Debonding detection of honeycomb sandwich structures using frequency response functions

A vibration-based non-destructive evaluation (NDE) method is proposed to determine the location and size of debonding in honeycomb sandwich beams. Although most of the existing vibration-based NDE methods need many measurement points, the method proposed here only utilizes the frequency response function (FRF) measured at one point. A parameterized damaged Timoshenko beam model is developed with the method of reverberation-ray matrix (MRRM) for the first time, and combined with the genetic algorithm (GA) to inverse the damage parameters from the measured FRF. The detection of a honeycomb sandwich beam can be divided into two steps: (1) identifying the equivalent elastic moduli and other parameters of the intact sandwich beam. (2) Identifying the debonding location and size of the damaged sandwich beam with the predetermined parameters. It is demonstrated experimentally that the method can inverse damage parameters with acceptable precision.     

Damage localization in linear-form structures based on sensitivity investigation for principal component analysis

This paper addresses the problem of damage detection and localization in linear-form structures. Principal component analysis (PCA) is a popular technique for dynamic system investigation. The aim of the paper is to present a damage diagnosis method based on sensitivities of PCA results in the frequency domain. Starting from frequency response functions (FRFs) measured at different locations on the structure; PCA is performed to determine the main features of the signals. Sensitivities of principal directions obtained from PCA to structural parameters are then computed and inspected according to the location of sensors; their variation from the healthy state to the damaged state indicates damage locations. It is worth noting that damage localization is performed without the need of modal identification. Influences of some features as noise, choice of parameter and number of sensors are discussed. The efficiency and limitations of the proposed method are illustrated using numerical and real-world examples.     

FRF-based damage localization method with noise suppression approach

In this paper a noise-robust damage identification method is presented for localization of structural damage in presence of heavy noise influences. The method works based on Frequency Response Functions (FRFs) of the damaged structure without any prior knowledge of the healthy state. The main innovation of this study starts with convolving FRFs with Gaussian kernel to suppress the noise. Denoised signals are then used to develop shape signals according to the second derivative of the operational mode shapes at frequencies in the half-power bandwidth of the center resonant frequencies. The scheme is followed by normalization of shape signals to create a two-dimensional map indicating the damage pattern. The validation of the method was carried out based on simulated data and experimental measurements. The simulated data polluted with 10 percent random noise considering four different conditions: (i) un-correlated noise with Gaussian distribution (ii) noise with non-Gaussian exponential distribution (iii) noise with non-Gaussian Log-normal distribution and (iv) correlated colored noise. The robustness of the method was examined with respect to the damage severity with various damage conditions. Finally, damage detection experiments of a fixed–fixed steel beam are presented to illustrate the feasibility and effectiveness of the proposed method. According to the numerical and experimental investigations, it was demonstrated that the proposed approach presents satisfactory damage indices both in single and multiple damage states in presence of high level noise. Hence, the method can overcome the problems of output measurement noise and deliver encouraging results on damage localization.     

含损伤黏弹性阻尼加筋层合板声功率和指向性变异

该文旨在研究损伤位置和程度对自由阻尼加筋层合板声辐射功率和指向性的影响.基于Mindlin和Timoshenko梁理论,建立了自由阻尼层合板-梁组合结构有限元模型.数值求解四边简支边界条件自由阻尼加筋层合板振动响应,继而通过Rayleigh积分计算加筋层合板辐射声功率和指向性.将计算得到的前4阶模态固有频率、声辐射功率...     

Vibration based damage detection of a beam-type structure using noise suppression method

In this paper, a method is presented for the localisation of structural damage. The validation of the method is based on simulated data and experimental measurements. Due to measurement errors near resonances, the mode shapes extracted from the frequency response functions (FRFs) and hence the damage indices (DI) can contain many false peaks. The method presented in this paper uses this set of damage indices from each mode generated by the Gapped-Smoothing Method (GSM), and suppresses the noise by allowing only those peaks which show the location of the damage. This paper details the theory of the noise suppression method and the experimental results for a steel beam, damaged with two narrow slots at different locations. A noise addition process was applied to the simulated data in order to more realistically represent experimental measurements. The steel beam was modelled in ANSYS and harmonic analysis was used to obtain FRFs at different locations of the beam. The results were checked for different slot depths by adding 5–10% noise in the simulated results.     

FRF-based structural damage detection of controlled buildings with podium structures: Experimental investigation

How to use control devices to enhance system identification and damage detection in relation to a structure that requires both vibration control and structural health monitoring is an interesting yet practical topic. In this study, the possibility of using the added stiffness provided by control devices and frequency response functions (FRFs) to detect damage in a building complex was explored experimentally. Scale models of a 12-storey main building and a 3-storey podium structure were built to represent a building complex. Given that the connection between the main building and the podium structure is most susceptible to damage, damage to the building complex was experimentally simulated by changing the connection stiffness. To simulate the added stiffness provided by a semi-active friction damper, a steel circular ring was designed and used to add the related stiffness to the building complex. By varying the connection stiffness using an eccentric wheel excitation system and by adding or not adding the circular ring, eight cases were investigated and eight sets of FRFs were measured. The experimental results were used to detect damage (changes in connection stiffness) using a recently proposed FRF-based damage detection method. The experimental results showed that the FRF-based damage detection method could satisfactorily locate and quantify damage.     

A damage identification technique based on embedded sensitivity analysis and optimization processes

A vibration based structural damage identification method, using embedded sensitivity functions and optimization algorithms, is discussed in this work. The embedded sensitivity technique requires only measured or calculated frequency response functions to obtain the sensitivity of system responses to each component parameter. Therefore, this sensitivity analysis technique can be effectively used for the damage identification process. Optimization techniques are used to minimize the difference between the measured frequency response functions of the damaged structure and those calculated from the baseline system using embedded sensitivity functions. The amount of damage can be quantified directly in engineering units as changes in stiffness, damping, or mass. Various factors in the optimization process and structural dynamics are studied to enhance the performance and robustness of the damage identification process. This study shows that the proposed technique can improve the accuracy of damage identification with less than 2 percent error of estimation.     

FINITE ELEMENT MODEL UPDATING USING ANTIRESONANT FREQUENCIES

This paper uses antiresonant frequencies in the finite element model updating of an experimental 6-m aluminum truss and analyzes the physical correctness of the updated model by using it to detect damage. Rigid elements are used to simplify the modelling of welded joints, and their dimensions are used as parameters in an iterative update based on eigenvalue and antiresonance sensitivities. An update using both natural frequencies and antiresonant frequencies is shown to produce a 48% better correlation to experimental frequency response functions (FRFs) than an update that uses only natural frequencies. The antiresonant updated model is used to predict FRFs for the truss in 112 damaged configurations. Pattern classification and curve-fit algorithms for damage detection are tested. The curve-fit method correctly identified damage 92·6% of the time compared to 76·1% for the pattern classifier. The high quality of the model is attributed to the use of rigid elements that are updated using antiresonant frequencies.     

Damage monitoring in sandwich beams by modal parameter shifts: A comparative study of burst random and sine dwell vibration testing

This paper presents an experimental study on the effects of multi-site damage on the vibration response of honeycomb sandwich beams, damaged by two different ways i.e., impact damage and core-only damage simulating damage due to bird or stone impact or due to mishandling during assembly and maintenance. The variation of the modal parameters with different levels of impact energy and density of damage is studied. Vibration tests have been carried out with both burst random and sine dwell testing in order to evaluate the damping estimation efficiency of these methods in the presence of damage. Sine dwell testing is done in both up and down frequency directions in order to detect structural non-linearities. Results show that damping ratio is a more sensitive parameter for damage detection than the natural frequency. Design of experiments (DOE) highlighted density of damage as the factor having a more significant effect on the modal parameters and also proved that sine dwell testing is more suitable for damping estimation in the presence of damage as compared to burst random testing.     

Mechanical behavior and acoustic emission technique for detecting damage in sandwich structures

The present study investigates the mechanical behavior under static and dynamic loadings and assesses damage by the acoustic emission method of two types of sandwich composite materials. The sandwich structures under study are both made of cross-ply laminates as skins and PVC closed-cell as foam with different densities: 60 kg m⁻³ and 100 kg m⁻³. The mechanical behavior tests were conducted in static and cyclic fatigue loadings under 4-point bending. The sandwich structures considered in fatigue tests were damaged by a various number of shear damages in the foam. Static tests were performed to determine the failure parameters and characteristics used in fatigue tests. The damage density effect on the stiffness, hysteresis loops, dissipated energy and damping of sandwich structures, were studied for various numbers of cycles during cyclic fatigue tests. The acoustic emission method was used to identify and characterize the local damage in both types of sandwich materials under static 4-point bending tests.     

Statistical damage identification of structures with frequency changes

Model updating methods based on structural vibration data have being rapidly developed and applied to detect structural damage in civil engineering. But uncertainties existing in the structural model and measured vibration data might lead to unreliable damage detection. In this paper a statistical damage identification algorithm based on frequency changes is developed to account for the effects of random noise in both the vibration data and finite element model. The structural stiffness parameters in the intact state and damaged state are, respectively, derived with a two-stage model updating process. The statistics of the parameters are estimated by the perturbation method and verified by Monte Carlo technique. The probability of damage existence is then estimated based on the probability density functions of the parameters in the two states. A higher probability statistically implies a more likelihood of damage occurrence. The presented technique is applied to detect damages in a numerical cantilever beam and a laboratory tested steel cantilever plate. The effects of using different number of modal frequencies, noise level and damage level on damage identification results are also discussed.     

Non-linear parameter estimation with Volterra series using the method of recursive iteration through harmonic probing

Volterra series provides a platform for non-linear response representation and definition of higher order frequency response functions (FRFs). It has been extensively used in non-parametric system identification through measurement of first and higher order FRFs. A parametric system identification approach has been adopted in the present study. The series response structure is explored for parameter estimation of polynomial form non-linearity. First and higher order frequency response functions are extracted from the measured response harmonic amplitudes through recursive iteration. Relationships between higher order FRFs and first order FRF are then employed to estimate the non-linear parameters. Excitation levels are selected for minimum series approximation error and the number of terms in the series is controlled according to convergence requirement. The problem of low signal strength of higher harmonics is investigated and a measurability criterion is proposed for selection of excitation level and range of excitation frequency. The procedure is illustrated through numerical simulation for a Duffing oscillator. Robustness of the estimation procedure in the presence of measurement noise is also investigated.     

Investigation of multi-layer sandwich beams through single degree-of-freedom transformation

The dynamic behaviors of multi-layer sandwich beams are investigated through single degree-of-freedom (SDOF) transformation. The frequency response of the multi-layer sandwich beam is obtained using finite element code COMSOL and is transformed to a SDOF system with the same frequency response. Hence, the mass, spring constant and damping coefficient of the sandwich beams with different lengths and number of visco-elastic layers can be investigated. Further, viscous damping and structural damping models are individually employed to simulate the damping effect of the sandwich beam. The frequency responses from both models are compared with that from COMSOL and experiment. The resonant peak and resonant frequency of the SDOF system using structural damping model is more consistent with that from COMSOL. The experimental result demonstrates that the response of the sandwich beam can be predicted through COMSOL and SDOF transformation.     

A FREQUENCY-DOMAIN METHOD OF STRUCTURAL DAMAGE IDENTIFICATION FORMULATED FROM THE DYNAMIC STIFFNESS EQUATION OF MOTION

This paper introduces a frequency-domain method of structural damage identification. It is formulated in a general form from the dynamic stiffness equation of motion for a structure and then applied to a beam structure. Only the dynamic stiffness matrix for the intact state appears in the final form of the damage identification algorithm as the structure model. The appealing features of the present damage identification method are: (1) it requires only the frequency response functions experimentally measured from the damaged structure as the input data, and (2) it can locate and quantify many local damages at the same time. The feasibility of the present damage identification method is tested through some numerically simulated damage identification analyses and then experimental verification is conducted for a cantilevered beam with damage caused by introducing three slots.     

Structural damage detection of controlled building structures using frequency response functions

If a building structure requires both a vibration control system and a health monitoring system, the integration of the two systems will be cost-effective and beneficial. One of the key problems of this integrated system is how to use control devices to enhance system identification and damage detection. This paper presents a new method for system identification and damage detection of controlled building structures equipped with semi-active friction dampers through model updating based on frequency response functions. The two states of the building are first created by adding a known stiffness using semi-active friction dampers. A scheme based on the frequency response functions of the two states of the building is then presented to identify stiffness parameters of structural members in consideration of structural connectivity and transformation information. By applying the proposed model updating scheme to the damaged building, a damage detection scheme is proposed based on the identified stiffness parameters of structural members of both the original and damaged buildings. The feasibility of the proposed schemes is finally demonstrated through a detailed numerical investigation in terms of an example building, in which the effects of measurement noise and excitation conditions are discussed. The numerical results clearly show that the proposed method can locate and quantify damage satisfactorily even though measurement noise is taken into consideration.     

Interfacial debonding and slipping of carbon fiber-reinforced ceramic-matrix composites under two-stage cyclic loading

In this paper, the interface debonding and frictional slipping of carbon fiber-reinforced ceramic-matrix composites (CMCs) under two-stage cyclic fatigue loading have been investigated using micromechanics approach. Under cyclic fatigue loading, the fiber/matrix interface shear stress degrades with increasing cycle number due to interface wear. The synergistic effect of interface wear and fatigue loading sequence on interface debonding and frictional slipping has been analyzed. Based on the fatigue damage mechanism of fiber slipping relative to matrix, in the interface debonded region, upon unloading and subsequent reloading, the interface debonded length and interface slip lengths, i.e. interface counter-slip length and interface new-slip length, are determined using the fracture mechanics approach. The relationships between interface debonding, interface slipping, interface wear, cycle number, and different loading sequences are determined. There are two types of fatigue loading sequences considered, i.e. (1) cyclic loading under low peak stress for N₁ cycles, and then high peak stress; and (2) cyclic loading under high peak stress for N₁ cycles, and then low peak stress. The effects of peak stress level, interface wear, cycle number, and loading sequence on interface debonding and frictional slipping of fiber-reinforced CMCs have been analyzed. The fatigue hysteresis loops of cross-ply carbon fiber-reinforced silicon carbide composite corresponding to different cycle number under two-stage cyclic fatigue loading have been predicted.     

Modified null field method for elastic wave scattering from a partially debonded fiber-SH-waves

Debonded fibers influence the macro-mechanical behavior of fiber-reinforced composite materials. Debonded fibers contribute to the initiation and growth of cracks at the fiber/matrix interface. To examine such problems, the scattering of elastic SH-waves (problem of anti-plane strain) from debonded fibers is studied with a numerical method which can handle the mixed boundary conditions on the partially bonded fiber. A modification of the null field of T-matrix method is developed for this purpose. The modification is achieved by the introduction of a mathematical surface. The simultaneous solution of the integral representations of the field scattered by the mathematical surface and the actual fiber surface give rise to sufficient equations that permit solution of the debonded fiber problem. The scattering cross-section and the far field amplitude are calculated as a function of frequency, fiber properties and debonding area. This will be of interest in structural applications where such cross-sections can be used to compute the dynamical effective properties of damaged composites.     

PREDICTION AND MEASUREMENT OF SOME DYNAMIC PROPERTIES OF SANDWICH STRUCTURES WITH HONEYCOMB AND FOAM CORES

Some dynamical properties of sandwich beams and plates are discussed. The types of elements investigated are three-layered structures with lightweight honeycomb or foam cores with thin laminates bonded to each side of the core. A six order differential equation governing the apparent bending of sandwich beams is derived using Hamilton's principle. Bending, shear and rotation are considered. Boundary conditions for free, clamped and simply supported beams are formulated. The apparent bending stiffness of sandwich beams is found to depend on the frequency and the boundary conditions for the structure. Simple measurements on sandwich beams are used to determine the bending stiffness of the entire structure and at the same time the bending stiffness of the laminates as well as the shear stiffness of the core. A method for the prediction of eigenfrequencies and modes of vibration are presented. Eigenfrequencies for rectangular and orthotropic sandwich plates are calculated using the Rayleigh-Ritz technique assuming frequency dependent material parameters. Predicted and measured results are compared.     

A method for determining the location and depth of cracks in double-cracked beams

The influence of two transverse open cracks on the antiresonances of a double cracked cantilever beam is investigated both analytically and experimentally. It is shown that there is a shift in the antiresonances of the cracked beam depending on the location and size of the cracks. These antiresonance changes, complementary with natural frequency changes, can be used as additional information carrier for crack identification in double cracked beams. Experimental results from tests on plexiglas beams damaged at different locations and different magnitudes are found to be in good agreement with theoretical predictions. Based on the results of the present work, an efficient prediction scheme for crack localization and characterization in double cracked beams is proposed.     

小型风机叶片结构损伤识别实验模拟研究

搭建小型风机叶片振动检测实验平台,采集风机叶片振动响应数据,利用自互功率谱法辨别叶片损伤前后的模态参数,通过实验数据对比风机叶片损伤前后固有频率的变化,当风机叶片发生损伤时,其各阶固有频率会下降,且随着损伤程度的增加,各阶固有频率的下降幅度越大,并利用轴向振型差法对叶片损伤进行了定位,在实验室条件下完成了风机叶片结构损伤的识别。