Carlos E. S. Cesnik

Review of guided-wave structural health monitoring

In this paper we present the state of the art in the field of guided-wave structural health monitoring (SHM). We begin with an overview of damage prognosis, and a description of the basic methodology of guided-wave SHM. We then review developments from the open literature in various aspects of this truly multidisciplinary field. First, we discuss different transducer technologies, including both piezoelectric and non-conventional popular and non-conventional piezoelectric transducers. Next, we examine guided-wave theory, tracing its early history down to modern developments. Following this, we detail the efforts into models for guided-wave excitation by SHM transducers. Then, we review several signal processing related works. The next topic in Section 6 is guided-wave SHM system development, and we explore various packaging ideas, integrated solutions and efforts to examine robustness to different service conditions. We also highlight the broad spectrum of applications in which this technology has been tested. We then present some investigations that have attempted to combine guided-wave approaches with other complementary SHM technologies for better system performance. Finally, we propose desirable developments for further advancement of this field.

On Timoshenko-like modeling of initially curved and twisted composite beams

Abstract A generalized, finite-element-based, cross-sectional analysis for nonhomogenous, initially curved and twisted, anistropic beams is formulated from geometrically nonlinear, three-dimensional (3-D) elasticity. The 3-D strain field is formulated based on the concept of decomposition of the rotation tensor and is given in terms of one-dimensional (1-D) generalized strains and a 3-D warping displacement that is obtained from the formulation, not assumed. The warping is found in terms of the 1-D strains via the variational asymptotic method (VAM). In this paper a Timoshenko-like model is presupposed for a beam with cross-sectional characteristic length h, wavelength of deformation given by l, and the magnitude of the radius of initial curvature and/or twist is taken to be of the order R. First, a solution for the asymptotically correct refinement of classical anisotropic beam theory for initially curved and twisted beams through O(h2/R2) is obtained. Next, the O(h2/l2) correction is computed. It is known that Timoshenko-like theory is not capable of capturing all the O(h2/l2) corrections for generally anisotropic beams. However, if all the O(h2/l2) terms are known, then the corresponding Timoshenko-like theory is uniquely defined. Numerical results are presented to illustrate the trends of the various classical (extension-twist, bending-twist, and extension-bending) and nonclassical couplings (extension-shear, bending-shear, and shear-torsion) as the initial twist and curvatures are varied.

Nonlinear Aeroelasticity and Flight Dynamics of High-Altitude Long-Endurance Aircraft

High-Altitude Long-Endurance (HALE) aircraft have wings with high aspect ratios. During operations of these aircraft, the wings can undergo large de∞ections. These large de∞ections can change the natural frequencies of the wing which, in turn, can produce noticeable changes in its aeroelastic behavior. This behavior can be accounted for only by using a rigorous nonlinear aeroelastic analysis. Results are obtained from such an analysis for aeroelastic behavior as well as overall ∞ight dynamic characteristics of a complete aircraft model representative of HALE aircraft. When the nonlinear ∞exibility efiects are taken into account in the calculation of trim and ∞ight dynamics characteristics, the predicted aeroelastic behavior of the complete aircraft turns out to be very difierent from what it would be without such efiects. The overall ∞ight dynamic characteristics of the aircraft also change due to wing ∞exibility. For example, the results show that the trim solution as well as the short-period and phugoid modes are afiected by wing ∞exibility.

Damage detection in composite materials using frequency response methods

Cost-effective and reliable damage detection is critical for the utilization of composite materials. This paper presents part of an experimental and analytical survey of candidate methods for the in situ detection of damage in composite materials. The experimental results are presented for the application of modal analysis techniques applied to graphite/epoxy specimens containing representative damage modes. Changes in natural frequencies and modes were found using a laser vibrometer, and 2-D finite element models were created for comparison with the experimental results. The models accurately predicted the response of the specimens at low frequencies, but coalescence of higher frequency modes makes mode-dependant damage detection difficult for structural applications. The frequency response method was found to be reliable for detecting even small amounts of damage in a simple composite structure, however the potentially important information about damage type, size, location and orientation were lost using this method since several combinations of these variables can yield identical response signatures.

Nonlinear Flight Dynamics of Very Flexible Aircraft

This paper focuses on the characterization of the response of a very ∞exible aircraft in ∞ight. The 6-DOF equations of motion of a reference point on the aircraft are coupled with the aeroelastic equations that govern the geometrically nonlinear structural response of the vehicle. A low-order strain-based nonlinear structural analysis coupled with unsteady flnite-state potential ∞ow aerodynamics form the basis for the aeroelastic model. The nonlinear beam structural model assumes constant strain over an element in extension, twist, and in/out of plane bending. The geometrically nonlinear structural formulation, the flnite state aerodynamic model, and the nonlinear rigid body equations together provide a low-order complete nonlinear aircraft analysis tool. The equations of motion are integrated using an implicit modifled generalized-alpha method. The method incorporates both flrst and second order nonlinear equations without the necessity of transforming the equations to flrst order and incorporates a Newton-Raphson sub-iteration scheme at each time step. Using the developed tool, analyses and simulations can be conducted which encompass nonlinear rigid body, nonlinear rigid body coupled with linearized structural solutions, and full nonlinear rigid body and structural solutions. Simulations are presented which highlight the importance of nonlinear structural modeling as compared to rigid body and linearized structural analyses in a representative High Altitude Long Endurance (HALE) vehicle. Results show signiflcant difierences in the three reference point axes (pitch, roll, and yaw) not previously captured by linearized or rigid body approaches. The simulations using both full and empty fuel states include level gliding descent, low-pass flltered square aileron input rolling/gliding descent, and low-pass square elevator input gliding descent. Results are compared for rigid body, linearized structural, and nonlinear structural response.

Finite-dimensional piezoelectric transducer modeling for guided wave based structural health monitoring

Among the various schemes being considered for structural health monitoring (SHM), guided wave (GW) testing in particular has shown great promise. While GW testing using hand-held transducers for non-destructive evaluation (NDE) is a well established technology, GW testing for SHM using surface-bonded/embedded piezoelectric wafer transducers (piezos) is relatively in its formative years. Little effort has been made towards a precise characterization of GW excitation using piezos and often the various parameters involved are chosen without mathematical foundation. In this work, a formulation for modeling the transient GW field excited using arbitrary shaped surface-bonded piezos in isotropic plates based on the 3D linear elasticity equations is presented. This is then used for the specific cases of rectangular and ring-shaped actuators, which are most commonly used in GW SHM. Equations for the output voltage response of surface-bonded piezo-sensors in GW fields are derived and optimization of the actuator/sensor dimensions is done based on these. Finally, numerical and experimental results establishing the validity of these models are discussed.

Nonlinear aeroelastic analysis of complete aircraft in subsonic flow

Aeroelastic instabilities are among the factors that may constrain the flight envelope of aircraft and, thus, must be considered during design. As future aircraft designs reduce weight and raise performance levels using directional material, thus leading to an increasingly flexible aircraft, there is a need for reliable analysis that models all of the important characteristics of the fluid-structure interaction problem. Such a model would be used in preliminary design and control synthesis. A theoretical basis has been established for a consistent analysis that takes into account 1) material anisotropy, 2) geometrical nonlinearities of the structure, 3) unsteady flow behavior, and 4) dynamic stall for the complete aircraft. Such a formulation for aeroelastic analysis of a complete aircraft in subsonic flow is described. Linear results are presented and validated for the Goland wing (Goland, M., The Flutter of a Uniform Cantilever Wing, Journal of Applied Mechanics, Vol. 12, No. 4, 1945, pp. A197-A208). Further results have been obtained that highlight the effects of structural and aerodynamic nonlinearities on the trim solution, flutter speed, and amplitude of limit-cycle oscillations. These results give insight into various nonlinear aeroelastic phenomena of interest: 1) the effect of steady-state lift and accompanying deformation on the speed at which instabilities occur, 2) the effect on nonlinearities in limiting the amplitude of oscillations once an instability is encountered, and 3) the destabilizing effects of nonlinearities for finite disturbances at stable conditions.

On a simplified strain energy function for geometrically nonlinear behaviour of anisotropic beams

Abstract An asymptotically exact methodology, based on geometrically nonlinear, three-dimensional elasticity, is presented for analysis of prismatic, nonhomogeneous, anisotropic beams. The analysis is subject only to the restrictions that the strain is small relative to unity and that the maximum dimension of the cross-section is small relative to a length parameter which is characteristic of the rapidity with which the deformation varies along the beam; thus, restrained warping effects are not considered. A two-dimensional function is derived which enables the determination of sectional elastic constants, as well as relations between the beam (i.e. one-dimensional) displacement and generalized strain measures and the three-dimensional displacement and strain fields. Since the three-dimensional foundation of the formulation allows for all possible deformations, the complex coupling phenomena associated with shear deformation are correctly accounted for. The final form of the strain energy contains only extensional, bending and torsional deformation measures—identical to the form of classical theory, but with stiffness constants that are numerically quite different from those of a purely classical theory. Indeed, the stiffnesses obtained from classical theory may, in certain extreme cases, be more than twice as stiff in bending as they should be. Stiffness constants which arise from these various models are used to predict beam deformation for different types of composite beams. Predictions from the present reduced stiffness model are essentially identical to those of more sophisticated models and agree very well with experimental data for large deformation.

Dynamic Response of Highly Flexible Flying Wings

*† This paper presents a method to model the coupled nonlinear flight dynamics and aeroelasticity of highly flexible flying wings, as well as analyze their nonlinear characteristics. A low-order, nonlinear, strain-based finite element framework is used, which is capable of assessing the fundamental impact of structural nonlinear effects in a computationally effective formulation target for preliminary vehicle design and control synthesis. The crosssectional stiffness and inertia properties of the wings are calculated along the wing span, and then incorporated into the 1-D nonlinear beam model. A proposed model for the effects in the torsional stiffness of skin wrinkling due to large bending curvature of the wing is also presented. Finite-state unsteady subsonic aerodynamic loads are incorporated to complete the aeroelastic representation of a flying wing. In studying flying wing dynamic response, a spatially-distributed discrete gust model is introduced and its impact on the time-domain solutions is investigated.

Computational Aeroelasticity Framework for Analyzing Flapping Wing Micro Air Vehicles

Because of their small size and flight regime, coupling of aerodynamics, structural dynamics, and flight dynamics are critical for micro aerial vehicles. This paper presents a computational framework for simulating structural models of varied fidelity and a Navier-Stokes solver, aimed at simulating flapping and flexible wings. The structural model uses either 1) the in-house developed UM/NLABS, which decomposes the equations of 3-D elasticity into cross-sectional and spanwise analyses for slender wings, or 2) MSC.Marc, which is a commercial finite-element solver capable of modeling geometrically nonlinear structures of arbitrary geometry. The flow solver employs a well-tested pressure-based algorithm implemented in STREAM. A NACA0012 cross-sectional rectangular wing of aspect ratio 3, chord Reynolds number of 3 x 10 4 , and reduced frequency varying from 0.4 to 1.82, with prescribed pure plunge motion is investigated. Both rigid and flexible wing results are presented, and good agreement between experiment and computation are shown regarding tip displacement and thrust coefficient. Issues related to coupling strategies, fluid physics associated with rigid and flexible wings, and implications of fluid density on aerodynamic loading are also explored in this paper.