VIBRATION-BASED DAMAGE IDENTIFICATION USING RECONSTRUCTED FRFS IN COMPOSITE STRUCTURES

This work aims to establish a vibration-based damage identification method for fiber-reinforced laminated composites and their sandwich construction. This new on-line structural damage identification technique uses the structural dynamic system reconstruction method exploiting the frequency response functions (FRFs) of a damaged structure. To verify the effectiveness of this damage identification method, the frequency responses obtained by vibration testing of fatigue-damaged laminated composites and honeycomb sandwich beams with debonding are examined according to the extent of the damage via the fatigue-damage load cycle for laminated composites, and via the debonding extent for honeycomb sandwich beams. The changes of the peaks and valley of the FRFs according to the debonding extent and the fatigue load cycles are examined, and the area changes in the FRFs are also discussed as the damage index. The residual FRFs or the difference between intact and damaged FRFs are newly defined for application of the on-line damage identification method. Finally, the delamination extent for the sandwich beams and the fatigue damage level for the laminated composites can be easily identified in terms of the changes in natural frequencies and damping ratios of the reconstructed FRFs for these damaged composite structures.     

A new iterative model updating method using incomplete frequency response function data

A new iterative model updating method is proposed for reduced model using incomplete frequency response function (FRF) data. It uses a modified difference vector between the analytical and experimental FRF data to construct a linear sensitivity updating equation system. To improve the convergence performance of the proposed algorithm, a concept of pseudo master degree-of-freedom (DOF) is put forward and the finite element (FE) model is reduced to the measured and user selected pseudo DOFs. The FRFs at pseudo master DOFs are estimated using the impedance matrix of iteratively modified analytical model and the measured FRFs at master DOFs. They are only used to improve the sensitivity matrix and difference calculation between the analytical and experimental FRF data without introducing additional difference equation. At the end, a 25 truss structure is used to evaluate the performance of the proposed method.     

Experimental modal analysis of three small-scale vibration isolator models

This paper discusses the experimentally measured free–free dynamics of three small-scale vibration isolator models: two single-stage isolators and one two-stage isolator. The first comprises two steel plates and one rubber element, the second two steel plates and four rubber elements, and the third three steel plates and eight rubber elements. The natural frequencies, mode shapes and associated modal damping derived from curve-fitting procedures applied to the measured frequency-response functions (FRFs) are presented. The modal behaviour of the isolators is more complicated than might at first be assumed, a major feature being significant coupling between different degrees of freedom. The modal properties can be used to reconstruct a complete set of FRFs for the isolator, including FRFs which were not measured directly. Vibration isolators are often characterised through the use of four-pole parameters or various transmissibilities, and so methods for calculating these parameters from the reconstructed FRFs are also given.     

Vibration testing based on impulse response excited by laser ablation

This paper proposes an innovative vibration testing method based on impulse response excited by laser ablation. In conventional vibration testing using an impulse hammer, high-frequency elements of over tens of kilohertz are barely present in the excitation force. A pulsed high-power YAG laser is used in this study for producing an ideal impulse force on a structural surface. Illuminating a point on a metal with the well-focused YAG laser, laser ablation is caused by generation of plasma on the metal. As a result, an ideal impulse excitation force generated by laser ablation is applied to the point on the structure. Therefore, it is possible to measure high-frequency FRFs due to the laser excitation. A water droplet overlay on the metal is used to adjust the force magnitude of laser excitation. An aluminum block that has nine natural frequencies below 40 kHz is employed as a test piece. The validity of the proposed method is verified by comparing the FRFs of the block obtained by the laser excitation, impulse hammer, and finite element analysis. Furthermore, the relationship between accuracy of FRF measurements and sensitivity of sensors is investigated.     

Prediction of uncertain frequency response function bounds using polynomial chaos expansion

A probabilistic method is developed to predict the uncertainty bounds on Frequency Response Functions (FRFs) developed from Finite Element models. A non-intrusive Polynomial Chaos Expansion (PCE) method is used to predict uncertainty regression models of the various parameters that make up a curvefit of the FRF: natural frequencies, damping ratios, complex amplitudes, mass and stiffness residuals, by making use of an efficient Latin Hypercube technique. These uncertainty models are then combined to efficiently determine PDFs of the parameters and also the uncertainty bounds of the FRFs. The approach is demonstrated using two examples; a simple beam containing uncertainty in Young's Modulus, and a full-scale aircraft composite wing model containing uncertainties in both Young's modulus and the shear modulus. The results were compared with Monte Carlo Simulation (MCS) and it was found that the parameter PDFs and FRF error bounds obtained using a 2nd-order PCE model agreed very well whilst requiring significantly less computation.     

Structural model updating using incomplete transfer function of strain data

In this paper a model updating algorithm is presented to estimate structural parameters at the element level utilizing frequency domain representation of the strain data. Sensitivity equations for mass and stiffness parameters estimation are derived using decomposed form of the strain-based transfer functions. The rate of changes of eigenvectors and a subset of measured natural frequencies are used to assemble the sensitivity equation of the strain-based transfer function. Solution of the derived sensitivity equations through the least square method resulted in a robust parameters estimation method. Numerical examples using simulated noise polluted data of 2D truss and frame models confirm that the proposed method is able to successfully update structural models even in the presence of mass modeling errors.     

Improved eigenvalues for combined dynamical systems using a modified finite element discretization scheme

New approaches are presented to discretize an arbitrarily supported linear structure carrying various lumped attachments. Specifically, the exact eigendata, i.e., the exact natural frequencies and mode shapes, of the linear structure without the lumped attachments are first used to modify its finite element mass and stiffness matrix so that the eigensolutions of the discretized system coincide with the exact modes of vibration. This is achieved by identifying a set of minimum changes in the finite element system matrices and enforcing certain constraint conditions. Once the updated matrices for the linear structure are found, the finite element assembling technique is then used to include the lumped attachments by adding their parameters to the appropriate elements in the modified mass and stiffness matrices. Numerical experiments show that for the same number of elements, the proposed scheme returns higher natural frequencies that are substantially more accurate than those given by the finite element model. Alternatively, the proposed discretization scheme allows one to efficiently and accurately determine the higher natural frequencies of a combined system without increasing the number of elements in the finite element model.     

SIMPLIFIED MODELS FOR THE LOCATION OF CRACKS IN BEAM STRUCTURES USING MEASURED VIBRATION DATA

A new simplified approach to modelling cracks in beams undergoing transverse vibration is presented. The modelling approach uses Euler-Bernoulli beam elements with small modifications to the local flexibility in the vicinity of cracks. This crack model is then used to estimate the crack locations and sizes, by minimizing the difference between the measured and predicted natural frequencies via model updating. The uniqueness of the approach is that the simplified crack model allows the location and damage extent to be estimated directly. The simplified crack model may also be used to generate training data for pattern recognition approaches to health monitoring. The proposed method has been illustrated using the experimental data on beam examples.     

Single-beam analysis of damaged beams: Comparison using Euler–Bernoulli and Timoshenko beam theory

A new general formulation that is applicable to the damaged, linear elastic structures ‘unified framework’ is used to obtain analytical expressions for natural frequencies and mode shapes. The term mode shapes is used to mean the displacement modes, the section rotation modes, the sectional bending strain modes and sectional shear strain modes. The formulation is applicable to damaged elastic self-adjoint systems. The formulation has two unique aspects: First, the theory is mathematically rigorous since no assumptions are made regarding the physical behavior at a damage location, therefore there is no need to substitute the damage with a hypothetical elastic element such as a spring. Since the beam is not divided at the damage location, rather than an 8 by 8, only a 4 by 4 matrix is solved to obtain the natural frequencies and mode shapes. Second, the inertia effects due to damage which have till now been neglected by researchers are accounted for. The formulation uses a geometric damage model, perturbation of mode shapes and natural frequencies, and a modal superposition technique to obtain and solve the governing differential equation. Timoshenko beam theory is then taken as an example, and its results are compared with results using Euler–Bernoulli beam theory and finite element models. The range of applicability of the two theories is ascertained for damage characteristics such as depth and extent of damage and beam characteristics such as slenderness ratio and Poisson?s ratio. The paper considers rectangular notch like non-propagating damage as an example of the damage.     

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.     

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.     

Estimation of tensile force in tie-rods using a frequency-based identification method

A technique is developed to identify in-situ the tensile force in tie-rods which are used in ancient monumental masonry buildings to eliminate the lateral load exercised by the vaults and arcs. The technique is based on a frequency-based identification method that allows to minimize the measurement error and that is of simple execution. In particular, the first natural frequencies of the tie-rods are experimentally identified by measuring the frequency response functions (FRFs) with instrumented hammer excitation; four to six natural frequencies can be easily identified with a simple test. Then, a numerical model, based on the Rayleigh-Ritz method, is developed for the axially loaded tie-rod by using the Timoshenko beam theory retaining shear deformation and rotary inertia. Non-uniform section of the rod is considered since this is often the case for hand-made tie-rods in old buildings. The part of the tie-rod inserted inside the masonry wall is also modeled and a simple support is assumed at the extremities inside the walls. The constraints given to the part of the tie-rod inserted inside the masonry structure are assumed to be elastic foundations. The tensile force and the stiffness of the foundation are the unknowns. In some cases, the length of the rod inside the masonry wall can be also assumed as unknown. The numerical model is used to calculate the natural frequencies for a given set of unknowns. Then, a weighted difference between the calculated and identified natural frequencies is calculated and this difference is minimized in order to identify the unknowns, and in particular the tensile force. An estimation of the error in the identification of the force is given. The technique has been tested on five tie-rods at the ground floor of the famous castle of Fontanellato, Italy.     

AN INVERSE EIGENVALUE FORMULATION FOR OPTIMIZING THE DYNAMIC BEHAVIOUR OF PIN-JOINTED STRUCTURES

An efficient relationship between geometric and material properties of pin-jointed truss structures and their eigenvalues is established. The problem is formulated as an inverse eigenvalue problem. This formulation allows the determination of the required modifications on the structural members to achieve specified eigenfrequencies. In addition to the modification of the existing structural elements, the formulation also allows addition of new structural elements to obtain the desired frequencies. Using the proposed inverse method, two cases of plane as well as space truss structures are studied and the results are compared with those obtained using the conventional optimization techniques adopted by commercial finite element codes.     

Analysis of pipeline networks using two-ports

Majority of vibration problems arise in pipeline networks are attributed to the high-pressure pulsations. Pulsations are generated by fluid machines such as compressors and pumps. These pulsations turn into shaking forces at elements such as pipe bends and pipe reducers, which in turn excite vibrations in the connected piping network. High vibrations beyond the endurance limit of the pipe material may cause damage to pipes, supports, and equipment. In addition, if the source pulsation frequency coincides with one of the natural frequencies of the piping network, resonance will take place and the vibrations will be magnified to a large scale. Obviously, if these vibrations are not well controlled, they might cause damage to the whole system and foundation, and might lead to substantial financial losses. Thus, prediction of pulsations is important for safe and proper operation. In this paper, a pilot plant equipped with a reciprocating compressor, pipes, bends, and terminated by a vessel is built. The network is modeled using the two-port theory that splits the network into several cascaded elements, and predicts the response of the network. The prediction model uses the measured compressor source data as an input, which is determined by the indirect multi-load method that is usually used to characterize internal combustion engines. A pulsation suppression device is designed, modeled, manufactured and inserted into the pilot network. The pressure pulsations are measured with and without the pulsation suppression device, and compared to the predictions using the two-port theory.     

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.     

Active vibration control on a quarter-car for cancellation of road noise disturbance

In this paper, a methodology is presented for the cancellation of road noise, from the analysis of vibration transmission paths for an automotive suspension to the design of an active control system using inertial actuators on a suspension to reduce the vibrations transmitted to the chassis. First, experiments were conducted on a Chevrolet Epica LS automobile on a concrete test track to measure accelerations induced on the suspension by the road. These measurements were combined with experimental Frequency Response Functions (FRFs) measured on a quarter-car test bench to reconstruct an equivalent three dimensional force applied on the wheel hub. Second, FRFs measured on the test bench between the three-dimensional driving force and forces at each suspension/chassis linkage were used to characterize the different transmission paths of vibration energy to the chassis. Third, an experimental model of the suspension was constructed to simulate the configuration of the active control system, using the primary (disturbance) FRFs and secondary (control) FRFs also measured on the test bench. This model was used to optimize the configuration of the control actuators and to evaluate the required forces. Finally, a prototype of an active suspension was implemented and measurements were performed in order to assess the performance of the control approach. A 4.6 dB attenuation on transmitted forces was obtained in the 50–250 Hz range.     

Free vibration analysis of beams and frames with multiple cracks for damage detection

The problem of calculating the natural frequencies of beams with multiple cracks and frames with cracked beams is studied. The natural frequencies are obtained using a new method in which a rotational spring model is used to represent the cracks. For beams, dynamic stiffness matrices of order 4 are obtained in a recursive manner, according to the number of cracks, by applying partial Gaussian elimination. The Wittrick–Williams algorithm is used to compute the natural frequencies in the resulting transcendental eigenvalue problem. Published numerical examples for cracked beams are used for validation. The global dynamic stiffness matrix of a frame with multiply cracked members is then assembled. A published two bay frame example is used to evaluate the new method. The effect of changing the location of a crack in a two bay two storey frame is studied numerically, giving insight into the inverse problem of damage detection.     

Model updating using uncorrelated modes

FE model updating techniques are used to update dynamic FE models of structures in the light of modal test data. Iterative methods of model updating that update a set of chosen parameters of the model, so as to reduce the difference between the natural frequencies and the mode shapes of the FE model and the corresponding quantities obtained through a modal test on the structure, are probably the most widely used methods. Once experimental modal data has been identified, a necessary prior step, before updating can be carried out, is that of establishing the correspondence between the FE model modes and the experimentally identified modes.     

CRACK DETECTION IN BEAM-TYPE STRUCTURES USING FREQUENCY DATA

A practical method to non-destructively locate and estimate size of a crack by using changes in natural frequencies of a structure is presented. First, a crack detection algorithm to locate and size cracks in beam-type structures using a few natural frequencies is outlined. A crack location model and a crack size model are formulated by relating fractional changes in modal energy to changes in natural frequencies due to damage such as cracks or other geometrical changes. Next, the feasibility and practicality of the crack detection scheme are evaluated for several damage scenarios by locating and sizing cracks in test beams for which a few natural frequencies are available. By applying the approach to the test beams, it is observed that crack can be confidently located with a relatively small localization error. It is also observed that crack size can be estimated with a relatively small size error.