1. Introduction

Advanced Holographic Interferometry has been successfully employed to characterize the materials and behavior of diverse types of structures under stress [1–3]. Specialized variations of this technology have also been applied to define dynamic and vibration related structural behavior [4]. Such applications of holographic technique offer some of the most effective methods of modal and dynamic analysis available For developing significantly valuable analytic information not easily discernible employing other well known instrumentation-based techniques such as accellerometrically derived FFT, Spectral superposition, and strain gauge displacement mapping. These aforementioned methods all require, at least, modification and mass loading of a given specimen with instruments such as accelerometers and consideration of their ancillary attachment methods (i.e.: adhesives or bolts). Analysis also requires the mathematical manipulation of recorded data to derive a calculated model of the actual motion. Holographic analysis is non-contact and allows immediate and complete visualization of the true full-field motion of the specimen.

Real-time dynamic testing of the modal and mechanical behavior of aerodynamic control structures for advanced missiles systems has always required advanced instrumentation for data collection in either actual flight test or wind-tunnel simulations. Advanced optical holography techniques are alternate methods which define actual behavioral data on the ground in a noninvasive environment. These methods offer significant insight in both the development and subsequent operational test and modeling of advanced composite control structures and their integration with total vehicle system dynamics. Structures and materials can be analyzed with very low amplitude excitation and the resultant data can be used to adjust the accuracy of mathematically derived structural models.

Holographic Interferometry offers a powerful tool to aid in the primary engineering and development of advanced graphite-epoxy fiber composite materials for use in advanced aerodynamic platforms [5]. Aircraft, missile, and smart weapon control structure applications must consider environments where extremes in vibration and mechanical stresses can affect both operation and structural stability. These are ideal requisites for analysis using advanced holographic methods in the initial design and subsequent test of such advanced components. Holographic techniques are nondestructive, real-time, and definitive in allowing the identification of vibrational modes, displacements, and motion geometries. These characteristics can be directly affected by various types of induced mechanical, thermal, and acoustic structural stress related to hidden structural anomalies and defects. Deriving such information can be crucial to the determination of mechanical configurations and designs, as well as critical operational parameters of structures composed of advanced engineering materials.

2. Methods

The primary techniques and methods of applied holographic interferometry of interest to this discussion are called “real-time” and “time-average” holography. The first term refers to the superposition of a hologram of an object over the object itself during the time it is subjected to some small stress [6]. The nature of the applied stress can be designed to either mimic or derive from expected environmental conditions. It may also be defined as an extraneous stress applied to reveal certain aspects of the behavior of the structure of the object under test. Examples of stresses to be considered in all cases described in this discussion includes, but is not limited to, mechanical force, thermal gradient, and vibration. Real time holography allows the observation of the effects of minute changes in displacement on, or in, the structure of the object as stress affects it in real time. The second term (time-average holography) describes a hologram that is created while the object under study is subjected to some type of periodic displacement [7]. The resultant data maps the average displacement from maximum to minimum resulting from the induced vibration and is particularly useful in modal analysis. Both of the aforementioned techniques can reveal aspects of the geometry and magnitude of vibration induced displacements on the surface of a structure. Holographic structural analysis also includes a third method called “multi-exposure” holography. This term generally describes a pair of holograms that are created while the object under study is subjected to some type of differential stress between the exposures [8]. This is designed to create an effective before and after view of the stress induced displacement observed between the two states.

Stress induced displacements of the object under study cause each type of hologram to generate patterns of bright and dark lines which appear superimposed on the object. These are called interference fringes and define isobars of displacement on the surface of the object. The displacement characteristics are determined by the direction of the motion and stress producing the fringes. The most useful observations of interest to this discussion correspond to out-of-plane, or nearly out-of-plane displacement. Specific geometries and symmetries in the holographic fringe patterns map the behavior of the structure and can readily show distortions resulting from material, structural, or processing anomalies as changes in the topography of the surface of the object. Derivation of the magnitude of displacement is defined from the fringe pattern by the fringe density (number of fringes). This is well understood [10]. In the case of Real-Time and Multi-Exposure holograms, the displacement at any given point on the object is derived by counting the number of fringes to that point. Since the fringes are cosinusoidal in nature, each represents a nominal displacement value equal to 1/2 the wavelength of light with which the hologram was recorded, thus total out of plane displacement is given simply by:

where D is the total displacement in the orthogonal direction out of plane, N is the number of fringes, and λ is the wavelength of the laser light employed in recording the hologram. Absolute magnitude calculation depends on the viewing angle and is considered in these experiments to describe displacement in the orthogonal, out of plane direction.

For Time-Average holograms the displacement is derived from a fringe pattern that is modulated by the coefficients of the zero crossings of a Bessel function of the first kind of order zero as given by

where D is the total displacement, ξ_n is the coefficient of the nth zero of the Bessel function (corresponding to the nth fringe counted from the zero displacement nodal fringe), and l is the wavelength of the laser light. The absolute magnitude of the displacement analytically derived in this fashion also depends on the Sensitivity Vector in relation to the orthogonal, out of plane direction.

Modal analysis is initiated using real-time holography to visually identify and isolate structural effects and resonances. This is generally accomplished by sweeping through a frequency spectrum of interest and noting where the easily visible fringe patterns appear and at what frequency the maximum displacements occur. Fundamental and harmonic, as well as conjugate and degenerate modal geometries can be made visible. Time-average methods are subsequently employed to map the resonant modal geometries in a non-transient fashion. To accomplish this, the hologram is recorded while the structure is excited at a chosen resonant frequency in order to develop and record the fringe pattern characterizing the displacement associated with that specific resonant mode. Multi-exposure methods are employed to map changes in structural geometries differentially, prior to and following the application of a specifically induced stress characteristic.

3. Procedure

Structures composed of advanced materials such as metal and epoxy-matrix composite substrates are especially suited to holographic analysis because extremely small stresses and displacements can be induced without damaging the structures themselves. Excitation with low level vibration from either attached transducers or transmitted, uncoupled acoustic excitation sources generates and reveals modal geometry, resonant behavior, structural and material defects, as well as other characteristics which are observable employing holographic techniques while not adversely affecting the structure under test.

It was therefore undertaken to apply holographic techniques to characterize the dynamic behavior and structure of a prototype advanced graphite-epoxy aerodynamic control structure and its ancillary mounting geometry in a non-flight environment. The specimen discussed was produced to include certain defects and structural flaws. It was determined that such information was of great value in anticipating the system’s characteristics in the extreme aerodynamic stress and vibration of actual operational conditions. The test procedures employed for modal analysis depend on introducing low level, nondestructive vibration which propagates to induce corresponding resonant modal geometry in fringe patterns which map the minute displacements at the surface of the structure. This was accomplished using acoustic energy transmitted from a non-contact source. Structural characteristics were investigated in a similar fashion by employing nondestructive mechanical stress. In the case of modal analysis, holographic fringe maps of the nodes, maxima, minima, and geometry of the induced motion, were recorded by a photo-thermoplastic based Instant Holocamera system [9]. Structural analysis identifying flaws, defects, and anomalies in the material and structure of the specimen were mapped using holograms recorded by the same device.

A schematic diagram of the holographic system employed in this work is illustrated in Figure 1. The system incorporates an Argon-ion laser operating at a wavelength of .5145 microns at a single optical mode and frequency. One half the wavelength is 0.2573 microns (approximately 10.1 micro-inches). The optical system was configured to produce off-axis holograms which were imaged by a high resolution CCD-based television camera and monitor. Images are digitally recorded for later image processing when desired or required. Hard copy of the holographic data was also made from the video record on the monitor screen using direct video print-out. The holographic recording procedure generally required less than one minute per image due to the unique capabilities of the holocamera device employed.

Holograms were made with exposures controlled radiometrically by measuring the optimum energy density at the holographic plate. This method insured the high contrast ratios desired in interferograms of this type. The object beam was configured to illuminate the structure under study while the reference beam illuminated the holographic plate directly. Either real-time, time-average, or multi-exposure holograms of the composite structure assembly were possible in this configuration.

 

Figure 1. Off-Axis Holographic Interferometry Configuration

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Time average holograms of the vibrational modes of the structure identified the resonant frequencies and mapped the nodes, maxima, minima, and geometry of the induced motion. Holograms of the displacement patterns of induced stress in the structure are used to map the location and extent of nonuniformities, discontinuities, micro-cracks, and other structural defects in the volume and mounting of the component. Such data can be readily compared to the requirements imposed by the operational environment and allows the true, real-world behavior of the structure to govern its optimum design, engineering, and especially, operational inspection.

Data has been taken for several specimens of an advanced polymer matrix composite control structure assembly. The composite structure assembly under test is an advanced aerodynamic guidance fin. Mass loading, composite thickness, shape, as well as material density, homogeneity, and constraint were postulated to have great effect on the vibrational mode shapes, frequencies, and structural fringe patterns. Inclusions, flaws, and anomalies in the structural volume of the material were also expected to be highly discernible in the holographic fringe patterns as well. A schematic representation of the graphite-epoxy composite structure and it’s mounting geometry with an accompanying photo of the actual mounted assembly is illustrated in figure 2. Different constraint and stress geometries were applied to this assembly in order to develop an understandable characterization of its structural and vibrational dynamics.

 

Figure 2. Composite structure schematic diagram and photo of the actual assembly in place for holographic imaging. Photographic point of view from this image and all holograms is directly along a line of sight orthogonal to the object center. The structural curve is not apparent from this aspect. Fringe patterns will be superimposed over structure image in following data.

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The assembly was mounted and a holographic exposure made while it was in an “undisturbed” state (isolated from any induced vibrations or stresses). The resulting hologram was left in place superimposed on the image of the fin itself to produce a realtime holographic image which was displayed on the monitor. The real-time holographic images are observed while the fringe patterns are optimized by micrometrically adjusting the position of the holographic camera to negate rigid body motion anywhere in the holographic system which could affect the useful data. The interference fringes which were produced by subsequent mechanical or vibrational stress mapped the displacement characteristics.

For the vibration and modal analysis experiments the composite structure assembly was acoustically excited through a range of acoustic frequencies in a continuous spectrum from approximately 30 Hz. to 5 kHz. The resonant modal patterns that developed were noted in real time holography as the frequency was swept. Time-average holograms of the specifically chosen resonant mode shapes of most significant interest were made later and complete motion geometries of the assemblies were easily defined.

Mechanical and structural characteristics were subsequently investigated by employing real-time holograms to identify interesting and significant displacement patterns produced during the application of mechanical clamping stress, thermal stress, and direct bending stress on the fin itself to observe its behavior. Multi-exposure holograms were then employed to map the differential “before and after” behavior and subsequently recorded so the complete motion geometries caused by the induced stresses in the assemblies are easily defined.

4. Results

4.1 Modal analysis

The simple modal analysis of a homogeneous, symmetrically mounted composite control structure assembly presents primary modal maps like those shown in figures 3 through 6. These geometries vary with the frequency of the induced excitation. The mode shapes of fundamental resonances are generally distinctively developed. Figures 3 and 4 show holograms of the classical very strong first bending and first torsional modal geometries respectively, of the fin assembly. The nature of these mode shapes show no distortion or modification by constraint, mass loading, or other anomalous mechanical or structural effects.

 

Figure 3. The holographic fringe pattern shown here defines the primary bending mode of the structure. The frequency in this case was nominally 56 Hz. It is seen to be a clear displacement phenomenon whose amplitude increases linearly from the mounting clamp assembly of the component.

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Figure 4. This fringe geometry illustrates strong torsional displacement pattern produced at a nominal frequency of 121 Hz. The nodal ridge dividing the high amplitude fringe groups on the image top and bottom corners denotes that a phase change occurs between them. This defines a high stress point which could result if the inherent noise spectrum of the structure in its operational configuration includes a component at this frequency.

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Modal geometries are progressively more complex as the frequency increases. Nodes are points of zero displacement and are highly visible as significant bright fringes where displacement phase (direction) changes. Highly localized cyclic stress in the substrate is characteristic at locations indicated by the bright nodal fringe. Mode shapes can be modified by the physical constraint parameters such as material and mounting anomalies and asymmetries.

Examples of such higher frequency mode shapes are shown in figures 5 and 6. These illustrate holograms of bending/torsional conjugate modes. These are resonances showing essentially the same geometry with reversed displacement phase at slightly different frequencies. The cause in this set of images stems from the fundamental nodal geometries being distorted by nonisotropic mounting constraints. The clamping of the assembly was purposely made in a differential fashion to produce imbalance in the stress distribution on the fin. The modes shown in each figure are the fringe patterns which resulted. The distortion of the strong geometry is amplitude independent and defines the effect of differential constraint and imbalanced mechanical loading on the fin structure through distortion of the resonant modal geometry.

 

Figure 5. First bending/conjugate mode at 545 Hz.

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Figure 6. Second bending/conjugate mode at 564 Hz.

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Figure 7 shows the image of a hologram made at a higher frequency complex mode. The bright nodal area of essentially zero displacement is very broad and significant. The fringe pattern symmetry indicates even force and stress distribution in the assembly and the higher displacement areas are seen at the extreme right edge and Figure 7. Higher order complex mode is a superposition of a second bending and second torsional mode at 1.61 kHz. The broad nodal area varies smoothly into the sharp nodal lines in both torsional and bending stress showing the location of changes in direction between the high displacement edges and corners.

 

Figure 7. Higher order complex mode is a superposition of a second bending and second torsional mode at 1.61 kHz. The broad nodal area varies smoothly into the sharp nodal lines in both torsional and bending stress showing the location of changes in direction between the high displacement edges and corners.

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4.2 Mechanical analysis

The effects of mechanically induced stress are observed using previously described methods of real-time holography to examine behavior under conditions in which mechanical and thermal stress imbalances have been purposely applied to examine the response of the structure as it is affected by the applied stress. Examples of mechanically induced stress effects are shown in figures 8 and 9. Fringe geometries are progressively more complex as the displacement changes across the surface resulting from localized stress applied to the structure substrate. It was desired to investigate the characteristics of displacement fringe geometry when the assembly behavior was modified by material and mounting anomalies.

Figures 8 and 9 are holograms whose fundamental fringe geometries have been distorted by nonisotropic mounting constraints. The distortion defines the effect of non-uniform constraint and loading on the structure as asymmetries in the fringe patterns.

 

Figure 8. Constraint induced stress gradient.

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Figure 9. Differential stress loading.

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Figure 8 shows a real-time hologram which maps a high stress gradient in a simple bending geometry. Direct mechanical force was applied out of plane in the direction of the viewer uniformly at the free edge of the fin assembly from the back. The fringe pattern indicates that constraint is fairly isotropic along the image left side at the clamping mount assembly. The fringes defining large non-uniform displacements induced by the direct mechanical stress to the free right edge of the component are seen to vary considerably from an expected pattern of purely straight vertical fringes. This type of non-uniform effect could contribute to anomalous behavior or even component failure in the operational environment.

Figure 9 illustrates a hologram whose fringe pattern clearly denotes the result of highly differential loading on the imaged specimen. The stress concentration identified by the concentric fringes in the mounting clamp area contrast distinctly with the adjacent vertical fringe continuity which is expected to manifest in a continuous fashion over the entire surface under normal conditions. This situation is indicative of constraint or mass loading anomaly at the clamping mount which could also contribute to a catastrophic component failure in operation.

Figure 10 shows a multi-exposure hologram of the composite component responding a purposely applied thermal stress. The fringe pattern shows a distortion characteristic of a buried flaw in the composite substrate. The effect of this anomaly, though captured in the volume of the composite material, clearly induces a highly localized displacement at the surface of the composite substrate. Such flaws, in the nature of inclusions, entrapped gas, delaminations, as well as other fabrication errors, can be easily identified.

 

Figure 10. Internal structural flaw identified when local thermal stress from a 15 degree C increase in temperature is applied to the back of the composite material. The non-uniform displacement distribution indicates the location and extent of the internal flaw.

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5. Conclusion

It has been demonstrated that holographic interferometry can be successfully employed to characterize certain aspects of the vibration induced behavior of an advanced graphite-epoxy composite flight control structure. The frequency dependent characteristics of the structure are shown to be highly dependent on the assembly’s mechanical geometry and mounting constraints. Further analysis is underway to investigate the dependence on substrate materials and processing.

Complete vibration analysis depends on a direct comparison of the of the actual composite structure assembly configuration with associated operational noise spectrum to show its true effect on the complete mechanical system. If the spectrum does not contribute significant energy at the frequencies of excitable modes then the components of the assembly will experience minimal stress in the operational environment. If the converse is seen, the analysis enables the identification of the appropriate geometry for application of stiffening or damping constraints to change the mode shapes or strengths and shift or prevent their excitation.

Holographic analysis has also proven to be a uniquely effective method of defining and analyzing structural characteristics. These techniques also enable the identification of the appropriate geometry for application of structural or other composite substrate changes to modify the geometry of stress or obviate structural anomalies and flaws. The holographic data is, in many cases, ultimately employed to help define parameters for finite element modeling and modification of the substrate material itself or its processing to eliminate anomalous behavior. Holographic methods were included in ongoing development and subsequent testing of the prototype assemblies illustrated and have proven to be the most effective method of evaluating the characteristics of interest.