Damage Quantification and Identification in Structural Joints through Ultrasonic Guided Wave-Based Features and an Inverse Bayesian Scheme.

In this paper, defect detection and identification in aluminium joints is investigated based on guided wave monitoring. Guided wave testing is first performed on the selected damage feature from experiments, namely, the scattering coefficient, to prove the feasibility of damage identification. A Bayesian framework based on the selected damage feature for damage identification of three-dimensional joints of arbitrary shape and finite size is then presented. This framework accounts for both modelling and experimental uncertainties. A hybrid wave and finite element approach (WFE) is adopted to predict the scattering coefficients numerically corresponding to different size defects in joints. Moreover, the proposed approach leverages a kriging surrogate model in combination with WFE to formulate a prediction equation that links scattering coefficients to defect size. This equation replaces WFE as the forward model in probabilistic inference, resulting in a significant enhancement in computational efficiency. Finally, numerical and experimental case studies are used to validate the damage identification scheme. An investigation into how the location of sensors can impact the identified results is provided as well.

A quantum graph approach to metamaterial design.

Since the turn of the century, metamaterials have gained a large amount of attention due to their potential for possessing highly nontrivial and exotic properties-such as cloaking or perfect lensing. There has been a great push to create reliable mathematical models that accurately describe the required material composition. Here, we consider a quantum graph approach to metamaterial design. An infinite square periodic quantum graph, constructed from vertices and edges, acts as a paradigm for a 2D metamaterial. Wave transport occurs along the edges with vertices acting as scatterers modelling sub-wavelength resonant elements. These resonant elements are constructed with the help of finite quantum graphs attached to each vertex of the lattice with customisable properties controlled by a unitary scattering matrix. The metamaterial properties are understood and engineered by manipulating the band diagram of the periodic structure. The engineered properties are then demonstrated in terms of the reflection and transmission behaviour of Gaussian beam solutions at an interface between two different metamaterials. We extend this treatment to N layered metamaterials using the Transfer Matrix Method. We demonstrate both positive and negative refraction and beam steering. Our proposed quantum graph modelling technique is very flexible and can be easily adjusted making it an ideal design tool for creating metamaterials with exotic band diagram properties or testing promising multi-layer set ups and wave steering effects.

A wave finite element approach for modelling wave transmission through laminated plate junctions.

We present a numerical method for computing reflection and transmission coefficients at joints connecting composite laminated plates. The method is based on modelling joints with finite elements with boundary conditions given by the solutions of the wave finite element method for the plates in the infinite half-spaces connected to the joint. There are no restrictions on the number of plates, inter-plate angles, and material parameters of individual layers forming the composite. An L-shaped laminated plate junction is discussed in more detail. Comparisons of numerically predicted scattering coefficients with semi-analytical solutions for the selected structures are presented. The results obtained are essential for statistical energy analysis and dynamical energy analysis based calculations of the wave energy distribution in full built-up structure.

Impact damping and vibration attenuation in nematic liquid crystal elastomers.

Nematic liquid crystal elastomers (LCE) exhibit unique mechanical properties, placing them in a category distinct from other viscoelastic systems. One of their most celebrated properties is the 'soft elasticity', leading to a wide plateau of low, nearly-constant stress upon stretching, a characteristically slow stress relaxation, enhanced surface adhesion, and other remarkable effects. The dynamic soft response of LCE to shear deformations leads to the extremely large loss behaviour with the loss factor tanδ approaching unity over a wide temperature and frequency ranges, with clear implications for damping applications. Here we investigate this effect of anomalous damping, optimising the impact and vibration geometries to reach the greatest benefits in vibration isolation and impact damping by accessing internal shear deformation modes. We compare impact energy dissipation in shaped samples and projectiles, with elastic wave transmission and resonance, finding a good correlation between the results of such diverse tests. By comparing with ordinary elastomers used for industrial damping, we demonstrate that the nematic LCE is an exceptional damping material and propose directions that should be explored for further improvements in practical damping applications.

Broadband Vibration Attenuation Achieved by 2D Elasto-Acoustic Metamaterial Plates with Rainbow Stepped Resonators.

This paper investigates the influences of nonperiodic rainbow resonators on the vibration attenuation of two-dimensional metamaterial plates. Rainbow metamaterial plates composed of thin host plates and nonperiodic stepped resonators are considered and compared with periodic metamaterial plates. The metamaterial plates are modelled with the finite element modelling method and verified by the plane wave expansion method. It was found that the rainbow metamaterial plates with spatially varying resonators possess broader vibration attenuation bands than the periodic metamaterial plate with the same host plates and total mass. The extension of attenuation bands was found not to be attributed to the extended bandgaps for the two-dimensional metamaterial plates, as is generally believed for a one-dimensional metamaterial beam. The complete local resonance bandgap of the metamaterial plates is separated to discrete bandgaps by the modes of nonperiodic resonators. Although the additional modes stop the formation of integrated bandgaps, the vibration of the plate is much smaller than that of resonators at these modal frequencies, the rainbow metamaterial plates could have a distinct vibration attenuation at these modal frequencies and achieve broader integrated attenuation bands as a result. The present paper could offer a new idea for the development of plate structures with broadband vibration attenuation by introducing non-periodicity.

Metamaterials for simultaneous acoustic and elastic bandgaps.

In this work, we present a single low-profile metamaterial that provides bandgaps of acoustic and elastic waves at the same time. This was done by ensuring impedance mismatch in two different domains, the fluid domain where the acoustic waves propagate and the solid domain where the elastic waves propagate. Through creatively designing the metamaterial, waves of certain nature and frequencies of interest were completely blocked in the solid and fluid domains simultaneously. The simulation results showed bandgaps with acoustic waves attenuation below 5 kHz and elastic waves attenuation below 10 kHz. The acoustic and elastic dispersion curves of the metamaterials were calculated for various designs with various diameters and neck lengths, and the bandgaps were calculated. These parameters can be used as means for tuning both the acoustic and elastic bandgaps. A representative design of the metamaterial was manufactured on a laser powder bed fusion system and the dynamic performance was measured at various points. The measurements were carried out using a dynamic shaker setup and the dynamic performance was in good agreement with the numerical modelling results. Such metamaterials can be used for simultaneous acoustic and elastic attenuation, as well as saving in space and material consumption, in various fields including building construction, automobile, aerospace and rocket design.

Investigation of 2D Rainbow Metamaterials for Broadband Vibration Attenuation.

Phononic crystals (PnCs) and metamaterials are widely investigated for vibration suppression owing to the bandgaps, within which, wave propagation is prohibited or the attenuation level is above requirements. The application of PnCs and metamaterials is, however, limited by the widths of bandgaps. The recently developed rainbow structures consisting of spatially varied profiles have been shown to generate wider bandgaps than periodic structures. Inspired by this design strategy, rainbow metamaterials composed of nonperiodic mass blocks in two-dimensional (2D) space were proposed in the present study. The blocks were connected by curved beams and tessellated with internal voids to adjust their masses. In order to demonstrate the effects of the rainbow design, two 2D metamaterials, with periodic and nonperiodic units, respectively, were investigated and manufactured using additive manufacturing technologies. Receptance functions, i.e., displacement frequency response functions, of the manufactured metamaterials were calculated with finite element models and measured with a testing system containing a mechanical shaker, an impedance head, and a laser Doppler vibrometer. The obtained numerical and experimental results showed that the metamaterial with rainbow blocks has extended bandgaps compared with the periodic metamaterial.

Numerical simulation data for the dynamic properties of rainbow metamaterials.

Simulation data are presented for identifying and analysing the dynamic properties of the rainbow metamaterials as presented in the articles "Rainbow metamaterials for broadband multi-frequency vibration attenuation: numerical analysis and experimental validation" (Meng et al., 2019 [1]) and "Optimal design of rainbow elastic metamaterials" (Meng et al., 2019 [2]). In this data article, the frequency response functions and mode shapes of the rainbow metamaterials are numerically calculated by Finite Element models set up in Ansys Mechanical APDL. Harmonic analysis was performed to figure out the receptance function values of the rainbow metamaterials within the frequency regime 0-500 Hz. Modal analysis was applied to estimate the mode shapes, which could be used to explain the critical peaks and dips in the receptance function curve. Source files of Finite Element models are provided in the data. The Finite Element simulation is not only an effective alternative way to estimate the dynamic properties of the rainbow metamaterials, the mode shape analysis, which is unlikely to be achieved with the analytical model, provides direct insights into the underlying vibration mechanism of the rainbow metamaterials.

Multidimensional Phononic Bandgaps in Three-Dimensional Lattices for Additive Manufacturing.

We report on numerical modelling of three-dimensional lattice structures designed to provide phononic bandgaps. The examined lattice structures rely on two distinct mechanisms for bandgap formation: the destructive interference of elastic waves and internal resonance. Further to the effect of lattice type on the development of phononic bandgaps, we also present the effect of volume fraction, which enables the designer to control the frequency range over which the bandgaps exist. The bandgaps were identified from dispersion curves obtained using a finite element wave propagation modelling technique that provides high computational efficiency and high wave modelling accuracy. We show that lattice structures employing internal resonance can provide transmissibility reduction of longitudinal waves of up to -103 dB. Paired with the manufacturing freedom and material choice of additive manufacturing, the examined lattice structures can be tailored for use in wide-ranging applications including machine design, isolation and support platforms, metrology frames, aerospace and automobile applications, and biomedical devices.

Damping Enhancement of Composite Panels by Inclusion of Shunted Piezoelectric Patches: A Wave-Based Modelling Approach.

The waves propagating within complex smart structures are hereby computed by employing a wave and finite element method. The structures can be of arbitrary layering and of complex geometric characteristics as long as they exhibit two-dimensional periodicity. The piezoelectric coupling phenomena are considered within the finite element formulation. The mass, stiffness and piezoelectric stiffness matrices of the modelled segment can be extracted using a conventional finite element code. The post-processing of these matrices involves the formulation of an eigenproblem whose solutions provide the phase velocities for each wave propagating within the structure and for any chosen direction of propagation. The model is then modified in order to account for a shunted piezoelectric patch connected to the composite structure. The impact of the energy dissipation induced by the shunted circuit on the total damping loss factor of the composite panel is then computed. The influence of the additional mass and stiffness provided by the attached piezoelectric devices on the wave propagation characteristics of the structure is also investigated.