P.M. Mujumdar

Flexural vibrations of beams with delaminations

Abstract The effect of delamination on the natural vibration characteristics of laminated beam type structures is studied. An analytical model is presented for beams with through-width delaminations parallel to the beam surface located arbitrarily in both the spanwise and thicknesswise directions. The beam is modelled as four separate component segments, each analyzed as an Euler beam. An analysis is presented of the case of vibration when the two segments of the beam in the delamination region are constrained to have identical transverse deformation. A critical assessment of the analytical models available in the literature and a comparative study with the analytical model proposed here is presented. Numerical results for frequencies and mode shapes are presented for various boundary conditions and mode numbers for a wide range of values of the size, thicknesswise and spanwise location of the delamination. Results from an extensive experimental investigation are also presented which show excellent agreement with the analytical results obtained by using the model proposed in this paper.

Time reversibility of a Lamb wave for damage detection in a metallic plate

In this paper, an experimental study has been carried out to develop a baseline-free damage detection technique using the time reversibility of a Lamb wave. The experiments have been carried out on a metallic plate. Time reversibility is the process in which a response signal recorded at a receiver location is reversed in time and transmitted back through the receiver to the original transmitter location. In the absence of any defect or damage in the path between the transmitter–receiver locations, theoretically the signal received back at the original transmitter location (reconstructed signal) is identical to the original input signal. The initial part of the present work is aimed at understanding the time reversibility of a Lamb wave in an undamaged metallic plate. This involves a thorough study of different parameters such as frequency, pulse frequency band width, transducer size and the effects of tuning these parameters on the quality of a reconstructed input signal. This paper also suggests a method to mitigate the effects of the frequency dependent attenuation of Lamb wave modes (amplitude dispersion) and thus achieve better reconstruction for an undamaged plate. Finally, the time reversal process (TRP) is used to detect damage in an aluminium plate without using any information from the undamaged structure. A block mass, a notch and an area of surface erosion are considered as representative of different types of damage. The results obtained show that the effect of damage on TRP is significant, contrary to the results reported earlier.

Time reversed Lamb wave for damage detection in a stiffened aluminum plate

According to the concept of time reversibility of the Lamb wave, in the absence of damage, a Lamb wave signal can be reconstructed at the transmitter location if a time reversed signal is sent back from the receiver location. This property is used for baseline-free damage detection, where the presence of damage breaks down the time reversibility and the mismatch between the reconstructed and the input signal is inferred as the presence of damage. This paper presents an experimental and a simulation study of baseline-free damage detection in a stiffened aluminum plate by time reversed Lamb wave (TRLW). In this study, single Lamb wave mode (A0) is generated and sensed using piezoelectric (PZT) transducers through specific transducer placement and amplitude tuning. Different stiffening configurations such as plane and T-stiffeners are considered. Damage cases of disbonding of stiffeners from the base plate, and vertical and embedded cracks in the stiffened plate, are studied. The results show that TRLW based schemes can efficiently identify the presence of damage in a stiffened plate.

Damage detection in a woven-fabric composite laminate using time-reversed Lamb wave

Time reversibility is the process in which a response signal recorded at a receiver location is reversed in time and transmitted back through the receiver to the original transmitter location. In the absence of any defect or damage in the path between the transmitter and the receiver locations, theoretically, the signal received back at the original transmitter location (reconstructed signal) is identical to the original input signal. Therefore, differences in the transmitted and reconstructed signals are an indication of the possibility of a defect being present. An experimental study of a baseline-free damage detection technique using time reversibility of Lamb wave for a woven-fabric composite laminate is presented in this article. The initial part of the study is aimed towards obtaining the best possible reconstruction of the input signal by tuning various parameters of interest, including an experimental study of the frequency-dependent attenuation of Lamb wave modes (amplitude tuning). A finite element simulation has also been carried out to study the effect of amplitude tuning. Finally, the time-reversal concept is used to detect damage in woven composite laminates without using any information from the undamaged structure. In this study, a small block mass bonded to the surface, surface erosion and local impact are considered as representative of different types of damage. The results obtained show that the Lamb wave technique using time-reversal concept identifies correctly the presence of damage in woven-fabric composite laminates, thus providing a basis for baseline-free damage detection in composite structures.

3D-Duct Design Using Variable Fidelity Method

Low Fidelity Analysis (LFA) modules, Design of Experiment (DOE), and surrogate modeling are brought together with High Fidelity Analysis (HFA) based on Computational Fluid Dynamics (CFD) to provide an optimization methodology for the design of an intake duct of a fighter aircraft. Issues such as time scales, gradient information, and automation, related to the use of HFA in optimization cycles, have been successfully addressed in the study.

A hybrid method based upon nonlinear Lamb wave response for locating a delamination in composite laminates

A new hybrid method based upon nonlinear Lamb wave response in time and frequency domains is introduced to locate a delamination in composite laminates. In Lamb wave based nonlinear method, the presence of damage is shown by the appearance of higher harmonics in the Lamb wave response. The proposed method not only uses this spectral information but also the corresponding temporal response data, for locating the delamination. Thus, the method is termed as a hybrid method. The paper includes formulation of the method and its application to locate a Barely Visible Impact Damage (BVID) induced delamination in a Carbon Fiber Reinforced Polymer (CFRP) laminate. The method gives the damage location fairly well. It is a baseline free method, as it does not need data from the pristine specimen.

Coupling effect of piezoelectric wafer transducers in distortions of primary Lamb wave modes

Piezoelectric wafer transducers (PWT) are widely used for Lamb wave based damage detection schemes. The size of the damage that can be detected is dependent on the wavelength of the Lamb wave employed. Thus it is essential to explore the higher frequency range within the (fundamental) bandwidth of S0 and A0 modes, however below the cut-off frequencies of A1 and S1. It is observed that the Lamb wave modes S0 and A0 generated using PWT undergo distortion within this fundamental bandwidth. This behavior is experimentally observed for different PWT sizes and types. The nature of this observed distortion is very different from the distortion of wave modes due to dispersion. In addition, the distortion, in many cases, tends towards the appearance of new wave modes close to the S0 and A0 modes. To understand this experimental observation, a theoretical study is performed. First, finite element (FE) simulations of Lamb waves considering pin-force, thermal analogy, and couple field models of surface mounted PWT are carried out. These simulation studies reveal that the wavepacket distortion can be attributed mostly to electro-mechanical coupling effect of the PWT. Next, the dispersion plot of piezoelectric layer considering electro-mechanical coupling is obtained using spectral finite element (SFE) method. These dispersion characteristics of the PWT are found to be significantly different from the conventional Lamb wave dispersion characteristics and may explain the experimental observation.

Ranking Based Uncertainty Quantification for a Multifidelity Design Approach

Computer simulation based design processes are being extensively used in complex systems like scramjet powered hypersonic vehicles. The computational demands associated with the high-fidelity analysis tools for predicting the system performance restrict the number of simulations that are possible within the design cycle time. Hence, analysis tools of lower fidelity are generally used for design studies. To enable the designer to make better design decisions in such situations, the lower fidelity analysis tool is complemented with an uncertainty model. An approach based on ranks is proposed in this study to aggregate high-fidelity information in a cost effective manner. Based on this information, a cumulative distribution function for the difference between high-fidelity response and low-fidelity response is constructed. The approach is explained initially for uncertainty quantification in a synthetic example. Subsequently an uncertainty model for estimating the mass flow capture of air, a typical disciplinary performance metric in hypersonic vehicle design, is presented.

A parameter identification technique for detection of spacer locations in an assembly of two coaxial flexible tubes

Assemblies of two horizontal coaxial flexible tubes with loosely held spacers to maintain the annular gap between the coaxial tubes, are generally used in nuclear reactor for carrying hot fluid inside the inner tube with an insulating gas filled annulus between the outer and inner tubes to reduce heat losses. The appropriate location of these spacers is important for maintaining coaxiality and preventing contact between inner and outer tubes due to bending creep of inner tube. Determination of spacer locations is therefore an important task. The conventional method of inspection may be costly and time consuming. This paper presents a non-intrusive technique based on vibration measurement, developed for the detection of such spacer spring locations in the assembly of the two coaxial tubes. The technique is based on a parameter identification approach. It involves the identification of spacer locations by updating the position parameters of the spacer in a Finite Element (FE) structural model through the optimization of an error criterion based on the difference between measured and computed natural frequencies of the assembly of the two coaxial tubes. A gradient-based method is used for optimization in the FE model updating problem. The proposed technique has been validated by numerical simulation as well as on a laboratory scale experimental setup.

Ranking Based Model-Form Uncertainty Quantification for a Multi-fidelity Design Approach

Computer simulation based design processes are being extensively used in preliminary design phase of complex aerospace vehicles like scramjet powered hypersonic vehicles. Analysis tools of varying fidelity are generally used to assess the system performance metrics. Often there is a constraint on the number of simulations using high fidelity analysis tools to predict the performance metrics, due to attendant computational demands. A low fidelity analysis tool complemented with an uncertainty model enables the designer to make better design decisions in such situations. A novel approach based on ranks is proposed in this study to aggregate high fidelity information in a cost effective manner. Based on this information, a cumulative distribution function for the difference between high fidelity and low fidelity responses is constructed. The approach is demonstrated initially for a synthetic example and subsequently for quantification of uncertainty in a typical disciplinary metric for hypersonic vehicle design.