main goal for the optimization of the geometrical parameters, and its structural and RF parameters are obtained with E peak/E acc of 2.17, B peak/E acc of 5.12 mT/(MV/m) and G · R/Q of 25052 at 2 K. A pair of fluted beam pipes are used to propagate the higher order modes (HOMs) of the harmonic cavity, allowing a smooth transition of the first dipole mode to the absorber located at room temperature area. For the frequency sensitivity analysis, the frequency variations of the cavity in fabrication are obtained by multi-physics coupling simulation in the paper, which gives the target frequency of the cavity between welding and preloading. After electron beam welding (EBW), the resonant frequency of the cavity should be maintained at 1500.096 MHz, and the pre-tuning target frequency is 1497.456 MHz. The slow tuning range is ±400 kHz, the fast-tuning range is 600 Hz, and the maximum allowable tuning force is 15 kN.

Fabrication and characterization of a tiny PZT thick-film longitudinal-bending coupled drive vibrator using electrohydrodynamic jet printing

This paper describes a fabrication method of a novel type of micro piezoelectric thick-film longitudinal-bending coupled (LBC) vibrator with a length of 8 mm and thickness of 0.34 mm using electrohydrodynamic jet (E-jet) printing. The LBC micro-vibrator was designed, and a frequency sensitivity analysis of the structural parameters was implemented. When the thickness of the lead zirconate titanate (PZT) thick-film element of the vibrator reached 76 μm, tuning of the composite-mode frequency consistency could be achieved. The micro-vibrator was then fabricated by depositing the PZT thick film directly on the surface of the elastic body using E-jet printing, and the film thickness was flexibly adjusted by tuning the number of prints, thus avoiding the problems of insufficient PZT thin film thickness (≤1 μm) and excessive bulk PZT ceramic volume. Micro-morphological observations showed that the printed thick film was dense and smooth, with a thickness of approximately 76 μm. Furthermore, the vibration mode frequency of the vibrator differed from the test resonant frequencies by only 0.92%, and the vibrator could achieve driving motion with a volume and an excitation voltage approximately one-tenth of that of a bulk piezoelectric motor. Moreover, the unit power density was 0.36 W kg−1 V−1, which is 1.6 times higher than that of a large bulk piezoelectric motor, indicating that the vibrator has good potential for small-space and low-voltage applications.

Sensitivity Analysis and Robust Assignment of Natural Frequencies for Vibrating Systems Using the Receptance Method

This paper presents a new receptance-based method for the robust assignment of natural frequencies. This method aims to address the deviation of the actually achieved natural frequencies for target natural frequencies when assigning natural frequencies, which usually arises due to uncertainties in passive structural modifications (i.e. mass and stiffness modifications). The mathematical expression is derived for the sensitivity of the target natural frequency to the uncertainties in modification parameters, which are subsequently employed to characterize the potential deviations of the target natural frequencies in the total differential form. The obtained deviation expression is integrated into the optimization calculation of the natural frequency assignment as an extra penalty term to boost the acquisition of highly robust modification parameters. The proposed robust assignment method, as a non-probabilistic technique, can be employed without any knowledge of the probabilistic distribution of uncertainty in modification parameters. Moreover, it uses only the measured frequency response functions (FRFs), preserving the advantage of the receptance method not needing a numerical model. Two numerical examples and a comparison with a typical eigenstructure assignment method (reported in the literature) demonstrate that the proposed method can provide highly robust modification parameter solutions. The application of the proposed method to the natural frequency assignment of a laboratory water-filled pipeline system gives experimental evidence of its effectiveness.

On frequency response modeling of interconnected microgrids: Two different perspectives

This paper deals with the frequency response modeling of interconnected microgrids. The frequency response model is used for frequency and tie-line power control analysis and synthesis. The proposed frequency response model is obtained using two different perspectives: (1) based on frequency sensitivity analysis, (2) based on the inertia concept. Besides, the dynamic of back-to-back converters and controllable active power sources are also included to obtain a generalized frequency response model with desirable performance. Indeed, it can be observed that in the first method, some circuit parameters can be neglected in the frequency response model. This finding is effective in providing a more simplified model. In the second method, the frequency response model has been presented as an innovative approach. In a way, we have selected the nature of distributed generations as an indicator of source classification in the model. This model is also enhanced by considering the inertia dynamics and controllable power source and has a better performance to show the network status. Since the microgrid frequency response model only covers the low-frequency dynamics, the fast dynamics of inner control loops as well as the modulation units and sensors are not considered. The proposed frequency response model can be used for frequency stability analysis studies as well as frequency and tie-line power control analysis and synthesis. Comprehensive simulation studies are carried out using the MATLAB simulation environment to compare and evaluate the developed models. Further, the proposed models are verified via PSCAD/EMTDC, considering two microgrids interconnected through back-to-back converters. The results showed that the proposed models are suitable and efficient for frequency response studies.

Data-Driven Extraction of Uniformly Stable and Passive Parameterized Macromodels

A robust algorithm for the extraction of reduced-order behavioral models from sampled frequency responses is proposed. The system under investigation can be any Linear and Time Invariant structure, although the main emphasis is on devices that are relevant for Signal and Power Integrity and RF design, such as electrical interconnects and integrated passive components. We assume that the device under modeling is parameterized by one or more design variables, which can be related to geometry or materials. Therefore, we seek for multivariate macromodels that reproduce the dynamic behavior over a predefined frequency band, with an explicit embedded dependence of the model equations on these external parameters. Such parameterized macromodels may be used to construct component libraries and prove very useful in fast system-level numerical simulations in time or frequency domain, including optimization, what-if, and sensitivity analysis. The main novel contribution is the formulation of a finite set of convex constraints that are applied during model identification, which provide sufficient conditions for uniform model stability and passivity throughout the parameter space. Such constraints are characterized by an explicit control allowing for a trade-off between model accuracy and runtime, thanks to some special properties of Bernstein polynomials. In summary, we propose a method to systematically address the longstanding problem of multivariate stability and passivity enforcement in data-driven model order reduction, which insofar has been tackled only via either over-conservative or heuristic and possibly unreliable methods.

Parameter identification of nonlinear structural systems through frequency response sensitivity analysis

Nonlinearity is ubiquitously encountered in structural systems, and it may have a great and complicated influence on the dynamic behaviours, including bifurcation, internal resonance, load history dependence, etc. Identifying the nonlinear system parameters is essential for analysis and design of the structure. To this end, a new approach is developed in this paper for nonlinear system parameter identification from frequency response sensitivity analysis. At first, the harmonic balance equation is established to govern the frequency response of the nonlinear system, upon which the frequency response and sensitivity analysis can be conducted. A remarkable feature is that the harmonic balance equation is algebraic so that the sensitivity analysis, pertaining to a linearized equation, is rather simple and straightforward. Then, parameter identification is modelled as a nonlinear least-squares problem, and the sensitivity approach is adopted in conjunction with the trust-region constraint for convergent solution. Numerical examples are conducted to demonstrate the feasibility and performance of the proposed approach.

Mechanical Analysis and Experimental Research on Ultrasonic Levitated Conical Rotor Piezoelectric Actuator

This work presents a novel conical rotor non-contact piezoelectric actuator based on the principle of near-field acoustic levitation. The conical rotor is levitated and driven by a single stator, while generating two orthogonal standing waves and superimposing a travelling wave vibration on the stator. A frequency sensitivity analysis is conducted for the stator structural parameters, based on a dynamics calculation. An acoustic field simulation is conducted and the sound pressure distribution is obtained. The acoustic radiation force is calculated at different voltages and frequencies. A prototype is fabricated, and the vibration characteristics are experimentally obtained. A test system is built for the actuator, and the conical rotor successfully achieves levitation and rotation. The levitation height and rotation speed of the 3.37[Formula: see text]g rotor are 0.4[Formula: see text]mm and 2300[Formula: see text]r/min, respectively. The acoustic simulations are validated experimentally and show reasonable agreement.

High-Order Frequency Derivatives in Variational Eddy Current System

In a linear eddy current system excited by a current source, a high-order frequency sensitivity is derived in variational formulation instead of as a discretized state equation. An analytic sensitivity formulation of order n is obtained by sequentially differentiating the variational eddy current system with respect to angular frequency. The high-order frequency sensitivity is implemented through a commercial finite element method. A frequency sensitivity analysis conducted based on two numerical examples verifies the results.

Mathematical modeling and dynamic characteristic analysis of a novel parallel tracking mechanism for inter-satellite link antenna

Inter-satellite link antenna tracking mechanism is an important enabling component of relay satellite for continuous real-time tracking of medium and low orbit target spacecraft. Facing the major demand of advanced technology development in aerospace engineering, this paper mainly tackles the problem on the rigid-flexible coupling dynamic modeling and dynamic characteristics analysis of a novel parallel tracking mechanism. Firstly, adopting a novel shape function of three-dimensional isoparametric beam element with curvature, the elasto-dynamic model is derived with floating coordinate method and Lagrangian equation. Then the natural frequencies of the system are investigated and ANSYS software is utilized to verify the model. An efficient numerical solution strategy consisting of the implicit integration algorithm and Baumgarte stabilization technology is employed to precisely evaluate the dynamic response of the system. Meanwhile, trajectory planning is carried out for high tracking precision. Furthermore, the validity of the numerical results of dynamic response is illustrated by simulations with the ADAMS software. Finally, the natural frequency sensitivity analysis is implemented by direct differential method with a novel sensitivity index to identify the structure weakness of the mechanism. A novel design idea for the cross-sectional parameters of each flexible beam is proposed with the sensitivity index. Above mentioned research results enrich the basic theoretical researches of parallel mechanism and lay a theoretical foundation for the practical application of tracking mechanism.

Modal analysis of cracked tower crane with an experimental validation

In this paper, dynamic stiffness model of a cracked frame structure that represents a planar tower crane is established in an explicit form based on general solution of cracked 2D-beam element vibration. The crack is modeled by a pair of equivalent springs of stiffness calculated from the crack depth. An explicit form of frequency equation is first established and then solved for numerical sensitivity analysis of natural frequencies of the structure to cracks. An experimental study is accomplished to validate the theoretical development

Finite element investigation on the dynamic mechanical properties of low-frequency vibrations on human L2-L3 spinal motion segments with different degrees of degeneration.

Exposure to low-frequency vibration is harmful to human lumbar health. However, the dynamic mechanical properties of lumbar spines with varying degrees of degeneration during time-dependent vibration remain incompletely understood. In this study, four poroelastic finite element models of human L2-L3 spinal motion segments, including the non-degeneration and the mild, moderate, and serious degeneration, were established. One-hour low-frequency vibrations with different frequencies were applied. Then, the dynamic mechanical properties of different degenerated lumbar models under the same vibration and the same lumbar model under vibrations at different frequencies were investigated. The results indicated and implied that the negative influences of 1-h vibration on the dynamic mechanical properties of the non-degenerated and mildly degenerated models were similar, but became obvious for the moderately and seriously degenerated models with time. Therefore, the damage caused by low-frequency vibration on the degenerated spinal motion segments was more serious compared with that on the healthy one. Meanwhile, the dynamic mechanical properties of the same lumbar model under vibrations at different frequencies expressed the negligible differences when the vibration frequency was not close to the lumbar natural frequency. Thus, the effects of the 1-h vibrations at different frequencies on one spinal motion segment were similar. Vibration frequency sensitivity analysis on the dynamic characteristics of human L2-L3 spinal motion segments with different degrees of degeneration.

Spatial frequency sensitivity analysis of polarized light perception on the human macular with 3D Stokes vector

This paper presents a matrix approach, developed using a 3D Stokes vector analysis, to simulate polarized light as perceived by the macular of the human eye, and views the human perception of polarized light as a multivariable applied optics problem then approached it in an analytical manner as a complex optical system. The objective is to give purpose and new understanding to a biomedical optical phenomenon. The approach is supported by simulated and experimental measurements. Based on the spatial sensitivity of the human eye, a Fourier transform-based spatial frequency sensitivity analysis of polarized images is performed. The approach uses the spatial frequency of the images and physical parameters of the macular to model and determine polarized images that elicit a heightened perception of polarization. An investigate is presented of the human perception of polarized grid images with lower and higher spatial frequencies against the perception of linear polarized images forming conventional Haidinger’s brushes. The approach paves the way for developing diagnostic images with improved perceived quality for patients vulnerable to macular degeneration.

Frequency control and sensitivity analysis of an isolated microgrid incorporating fuel cell and diverse distributed energy sources

In this manuscript, an off-grid or isolated microgrid (IMG) model has been considered, which consists of renewable power generating sources (RPGS) like solar photovoltaic (PV), solar thermal, wind and fuel cell (FC) along with diesel engine generator (DEG) and battery energy storage system (BESS). The paper emphasizes the analytical study of the impact of RPGS in the frequency control of IMG system. In an IMG integrating distributed energy sources (DES), proper frequency regulation is important because some RPGS do not take part in the frequency control technique and depend on weather conditions like solar insolation and wind speed. For frequency control of the IMG system, a linear quadratic regulator with an integral controller (LQR-I) has been used for its robust characteristics. For designing the LQR-I controller, the IMG system has been represented as a state-space model. The effectiveness of the proposed LQR-I controller has been validated through the dynamic response of the IMG system for a small load perturbation. Robustness of the controller has been verified by sensitivity analysis of the system for varying IMG system parameters such as KWTG, KPV, KS, KT, KAE, KFC, KDEG, KBESS, TFC, KP, TP as well as randomly varying load, varying wind speed and seasonal variation of solar insolation level.

Smith predictor embedded analytical fractional-order controller design: A delayed Bode’s ideal transfer function approach

Abstract The main contribution of this paper is to design an enhanced fractional-order controller for the higher-order system. The analytical design methodology utilizes a delayed Bode’s ideal transfer function in place of the conventional one as the reference model. A reduced fractional-order plus dead-time transfer function is used to represent a higher-order process. The design also embeds a Smith predictor for the enhanced closed-loop performance. Analytical tuning for the designed fractional-order controller is provided based on frequency domain specifications. The proposed methodology is applied to two higher-order systems, which can be represented by a reduced fractional-order plus dead-time transfer function. The closed-loop performance of the designed controller is compared with that of the three other related controllers. Frequency domain characteristics, load disturbance, sensitivity analysis, and model mismatch performance are demonstrated and compared with those of other controllers as well. The results of the paper reveal that the proposed controller leads to an overall enhanced closed-loop performance.

Diagnosis of urinary schistosomiasis among primary school pupils in Patigi local government: Haematuria Vs Microscopy

Objectives : To establish the reliability of haematuria in diagnosing Urinary Schistosomiasis infection. Methodology : The research was a cross sectional study. Information on demographic characteristics and history of haematuria was collected from 2000 primary school pupils aged 5-15 years. Urine samples were collected for microscopy. The data from completed questionnaires were sorted and edited manually to detect omissions and error. Analysis of data was done using SPSS software version 20.0 (Statistical Package for Social Sciences) using simple frequency counts, sensitivity and specificity analysis and chi square test. Results : Prevalence of Schistosomiasis by haematuria was 34.5% while that of microscopy was 35%. Diagnosis by haematuria compared to microscopy had 94.7% sensitivity and a specificity of 97.6%. About 94.6% of urine samples that were positive for haematuria were also positive for ova of Schistosoma haematobium on microscopy. The two diagnostic methods for urinary schistosomiasis showed strong positive relationship (p<0.001). Visible haematuria alone and history of haematuria alone had high positive predictive value (99.1% and 85% respectively) in diagnosis of urinary schistosomiasis. Conclusion : This study has shown that haematuria is as good as microscopy in diagnosing urinary schistosomiasis in endemic areas and should be used routinely. Keywords: Diagnosis, Haematuria, Microscopy, Urinary schistosomiasis, Patigi