Baiyang Ren

Second harmonic generation in composites: Theoretical and numerical analyses

Second harmonic generation in a transversely isotropic plate and a symmetric compositelaminate is analyzed from a theoretical perspective. The strain energy function for a nonlinear elastic transversely isotropic material is expressed in terms of the five invariants of the Green-Lagrange strain tensor. Internal resonance conditions for the generation of cumulative second harmonics indicate that a cumulative second harmonic exists when the primary-secondary mode pair satisfies the phase matching and non-zero power flux criteria. In particular, for transversely isotropic plates, when the primary mode propagates along the material principal direction, only symmetric second harmonic Lamb-like wave modes can be cumulative. Also, when the primary wave propagates along other directions, only symmetric second harmonic modes can be generated. Additionally, for the case of symmetric compositelaminates, only symmetric modes can be generated as cumulative second harmonics regardless of the propagation direction of the primary mode. To validate the above theoretical predictions, finite element simulations were conducted for mode pairs that are: (i) phase matched but have zero power flux, (ii) not phase matched but have non-zero power flux, and (iii) internally resonant i.e., satisfying both phase matching and non-zero power flux criterion. The results obtained from the simulations corroborate the theoretical findings for both transversely isotropic plates and symmetric compositelaminates.

PVDF Multielement Lamb Wave Sensor for Structural Health Monitoring

The characteristics of Lamb waves, which are multimodal and dispersive, provide both challenges and opportunities for structural health monitoring (SHM). Methods for nondestructive testing with Lamb waves are well established. For example, mode content can be determined by moving a sensor to different positions and then transforming the spatial-temporal data into the wavenumber-frequency domain. This mode content information is very useful because at every frequency each mode has a unique wavestructure, which is largely responsible for its sensitivity to material damage. Furthermore, mode conversion occurs when the waves interact with damage, making mode content an excellent damage detection feature. However, in SHM, the transducers are typically at fixed locations and are immovable. Here, an affixed polyvinylidene fluoride (PVDF) multielement sensor is shown to provide these same capabilities. The PVDF sensor is bonded directly to the waveguide surface, conforms to curved surfaces, has low mass, low profile, low cost, and minimal influence on passing Lamb waves. While the mode receivability is dictated by the sensor being located on the surface of the waveguide, both symmetric and antisymmetric modes can be detected and group velocities measured.

Ultrasonic guided wave propagation across waveguide transitions: energy transfer and mode conversion.

Ultrasonic guided wave inspection of structures containing adhesively bonded joints requires an understanding of the interaction of guided waves with geometric and material discontinuities or transitions in the waveguide. Such interactions result in mode conversion with energy being partitioned among the reflected and transmitted modes. The step transition between an aluminum layer and an aluminum-adhesive-aluminum multi-layer waveguide is analyzed as a model structure. Dispersion analysis enables assessment of (i) synchronism through dispersion curve overlap and (ii) wavestructure correlation. Mode-pairs in the multi-layer waveguide are defined relative to a prescribed mode in a single layer as being synchronized and having nearly perfect wavestructure matching. Only a limited number of mode-pairs exist, and each has a unique frequency range. A hybrid model based on semi-analytical finite elements and the normal mode expansion is implemented to assess mode conversion at a step transition in a waveguide. The model results indicate that synchronism and wavestructure matching is associated with energy transfer through the step transition, and that the energy of an incident wave mode in a single layer is transmitted almost entirely to the associated mode-pair, where one exists. This analysis guides the selection of incident modes that convert into transmitted modes and improve adhesive joint inspection with ultrasonic guided waves.

Guided wave mode selection for inhomogeneous elastic waveguides using frequency domain finite element approach.

This article describes the use of the frequency domain finite element (FDFE) technique for guided wave mode selection in inhomogeneous waveguides. Problems with Rayleigh-Lamb and Shear-Horizontal mode excitation in isotropic homogeneous plates are first studied to demonstrate the application of the approach. Then, two specific cases of inhomogeneous waveguides are studied using FDFE. Finally, an example of guided wave mode selection for inspecting disbonds in composites is presented. Identification of sensitive and insensitive modes for defect inspection is demonstrated. As the discretization parameters affect the accuracy of the results obtained from FDFE, effect of spatial discretization and the length of the domain used for the spatial fast Fourier transform are studied. Some recommendations with regard to the choice of the above parameters are provided.

Modal content-based damage indicators for disbonds in adhesively bonded composite structures

Adhesive bonding is a promising joining method for composite materials. This article focuses on the use of modal content-based damage indicators to improve the sensitivity of guided waves to disbonds in the adhesive. Wave-defect interaction is modeled using frequency-domain finite element analysis in order to identify modes sensitive to adhesive degradation in joints between carbon fiber–reinforced polymer laminates. Phased array transducers and multielement array sensors designed for structural health monitoring are employed to enable preferential mode excitation and modal content extraction, respectively. The domains in dispersion curve space predicted to have good, intermediate, and no sensitivity to disbond were experimentally found to have good, intermediate, and limited sensitivity using a feature of the received signals associated with the modal amplitude or a modal amplitude ratio. Furthermore, the modal amplitude was found to decrease monotonically with increasing disbond size, demonstrating that it has potential to quantitatively size disbonds.

Adhesive defect detection in composite adhesive joints using phased array transducers

Composite materials are widely used in aircraft structures due to their high specific stiffness and strength. The laminated nature of composite structures makes them subject to disbond and delamination. These types of defects will compromise the integrity of the structure and therefore need to be monitored. To monitor aircraft structures, light weight transducers capable of large area coverage are beneficial. Ultrasonic guided waves are able to travel long distance and are sensitive to localized defects. The multi-modal characteristic of propagating guided waves requires optimal mode selection and excitation. Phased array transducers provide good versatility for optimal mode excitation since they can excite different guided wave modes preferentially. Phased array transducers designed for structural health monitoring (SHM) applications are employed in this work to study the interaction between adhesive defects and guided wave modes. Amplitude ratios and wave packet composition are utilized as defect indica...

A Guided Wave Sensor Enabling Simultaneous Wavenumber-Frequency Analysis for Both Lamb and Shear-Horizontal Waves

Guided waves in plate-like structures have been widely investigated for structural health monitoring. Lamb waves and shear horizontal (SH) waves, two commonly used types of waves in plates, provide different benefits for the detection of various types of defects and material degradation. However, there are few sensors that can detect both Lamb and SH waves and also resolve their modal content, namely the wavenumber-frequency spectrum. A sensor that can detect both waves is desirable to take full advantage of both types of waves in order to improve sensitivity to different discontinuity geometries. We demonstrate that polyvinylidene difluoride (PVDF) film provides the basis for a multi-element array sensor that detects both Lamb and SH waves and also measures their modal content, i.e., the wavenumber-frequency spectrum.

PVDF array sensor for Lamb wave reception: Aircraft structural health monitoring

Fracture critical structures need structural health monitoring (SHM) to improve safety and reliability as well as reduce downtime and maintenance costs. Lamb waves provide promising techniques for on-line SHM systems because of their large volumetric coverage and good sensitivity to defects. Extensive research has focused on using features derived from time signals obtained at sparse locations distributed across the structure. Commonly used features are wave amplitude, energy, and time of arrival. However, the modal content of received Lamb waves contains valuable information about the existence and characteristics of defects, but cannot be determined from these signal features. Wave scattering at a defect often results in mode conversions in both transmitted and reflected waves. Features like change in time of arrival or amplitude reduction can be interpreted as being a result of mode conversion. This work is focused on the design of a 1D array sensor such that received wave signals at equally spaced loc...

Quantitative verification of thin-film polyvinylidene fluoride (PVDF) transducer array performance up to 60 °C

Thin-film PVDF (polyvinylidene fluoride) transducers are appealing as low cost, light weight, durable, and flexible sensors for structural health monitoring applications in aircraft structures. However, due to the relatively low Curie temperature of PVDF, there is a concern that it’s performance will drop below acceptable levels during elevated-temperature operating conditions. To verify acceptable performance in these environmental operating conditions, temperature history data were collected between 23-60 °C. The effect of temperature on the thin-film PVDF was investigated and a temperature-independent damage feature was assessed. The temperature dependence of the signal’s peak amplitude was investigated in both the time domain and the spectral domain to get two damage features. It was found that the measurement of the incident guided wave by the thin-film PVDF transducer had a temperature dependence that varied with frequency. A third damage feature, the mode ratio, was also calculated in the spectral ...

A fully coupled model for actuation of higher order modes of Lamb waves

Lamb waves have proven to be a valuable tool for structural health monitoring (SHM) of plate-like structures susceptible to degradation and failure. It is well-known that their multi-modal propagation characteristic could be both a challenge and an opportunity. Piezoelectric transducers are widely used in SHM applications because of their low cost, small profile and high electromechanical coupling. Properly designing a piezoelectric transducer to excite a particular mode is of great importance to successful SHM practice. Mode tuning capability of piezoelectric transducers has been studied both theoretically and experimentally in the literature for exciting A0 and S0 modes. However, the higher order Lamb waves are not fully studied for their tuning capability. Also, the transducer is usually modeled separately from the waveguide and their coupling is through the in-plane surface traction. This assumption may induce inaccuracy if the dynamics of the actuator are not negligible. Additionally, the driving cir...