Alan A. Barhorst

Discrete wavelet decomposition of acoustic emission signals from carbon-fiber-reinforced composites

Abstract The wavelet transform is applied to the analysis of acoustic emission (AE) signals collected during static loading of unidirectional and cross-ply carbon-fiber-reinforced plastic (CFRP) composite specimens. With this technique, the AE signals are resolved both in the time and in the frequency domains and are then decomposed into various wavelet levels (11 in all). Each level is examined for its specific frequency range, energy change rate, and percentage of total energy. A general trend is observed by investigating the energy distribution of decomposed AE signals. This trend indicates that the energy in the AE signals is essentially concentrated in three levels (levels 7, 8, and 9) representing frequency ranges of 50–150 kHz, 150–250 kHz, and 250–310 kHz, respectively. Furthermore, the energy percentages in levels 7, 8, and 9 are determined to be 8, 15, and 75%, respectively. The analysis indicates that the information in the three dominant wavelet levels may be related to different failure modes associated with fracture of CFRP composites. In this paper, the results of the wavelet-transform-based decomposition of AE signals are presented. The results indicate that wavelets-based signal processing may be a useful tool in the analysis of acoustic emissions.

Modeling Hybrid Parameter Multiple Body systems: A different approach

Abstract In this paper, the Hybrid Parameter Multiple Body (HPMB) system modeling problem is addressed. Presented, is a systematic methodology for deriving equations of motion for these highly complex systems. The methodology is founded in variational principles, but uses vector algebra to eliminate tedium. The variational nature of the methodology allows rigorous equation formulation providing not only the complete non-linear, hybrid, differential equations, but also the boundary conditions. One novelty of the method lies in the fact that its variational nature is transparent to the user. This enables it to be effectively used by researchers having a working knowledge of Lagranges method. The methodology is formulated in the systems constraint-free sub-space of the configuration space, thus all constraints (holonomic and nonholonomic) are automatically satisfied. Since Lagrange multipliers are not needed, the method produces a minimal realization. The spatial dimensions of the continuum bodies are not restricted and the inter-body connections are completely general.

ON PREDICTING THE FRACTURE BEHAVIOR OF CFR AND GFR COMPOSITES USING WAVELET-BASED AE TECHNIQUES

Abstract The wavelet transform is applied to the analysis of acoustic emission (AE) signals collected during static fracture loading of carbon fiber reinforced (CFR) and glass fiber reinforced (GFR) composite specimens. Based on AE tests, the fracture behavior is studied. In the study of CFR and GFR composite fracture behavior, the ability of the wavelet transform to enhance the signal to noise ratio is employed. The exponential constant m values used to determine the relationship between stress and stress intensity factor are compared relative to classical fracture mechanics and AE techniques. The conventional and wavelet-based AE techniques are presented side-by-side to show the advantage of wavelet-based methods. The results verify that the wavelet-based method better approximates residual strength relative to classical AE techniques, using classical fracture mechanics as the base line.

Contact/Impact in Hybrid Parameter Multiple Body Mechanical Systems

The multiple motion regime (free/constrained) dynamics of hybrid parameter multiple body (HPMB) systems is addressed. Impact response has characteristically been analyzed using impulse-momentum techniques. Unfortunately, the classical methods for modeling complex HPMB systems are energy based and have proven ineffectual at modeling impact. The problems are exacerbated by the problematic nature of time varying constraint conditions. This paper outlines the reformulation of a recently developed HPMB system modeling methodology into an impulse-momentum formulation, which systematically handles the constraints and impact. The starting point for this reformulation is a variational calculus based methodology. The variational roots of the methodology allows rigorous equation formulation which includes the complete nonlinear hybrid differential equations and boundary conditions. Because the methodology presented in this paper is formulated in the constraint-free subspace of the configuration space, both holonomic and nonholonomic constraints are automatically satisfied. As a result, the constraint-addition/deletion algorithms are not needed. Generalized forces of constraint can be directly calculated via the methodology, so the condition for switching from one motion regime to another is readily determined. The resulting equations provides a means to determine after impact velocities (and velocity fields for distributed bodies) which provide the after collision initial conditions. Finally the paper demonstrates, via example, how to apply the methodology to contact/impact in robotic manipulators and structural systems.

Systematic closed form modeling of hybrid parameter multiple body systems

Abstract Presented in this paper is a systematic approach to modeling non-holonomic hybrid parameter multiple body systems. The continuum bodies are represented with the postulates usually associated to the non-linear theories, the Timoshenko (like) beam theories, the higher order plate and shell theories, and the rational theories (e.g. rods) with intrinsic rotary inertia properties. The methodology is an extension of previous work. It is founded in variational principles, but uses vector algebra to eliminate tedium. The variational nature of the methodology allows rigorous equation formulation providing not only the complete non-linear hybrid differential equations, but also the boundary conditions. The methodology is formulated satisfying general non-holonomic constraints; it produces a minimal realization. The spatial dimensions of the continuua are not restricted and the inter-body connections are completely general. To demonstrate the application of the technique, a two-link elastic pendulum or manipulator is modeled. The algorithmic modeling steps are demonstrated. Numerical simulations are presented.

Discrete-Wavelet Analysis of Acoustic Emissions During Fatigue Loading of Carbon Fiber Reinforced Composites

Wavelet transform decomposition was used to gather time-frequency-based information from acoustic emission signals generated during fatigue loading of unidirectional Carbon Fiber Reinforced Composite (FRC). The acoustic emissions were detected using a resonant sensor and were digitized for analysis. The sensor response was de-convolved from the acquired signal using a point-by-point divisional spectral method. The analysis of the collected signals revealed that friction-related emissions due to the fretting of fractured surfaces are of very high frequency and can mask emissions due to actual damage. Through utilization of wavelet transforms, it became possible to present the spectral composition of a transient signal (AK signal) in a time-frequency map which is not easily achieved through conventional spectral analysis techniques. It was determined that most of the acoustic energy (95%) was localized in levels corresponding to central frequencies of 120, 250, and 310 kHz. Results indicate friction-related emissions are associated with levels 8 and 9 and have a frequency range of 250-300 kHz. There are indications that matrix related emissions are of high frequency and high acoustic energy. The results indicate that wavelet analysis would be an effective tool in the analysis of AE by providing information relative to the frequency of the emissions.

Polynomial Interpolated Taylor Series Method for Parameter Identification of Nonlinear Dynamic System

This research work is in the area of structural health monitoring and structural damage mitigation. It addresses and advances the technique in parameter identification of structures with significant nonlinear response dynamics. The method integrates a nonlinear hybrid parameter multibody dynamic system (HPMBS) modeling technique with a parameter identification scheme based on a polynomial interpolated Taylor series methodology. This work advances the model based structural health monitoring technique, by providing a tool to accurately estimate damaged structure parameters through significant nonlinear damage. The significant nonlinear damage implied includes effects from loose bolted joints, dry frictional damping, large articulated motions, etc. Note that currently most damage detection algorithms in structures are based on finding changed stiffness parameters and generally do not address other parameters such as mass, length, damping, and joint gaps. This work is the extension of damage detection practice from linear structure to nonlinear structures in civil and aerospace applications. To experimentally validate the developed methodology, we have built a nonlinear HPMBS structure. This structure is used as a test bed to fine-tune the modeling and parameter identification algorithms. It can be used to simulate bolted joints in aircraft wings, expansion joints of bridges, or the interlocking structures in a space frame also. The developed technique has the ability to identify unique damages, such as systematic isolated and noise-induced damage in group members and isolated elements. Using this approach, not just the damage parameters, such as Youngs modulus, are identified, but other structural parameters, such as distributed mass, damping, and friction coefficients, can also be identified.

Large-displacement nonlinear sloshing in 2-D circular rigid containers — prescribed motion of the container

The two-dimensional large-displacement non-linear sloshing analysis of liquids in circular rigid containers is revisited. The updating of the free surface position is carried out using an adaptive technique for repositioning the computational nodes on the free surface avoiding the use of remeshing algorithms. Smoothing and volume correction approaches using polar co-ordinates are also presented. The fluid is modelled with potential flow theory using modified Rayleigh damping. All non-linear terms in the boundary conditions are taken into account. The known prescribed motion of the container is arbitrary. Boundary elements are used to solve the potential equations and standard techniques are used for the time integration. The analysis can be applied to arbitrarily shaped containers and is limited to the case of non-breaking waves.

On the efficacy of pseudo-coordinates: Part 2: moving boundary constraints

Abstract In this paper an argument is presented in favor of utilizing felicitous or natural coordinates in the model formulation of complex hybrid parameter multiple body mechanical systems (HPMBS). Specifically for this paper, HPMBS that consist of continuua that are subjected to spatially and temporally varying non-holonomic boundary conditions. This is the second paper of a two part series of papers that is presented to clarify the novelty and usefulness of a recently developed Gibbs–Appell type projection based HPMBS modeling tool. The purpose of the paper is to show that with the novel use of pseudo-coordinates and speeds (as defined by the author) it is completely natural to provide minimal configuration space dimensionality yet still retain rigorous analytical formulation tractability. Presented in this work, as a demonstrative arguing point, is the development of the hybrid parameter motion equations for a rolling flexible-disk material cutting device. This device consists of a circular flexible continuum (the cutter) along with the requisite mounting rigid hub and handle. This non-holonomically constrained device is modeled executing spatial motion constrained to the plane via moving constraints applied to the boundary of the planar continuum. Also included in this work are numerical results bolstering the claims made herein. These numerical results demonstrate that the methodology elucidated provides low-order models suitable for modeling complicated devices. These low-order models are in contrast to the current modeling trend of ever-increasing degrees of freedom.

On the efficacy of pseudo-coordinates—Part 1: moving interior constraints

Abstract In a recent publication, a Gibbs–Appell type projection methodology for modeling non-holonomic hybrid parameter multiple body systems (HPMBS) was presented. In this methodology, pseudo-coordinates and pseudo-speeds were introduced felicitously into the kinematic chain to allow rigorous inclusion of holonomic or non-holonomic constraints that occur among the hybrid parameter bodies; including intra-domain constraints applied within distributed parameter bodies in the system. In this paper, a HPMBS that exhibits intra-domain holonomic constraints and is, for comparison purposes, analytically tractable by hand via Hamiltons principle is studied. The purpose of this comparison and study is to evince the utility and effectiveness of the pseudo-variable based technique. This is accomplished by demonstrating the novel and judicious use of pseudo-coordinates and speeds in modeling HPMBS. It is shown, by allowing the natural description of the kinematic chain (open or closed) to be manifested with the natural pseudo-coordinates and speeds, that low-order models can accurately describe the dynamics of complicated HPMBS. Thus, the trend of ever-increasing degrees of freedom in the modeling of complicated flexible systems is also shown to be unnecessary, provided the proper natural finesse is applied.