Frequency Response Function Method Research Articles

Damage Detection in Frame Structure Using Piezoelectric Actuator

Health-monitoring and On-line damage detection techniques on frame structures are stronglyneeded.Vibration based methods with piezoelectric sensor and actuator integrated into structures is a promising option to fulfil such requirements. This paper presents use of piezoelectric actuator to detect bolt loosening in a frame structure. Frequency response function (FRF) method is used along with piezoelectric actuator. These methods utilize finite element analysis techniques, together with to detect damage. They locate and estimate damage by comparing dynamic responses between damaged and undamaged structures. AFrame structure is modelled using finite element software ABAQUS. Frame structure is coupled with piezoelectric actuator which excites the structure for transient analysis. Acceleration responses are measured at various points in structure and this data is used to find out frequency response functions (FRF). The shift in the natural frequencies of the structure is observed for undamaged and damaged structure to detect the damage.

Numerical analysis and experimental investigation of modal properties for the gearbox in wind turbine

Wind turbine gearbox (WTG), which functions as an accelerator, ensures the performance and service life of wind turbine systems. This paper examines the distinctive modal properties of WTGs through finite element (FE) and experimental modal analyses. The study is performed in two parts. First, a whole system model is developed to investigate the first 10 modal frequencies and mode shapes of WTG using flexible multibody modeling techniques. Given the complex structure and operating conditions of WTG, this study applies spring elements to the model and quantifies how the bearings and gear pair interactions affect the dynamic characteristics of WTGs. Second, the FE modal results are validated through experimental modal analyses of a 1.5 WM WTG using the frequency response function method of single point excitation and multi-point response. The natural frequencies from the FE and experimental modal analyses show favorable agreement and reveal that the characteristic frequency of the studied gearbox avoids its eigenfrequency very well.

A multi-strategy improved particle swarm optimization algorithm and its application to identifying uncorrelated multi-source load in the frequency domain

As a type of indirect method, the traditional frequency approach to load identification establishes a systems frequency response function (FRF) and calculates loads using its inverse and the responses. Based on the established FRF method, a novel identification approach that transforms the inverse problem into a forward single-objective optimization model is proposed. Furthermore, a multi-strategy improved particle swarm optimization algorithm (MsiPSO) for identifying uncorrelated multi-source load in the frequency domain is also proposed. Depending on the specific application, MsiPSO initializes the swarm based on domain knowledge. It applies asymmetric and nonlinear strategies to adaptively set the control parameters and genetic operators to strengthen the diversity of the population and avoid local optima. In the experiments, MsiPSO is compared with the general particle swarm optimization (PSO) algorithm and some well-performing variants. A simulated model is then defined to validate the load recognition accuracy of the proposed approach. The experimental results show that MsiPSO is competitive with other methods in terms of convergence, stability, and precision. It has a higher recognition accuracy and is faster than traditional load identification methods and standard PSO.

Modal-based mixed vibration control for uncertain piezoelectric flexible structures

H-infinity norm relates to the maximum in the frequency response function and H-infinity control method focuses on the case that the vibration is excited at the fundamental frequency, while 2-norm relates to the output energy of systems with the input of pulses or white noises and 2-norm control method weighs the overall vibration performance of systems. The trade-off between the performance in frequency-domain and that in time-domain may be achieved by integrating two indices in the mixed vibration control method. Based on the linear fractional state space representation in the modal space for a piezoelectric flexible structure with uncertain modal parameters and un-modeled residual high-frequency modes, a mixed dynamic output feedback control design method is proposed to suppress the structural vibration. Using the linear matrix inequality (LMI) technique, the initial populations are generated by the designing of robust control laws with different H-infinity performance indices before the robust 2-norm performance index of the closed-loop system is included in the fitness function of optimization. A flexible beam structure with a piezoelectric sensor and a piezoelectric actuator are used as the subject for numerical studies. Compared with the velocity feedback control method, the numerical simulation results show the effectiveness of the proposed method.

Energy Absorption of Seated Body Exposed to Single and Three-Axis Whole Body Vibration

The absorbed power characteristics of seated body exposed to whole-body vibration along the individual and combined fore-aft ( x), lateral ( y) and vertical (z) axes are investigated through measurements of body-seat interactions at the two driving-points formed by the body and the seat-pan, and upper body and the seat backrest. The experiments involved two levels of back support (no back support and vertical backrest) and two levels of broad-band vibration with nearly constant acceleration power spectral density in the 0.5–20 Hz frequency range applied along the individual x-, y- and z- axis (0.25 and 0.4 m/s2 rms acceleration), and along the three-axis (0.23 and 0.4 m/s2 rms acceleration along each axis). The biodynamic responses, measured at the seat-pan and the backrest are applied to characterize the total seated body's energy transfer along each axis. Furthermore, an alternative frequency response function method Hv is employed to capture the coupling in the seated body responses to uncorrelated multi-axis vibration. The total vibration absorbed power responses to simultaneous x, y and z –axis vibration are subsequently derived as the summation of vibration absorbed power along the individual axis within each one-third frequency band. The mean responses measured at the seat-pan suggest strong effects of the back support, and the direction and magnitude of vibration. The total vibration power absorbed by the seated body is further estimated under a multi-axis vibration environment of four different work vehicles. The results suggest that total average power absorbed under reported vehicular vibration varies with the effective acceleration in a nearly quadratic manner.

Piezoelectric sensing and non-parametric statistical signal processing for health monitoring of hysteretic dampers used in seismic-resistant structures

The paper proposes a new application of non-parametric statistical processing of signals recorded from vibration tests for damage detection and evaluation on I-section steel segments. The steel segments investigated constitute the energy dissipating part of a new type of hysteretic damper that is used for passive control of buildings and civil engineering structures subjected to earthquake-type dynamic loadings. Two I-section steel segments with different levels of damage were instrumented with piezoceramic sensors and subjected to controlled white noise random vibrations. The signals recorded during the tests were processed using two non-parametric methods (the power spectral density method and the frequency response function method) that had never previously been applied to hysteretic dampers. The appropriateness of these methods for quantifying the level of damage on the I-shape steel segments is validated experimentally. Based on the results of the random vibrations, the paper proposes a new index that predicts the level of damage and the proximity of failure of the hysteretic damper.

Passive and active controllers for suppressing the torsional vibration of multiple-degree-of-freedom system

In this paper, passive and active control methods are applied to reduce the torsional vibration of a nonlinear dynamical system. This system is subjected to multi parametric excitation forces and modeled by the coupled nonlinear differential equations. This leads to two degrees of freedom and three degrees of freedom when the torsional absorber is connected to the system. A multiple scale perturbation technique is applied to obtain an approximate solution and investigate the response of the system. The stability and the steady-state response of the system near the simultaneous sub-harmonic and internal resonances are studied and discussed using the frequency response function method. The numerical solution and chaotic response of the nonlinear dynamical system for different parameters are also studied. The simulation results are achieved using MATLAB 7.0 programs.

Analytical Prediction of the Critical Depth of Cut and Worst Spindle Speeds for Chatter in End Milling

The frequency response function (FRF) method has been well used to determine the worst spindle speeds and their critical limiting chip width for turning operation by finding the maximum negative real part of the FRF. In this study, a modified FRF concept is adapted for a 2 DOF milling system of planar isotropic dynamics to determine the worst spindle speeds and the critical limiting axial depth of cut in explicit, analytic formulas. Analogous to the formulation of worst spindle speeds, similar expression for the best spindle speeds is also obtained. The modified FRF is obtained by multiplying the original FRF of the structure with a complex scaling factor, corresponding to a scaling and a rotation of its original Nyquist plot. The scaling factor is determined analytically from the system characteristic equation with the radial cutting constant and radial immersion angle as the major system parameters. Through the presented method, it is also shown that the worst spindle speeds for a milling operation can be found without the prior knowledge of modal dynamics and stability lobe diagram. The proposed analytical expressions are confirmed by the existing stability models and experimentally verified.

Nonlinear Study of Rotor-AMB System Subject to Multi-Parametric Excitations

The non-linear response of a rotor supported by active magnetic bearings (AMB) under multi-parametric excitations is investigated. The method of multiple scales is applied to analyze the response of two modes of a rotorAMB system near the primary resonance case. The steady-state response of the system is studied numerically, applying the frequency response function method. It is shown that the system exhibits many typical non-linear behaviors including multiple-valued solutions, jump phenomenon, hardening non-linearity. The effects of the different parameters on the steady state solutions are investigated and discussed.

Acoustic imaging of string instrument soundboxes

A circular 30-microphone array of 90 cm radius has been used to produce acoustic images of several string instruments. The soundboxes were excited by an automated impact hammer, and the instruments were suspended inside the array in such a manner that both the soundbox and hammer mechanism could be rotated in the horizontal plane. By normalizing all microphone signals to the hammer signal, data could be assembled as if from an array of many times 30 microphones. Images were formed using the inverse frequency response function method. The array and data analysis code were tested with a rectangular plate set in a large plywood baffle, a system that was straightforward to simulate numerically. Due to the limited spatial resolution set by the array geometry and frequency range—typically 200–1000 Hz—instruments with long soundboxes were chosen for initial testing: a gothic harp, a guzheng, and a guqin.

System Response Function–Based Leak Detection in Viscoelastic Pipelines

The possibility of leak detection in a viscoelastic pipe system is studied. The frequency response function method (FRFM) is used for leak detection, and the analytical expression for the FRFM originally developed for an elastic pipeline is extended to the viscoelastic situation in this study. The extended FRFM is validated from numerical experiments with one-dimensional viscoelastic transient models. The analysis shows that the pipe-wall viscoelasticity effect has significant impact on the amplitude damping and phase shift of the pressure wave, but little influence on the leak-induced patterns of pressure head peaks in transient system frequency responses. The results indicate that the extended FRFM is applicable to the viscoelastic situation. The impact of viscoelastic parameters and incident wave bandwidth on the applicability of the extended FRFM i also investigated in this paper, and the results imply that transient input signals with rapid changes in time are preferable for leak location in viscoelastic pipelines.

Natural Frequency Study of Automotive Engine Valve Spring by Experimental Method

This paper presents a frequency response function method to measure the natural frequency of automotive engine valve springs with respect to different spring height. A new apparatus is developed for changing the spring height within the range of valve lift. The test results indicate that the natural frequency changing highly depends on the different pitch type of the spring. The measured natural frequencies of valve spring can be direct applied to the estimation of valve spring surge characteristics.

Dynamic Analysis of a Rotating Composite Shaft

This paper is concerned with the dynamic analysis of a rotating composite shaft. The numerical finite element technique is utilized to compute the eigen pairs of laminated composite shafts. A finite element model has been developed to formulate the stiffness matrices using lamination theory. These matrices take into account the effects of axial, flexural and rotating on the eigen-nature of rotating composite shaft. The Campbell diagram is utilized to compute the critical speed of rotating composite shaft and instability regions to achieve accuracy and for controlling the dynamic behavior of the system in resonance state. The influence of laminate parameters: stacking sequences, fiber orientation, boundary conditions and fiber volume fractions effect on natural frequencies and instability thresholds of the shaft are studied. The results are compared to those obtained by using the finite element method and experimental measurements using frequency response function method (FRF) by applying the autogenously excitation from self excitation due to driving motor. In the experimental part, the response of composite shaft with various types of boundary conditions and five lamina orientations were recorded and analyzed by utilizing fast Fourier transform dual channel analyzer in conjunction with the computer. The comparison between the numerical and experimental results proves that the suggested finite element models of the composite shaft provide an efficient accurate tool for the dynamic analysis of rotating composite shaft.

Leak detection in complex series pipelines by using the system frequency response method

This research investigates the applicability of the transient-based frequency-response function (FRF) method for detecting leaks in complex series pipelines. The behaviour of transient waves in these pipelines with internal series junctions indicates that junction reflections modify the system resonant frequencies but have a small effect on the leak-induced information contained within the system frequency responses. The analogous method previously developed for single pipelines is extended to complex series pipe systems by using the analytical transfer matrix method herein and the extended method is validated by two simple numerical experimental cases consisting of 3-series pipes and 10-series pipes, respectively. The applied results indicate that the extended FRF method can be applied to detect single and multiple leaks in complex series pipelines as long as the location and size of the resonant peaks of system frequency responses are accurately determined.

Experimental and Analytical Investigations of the Dynamic Analysis of Adhesively Bonded Joints for Composite Structures

Adhesively bonded joints are used extensively in various industries. Some imperfections like holes, thermal residual stresses occurring in the bolted, welded, riveted, and soldered joints don't take place in adhesively bonded joints. Hence, the main advantages of bonded joint are lightness, sealing, corrosion resistance, heat and sound isolation, damping, and quickly mounting facility which have been highly proved. This paper introduces an attempt to study the dynamic analysis of adhesively bonded joint for composite structures to investigate mainly the influences of lamina code number, bonded adhesive line configuration and boundary condition on the dynamic behavior of the test specimens containing composite assembly. The numerical based on the use of finite element model (FEM) modified by introducing unified mechanical properties are represented and applied to compute efficiently the Eigen-nature for composite bonded structures. The experimental tests are conducted to investigate such adhesive bonded joints using two different techniques. The first technique includes an ultrasonic technique in which the magnetostractive pulse echo delay-line for material characterization of composite material is used. The second technique is bassed on the use of the frequency response function method (FRF) applying the hammering method. The comparison between the numerical and experimental results proves that the suggested finite element models of the composite structural beams with bonded joints provide an efficient by accurate tool for the dynamic analysis of adhesive bonded joints. The damping capacity is inversely proportional to the stiffness of the bonded joint specimens. The type of the proportionality depends mainly on the bond line configuration type, lamina orientation, and boundary conditions. This in turn enables an accurate evaluation for selecting the proper characteristics of the specimens for controlling the present damping capacity and the proper resistance against deformation during the operating process. The present study provides an efficient non-destructive technique for the prediction of dynamic properties for an adhesive bonded joint for the studied composite structure systems. The coordination of the experimental and numerical techniques makes it possible to find an efficient tool for studying the dynamic performance of adhesively bonded joint for composite structures.

A time-varying stiffness rotor-active magnetic bearings system under parametric excitation

The method of multiple scales is applied to investigate the non-linear oscillations and dynamic behaviour of a rotor-active magnetic bearings (AMBs) system, with time-varying stiffness. The rotor-AMB model is a two-degree-of-freedom non-linear system with quadratic and cubic non-linearities and parametric excitation in the horizontal and vertical directions. The case of principal parametric resonance is considered and examined. The steady-state response and the stability of the system at the principal parametric resonance case for various parameters are studied numerically, applying the frequency response function method. It is shown that the system exhibits many typical non-linear behaviours including multiple-valued solutions, jump phenomenon, hardening and softening non-linearity. Different effects of the system parameters on the non-linear response of the rotor are also reported. Results are compared with available published work.

A Time-Varying Stiffness Rotor Active Magnetic Bearings Under Combined Resonance

This paper is concerned with the nonlinear oscillations and dynamic behavior of a rigid disk-rotor supported by active magnetic bearings (AMB), without gyroscopic effects. The nonlinear equations of motion are derived considering a periodically time-varying stiffness. The method of multiple scales is applied to obtain four first-order differential equations that describe the modulation of the amplitudes and the phases of the vibrations in the horizontal and vertical directions. The stability and the steady-state response of the system at a combination resonance for various parameters are studied numerically, applying the frequency response function method. It is shown that the system exhibits many typical nonlinear behaviors, including multiple-valued solutions, jump phenomenon, hardening, and softening nonlinearity. A numerical simulation using a fourth-order Runge-Kutta algorithm is carried out, where different effects of the system parameters on the nonlinear response of the rotor are reported and compared to the results from the multiple scale analysis. Results are compared to available published work.

An identification method for joint structural parameters using an FRF-based substructuring method and an optimization technique

A new method is proposed to identify the joint structural parameters of complex systems using a frequency response function (FRF)-based substructuring method and an optimization technique. The FRF method is used to estimate the joint parameters indirectly by minimizing the difference between the reference and calculated responses using a gradient-based optimization technique with analytical gradient information. To assess the robustness of the identification method with respect to noisy input data, FRFs contaminated by uniformly distributed random noise were tested in a numerical example. The effects of the random noise and the magnitude of the connection stiffness values on the accuracy of the method were investigated while identifying the joint parameters. When the FRFs were contaminated with random noise, the proposed procedure performed well when used to identify the stiffness values, but the accuracy of identification is deteriorative when used to identify the damping coefficients. The joint parameters of a real bolted structure were also identified by the proposed method. The results show that it can be applied successfully to real structures, and that a hybrid approach using both calculated and measured FRFs in the substructure model can enhance the quality of the identification results.

Crack detection using a frequency response function in offshore platforms

Structural cracks can change the frequency response function (FRF) of an offshore platform. Thus, FRF shifts can be used to detect cracks. When a crack at a specific location and magnitude occurs in an offshore structure, changes in the FRF can be measured. In this way, shifts in FRF can be used to detect cracks. An experimental model was constructed to verify the FRF method. The relationship between FRF and cracks was found to be non-linear. The effect of multiple cracks on FRF was analyzed, and the shift due to multiple cracks was found to be much more than the summation of FRF shifts due to each of the cracks. Then the effects of noise and changes in the mass of the jacket on FRF were evaluated. The results show that significant damage to a beam can be detected by dramatic changes in the FRF, even when 10% random noise exists. FRF can also be used to approximately locate the breakage, but it can neither be efficiently used to predict the location of breakage nor the existence of small hairline cracks. The FRF shift caused by a 7% mass change is much less than the FRF shift caused by the breakage of any beam, but is larger than that caused by any early cracks.

Dynamic behavior of an AMB supported rotor subject to harmonic excitation

This paper presents a study of the non-linear response of a simple rigid disk-rotor, supported by active magnetic bearings (AMB), without gyroscopic effects. The case of primary resonance is examined under multi-excitation forces. The rotating shaft is described by a coupled second order non-linear ordinary differential equations. Approximate solutions are sought applying the method of multiple scales. Numerical simulations are carried out to illustrate the steady-state response and the stability of the solutions for various parameters using the frequency response function method. It is shown that the system parameters have different effects on the non-linear response of the rotor. For steady-state response, however, multiple-valued solutions and jump phenomenon occur. Results are compared to previously published work.