P. Frank Pai

Structural health monitoring techniques for wind turbine blades

Abstract Wind turbine blades are made of fiberglass material to be cost effective, but they can be damaged by moisture absorption, fatigue, wind gusts or lightening strikes. It is important to detect the damage before the blade fails catastrophically which could destroy the entire wind turbine. In this paper, four different algorithms are tested for detecting damage on wind turbine blades. These are the transmittance function, resonant comparison, operational deflection shape, and wave propagation methods. The methods are all based on measuring the vibration response of the blade when it is excited using piezoceramic actuator patches bonded to the blade. The vibration response of the blade is measured using either piezoceramic sensor patches bonded to the blade, or a scanning laser doppler vibrometer. The sensitivity of the techniques to detect a reversible damage simulated by a steel plate clamped to a section of a wind turbine blade is compared in this paper.

Damage detection of beams using operational deflection shapes

This work is an in-depth study of a boundary effect detection (BED) method for pinpointing locations of small damages in beams using operational deflection shapes (ODSs) measured by a scanning laser vibrometer. The BED method requires no model or historical data for locating structural damage. It works by decomposing a measured ODS into central and boundary-layer solutions using a sliding-window least-squares curve-fitting technique. For high-order ODSs of an intact beam, boundary-layer solutions are non-zero only at structural boundaries. For a damaged beam, its boundary-layer solutions are non-zero at the original boundaries and damage locations because damage introduces new boundaries. At a damage location, the boundary-layer solution of slope changes sign, and the boundary-layer solution of displacement peaks up or dimples down. The theoretical background is shown in detail. Noise and different types of damage are simulated to show how they affect damage locating curves. Experiments are performed on several different beams with different types of damage, including surface slots, edge slots, surface holes, internal holes, and fatigue cracks. Experimental results show that this damage detection method is sensitive and reliable for locating small damages in beams.

Metamaterial-based Broadband Elastic Wave Absorber

This article presents modeling and analysis techniques for and reveals the actual working mechanism of longitudinal metamaterial bars as elastic wave absorbers. A metamaterial-based elastic wave absorber can be a uniform isotropic bar with many tiny spring-mass subsystems attached at separated longitudinal locations. In the literature, each cell that consists of a bar segment and an attached spring-mass subsystem is modeled as a discrete system of two degrees of freedom by integration and/or finite difference, and the idealized model becomes a dispersive medium for elastic waves and has a stop band that allows no waves to propagate forward. This work shows that these idealized models can be used only for elastic waves having wavelengths much longer than the unit cell’s length. Moreover, it is revealed that a metamaterial-based elastic wave absorber is actually based on the concept of conventional mechanical vibration absorbers, which uses the local resonance of subsystems to generate inertia forces to work against the external load and prevent elastic waves from propagating forward. This concept is extended to design a broadband absorber that works for elastic waves of any wavelengths, including waves having wavelengths shorter than the unit cell’s length. Numerical examples validate the design and reveal the cause of stop band. Moreover, the effect of negative effective mass and acoustic and optical modes are explained.

A higher-order sandwich plate theory accounting for 3-D stresses

In this paper we extend a layerwise higher-order shear-deformation theory to model a sandwich plate impacting with an elastic foundation at a low velocity. A new concept of sublaminates is introduced, and the new sandwich plate theory satisfies the continuity conditions of interlaminar shear and normal stresses, accommodates the normal and shear stresses on the bonding surfaces, and accounts for non-uniform distributions of transverse shear stresses in each layer. Moreover, the use of sublaminates enables the modeling of shear warpings that change with the spatial location, vibration frequency, and loading and boundary conditions. A finite-element model based on this sandwich plate theory is derived for performing direct transient analyses to predict the initiation and location of critical matrix crack and the threshold of impact damage. Moreover, analytical shear warping functions, shear coupling functions, and normal strain functions due to in-plane stretching, bending, transverse shearing, and surface loading are presented.

Theory of Metamaterial Beams for Broadband Vibration Absorption

This article presents methods for modeling, analysis, and design of metamaterial beams for broadband vibration absorption/isolation. The proposed metamaterial beam consists of a uniform isotropic beam with many small spring-mass-damper subsystems integrated at separated locations along the beam to act as vibration absorbers. For a unit cell of an infinite metamaterial beam, governing equations are derived using the extended Hamilton principle. The existence of stopband is demonstrated using a model based on averaging material properties over a cell length and a model based on finite element modeling and the Bloch-Floquet theory for periodic structures. However, these two idealized models cannot be used for finite beams and/or elastic waves having short wavelengths. For finite metamaterial beams, a linear finite element method is used for detailed modeling and analysis. Both translational and rotational absorbers are considered. Because results show that rotational absorbers are not efficient, only translational absorbers are recommended for practical designs. The concepts of negative effective mass and stiffness and how the spring-mass-damper subsystems create a stopband (i.e., no elastic waves in this frequency range can propagate forward) are explained in detail. Numerical simulations reveal that the actual working mechanism of the proposed metamaterial beam is based on the concept of conventional mechanical vibration absorbers. It uses the incoming elastic wave in the beam to resonate the integrated spring-mass-damper absorbers to vibrate in their optical mode at frequencies close to but above their local resonance frequencies to create shear forces and bending moments to straighten the beam and stop the wave propagation. This concept can be easily extended to design a broadband absorber that works for elastic waves of short and long wavelengths. Numerical examples validate the concept and show that, for high-frequency waves, the structure’s boundary conditions do not have significant influence on the absorbers’ function. However, for absorption of low-frequency waves, the boundary conditions and resonant modes of the structure need to be considered in the design. With appropriate design calculations, finite discrete spring-mass-damper absorbers can be used, and hence expensive micro- or nanomanufacturing techniques are not needed for design and manufacturing of such metamaterial beams for broadband vibration absorption/isolation.

Shear correction factors and an energy-consistent beam theory

Abstract Presented here is a new derivation of shear correction factors for isotropic beams by matching the exact shear stress resultants and shear strain energy with those of the equivalent first-order shear deformation theory. Moreover, a new method of deriving in-plane and shear warping functions from available elasticity solutions is shown. The derived exact warping functions can be used to check the accuracy of a two-dimensional sectional finite-element analysis of central solutions. The physical meaning of a shear correction factor is shown to be the ratio of the geometric average to the energy average of the transverse shear strain on a cross section. Examples are shown for circular and rectangular cross sections, and the obtained shear correction factors are compared with those of Cowper (1966) . The energy-averaged shear representative is also used to derive Timoshenkos beam theory.

Locating Structural Damage Using Frequency Response Reference Functions

A technique for monitoring vibration measurements to detect structural damage is presented. Frequency response functions from a healthy structure are measured for reference data, then cross-spectral densities between pairs of combined damage and external forces are computed to detect any occurring damage. The excitation forces are not measured, and can be uniform, random, and uncorrelated, or applied at a single point on the structure. The technique bounds the damage location between the closest sensors on the structure, only a small number of sensors are needed, the damage force is approximated, and no model of the structure is used. For bending vibrations, rotations must also be measured which in practice is often difficult. In a finite-element simulation, the method located small damage and approximated the damage force for a beam structure.

Large-deformation tests and total-Lagrangian finite-element analyses of flexible beams

Presented here is a total-Lagrangian displacement-based finite-element formulation for general anisotropic beams undergoing large displacements and rotations. The theory fully accounts for geometric nonlinearities (large rotations), general initial curvatures, and extensionality by using Jaumann stress and strain measures, an exact coordinate transformation, and a new concept of orthogonal virtual rotations. Moreover, transverse shear deformations are accounted for by using a first-order shear-deformation theory. To verify the accuracy of the finite-element model, two test fixtures have been built for bending and twisting experiments. Large static deformation tests of beams with different loading conditions have been performed. The finite-element results agree closely with the experimental results and numerically exact solutions obtained by using a multiple shooting method to solve for post-buckling deformations of highly flexible beams undergoing large static rotations and displacements in three-dimensional space.

Uncertainty Analysis of Solid-Liquid-Vapor Phase Change of a Metal Particle Subject to Nanosecond Laser Heating

The effects of the uncertainties of various parameters, including the laser fluence, diameter of metal powder particles, laser pulse width, and the initial temperature of metal particles on solid-liquid-vapor phase change processes of metal particles under nanosecond laser heating are investigated in this paper. A systematic approach of simulating the phase change with uncertain parameters is presented and a sample-based stochastic model is established in order to investigate the influence of different uncertain parameters on the maximum surface temperature of metal particles, the maximum solid-liquid interface location, maximum liquid-vapor interface location, maximum saturation temperature, and maximum recoil pressure and the time needed to reach the maximum solid-liquid interface location. The results show that the mean value and standard deviation of the laser fluence have dominant effects on all output parameters. [DOI: 10.1115/1.4023714]

Experimental Damage Detection on a Wing Panel Using Vibration Deflection Shapes

This paper discusses the use of a vibration method to detect fatigue cracks in inaccessible internal structures. On aircraft, the lower wing panels are highly stressed causing cracks to initiate from fastener holes inside the wing box. The wing panel internal sections are usually inspected using conventional nondestructive inspection techniques after removing the wing panels from the wing box structure. When a crack is detected during the inspection, it can sometimes be repaired by reinforcing the damaged wing panel integral stiffener with a set of repair doublers. Of concern is whether the repair is intact for extended periods of aircraft service. The integrity of the repair and the condition of the wing interior structure might be determined by measuring the vibration of the outer surface. To investigate this approach, a series of experiments was conducted. Two piezoceramic actuator patches were bonded on the outside of a wing panel above a stiffener to generate vibration up to 80 kHz. A scanning laser doppler vibrometer was used to measure the normal vibration of the outside of the panel over the crack/repair. The measurements were performed for both the healthy and damaged panel. It was found that a crack extending from a fastener hole to the free edge of a stiffener and loosening of a repair doubler could be detected by changes in the vibration response of the outside of the panel. The crack from the fastener hole was not detectable until it reached the free edge of the stiffener.