Massimo Ruzzene

Frequency–wavenumber domain filtering for improved damage visualization

This paper presents a technique for the analysis of full wavefield data in the wavenumber/frequency domain as an effective tool for damage detection, visualization and characterization. Full wavefield data contain a wealth of information regarding the space and time variation of propagating waves in damaged structural components. Such information can be used to evaluate the response spectrum in the frequency/wavenumber domain, which effectively separates incident waves from reflections caused by discontinuities encountered along the wave paths. This allows removing the injected wave from the overall response through simple filtering strategies, thus highlighting the presence of reflections associated with damage. The concept is first illustrated on analytical and numerically simulated data, and then tested on experimental results. In the experiments, full wavefield measurements are conveniently obtained using a scanning laser Doppler vibrometer, which allows the detection of displacements and/or velocities over a user-defined grid, and it is able to provide the required spatial and time information in a timely manner. Tests performed on a simple aluminum plate with artificially seeded slits simulating longitudinal cracks, and on a disbonded tongue and groove joint, show the effectiveness of the technique and its potentials for the inspection of a variety of structural components.

Wave beaming effects in two-dimensional cellular structures

Cellular structures like honeycombs or reticulated micro-frames are widely used in sandwich construction because of their superior structural static and dynamic properties. The aim of this study is to evaluate the dynamic behavior of two-dimensional cellular structures, with the focus on the effect of the geometry of unit cells on the dynamics of the propagation of elastic waves within the structure. The characteristics of wave propagation for the considered class of cellular solids are analyzed through the finite element model of the unit cell and the application of the theory of periodic structures. This combined analysis yields the phase constant surfaces, which define the directions of waves propagating in the plane of the structure for the assigned frequency values. The analysis of iso-frequency contour lines in the phase constant surfaces allows the prediction of the location and extension of angular ranges, and therefore regions within the structures where waves do not propagate. The performance of honeycomb grids of regular hexagonal topology is compared with that of grids of various geometries, with the emphasis on configurations featuring a negative Poissons ratio behavior. The harmonic response of the considered structures at specified frequencies confirms the predictions from the analysis of the phase constant surfaces and demonstrates the strongly spatially-dependent characteristics of periodic cellular structures. The numerical results presented indicate the potentials of the phase constant surfaces as tools for the evaluation of the wave propagation characteristics of this class of two-dimensional periodic structures. Optimal design configurations can be identified in order to achieve the desired transmissibility levels in specified directions and to obtain efficient vibration isolation capabilities. The findings from the presented investigations and the described analysis methodology will provide invaluable guidelines for the prototyping of future concepts of honeycombs or cellular structures with enhanced vibro-acoustics performance.

Frequency-wavenumber domain analysis of guided wavefields.

Full wavefield measurements obtained with either an air-coupled transducer mounted on a scanning stage or a scanning laser vibrometer can be combined with effective signal and imaging processing algorithms to support characterization of guided waves as well as detection, localization and quantification of structural damage. These wavefield images contain a wealth of information that clearly shows details of guided waves as they propagate outward from the source, reflect from specimen boundaries, and scatter from discontinuities within the structure. The analysis of weaker scattered waves is facilitated by the removal of source waves and the separation of wave modes, which is effectively achieved via frequency-wavenumber domain filtering in conjunction with the subsequent analysis of the resulting residual signals. Incident wave removal highlights the presence and the location of weak scatterers, while the separation of individual guided wave modes allows the characterization of their separate contribution to the scattered field and the evaluation of mode conversion phenomena. The effectiveness of these methods is demonstrated through their application to detection of a delamination in a composite plate and detection of a crack emanating from a hole.

Spectral Finite Element Method

This chapter presents the procedures for the development of various types of spectral elements. The chapter begins with basic outline of spectral finite element formulation and illustrates its utility for wave propagation studies is complex structural components. Two variants of spectral formulations, namely the Fourier transform-based, and Wavelet transform-based spectral FEM are presented for both 1D and 2D waveguides. A number of examples are solved using the formulated elements to show the effectiveness of the spectral FEM approach to solve problems involving high frequency dynamic response.

Broadband Vibration Control Through Periodic Arrays of Resonant Shunts: Experimental Investigation on Plates

In this work, a periodic 4 × 4 lay-out of resistive inductive (RL) shunted piezoelectric transducer (PZT) patches is designed and applied to achieve broadband vibration reduction of a flexible isotropic plate over tunable frequency bands. Each surface-bonded PZT patch is connected to a single independent RL circuit and all shunt circuits are tuned at the same frequency. A finite element-based design methodology is used to predict the attenuation properties of the unit cell that characterize the periodic assembly. The predictions are experimentally validated by measuring the spatial average harmonic response of the plate. Significant broadband attenuation is obtained over frequency bands centered at the resonance frequency of the shunting circuit.

Control of Wave Propagation in Periodic Composite Rods Using Shape Memory Inserts

Longitudinal wave propagation is controlled using shape memory inserts placed periodically along rods. The inserts act as sources of impedance mismatch with tunable characteristics. Such characteristics are attributed to the unique behavior of the shape memory alloy whereby the elastic modulus of the inserts can be varied up to three times as the alloy undergoes a phase transformation from martensite to austenite, With such controllable capability, the inserts can introduce the proper impedance mismatch necessary to impede the wave propagation along the rods. An analytical model is presented to study the attenuation capabilities of the composite rods and to determine the influence of the various design parameters of the inserts that can control the width of the pass and stop-bands. The numerical results demonstrate the potential of shape memory alloys in controlling the dynamics of wave propagation in rods. Furthermore, the obtained results provide a guideline for designing inserts that are capable of filtering out selected excitation frequencies through proper adjustment of the geometry of the inserts as well as their activation strategies.

Design of tunable acoustic metamaterials through periodic arrays of resonant shunted piezos

Periodic shunted piezoelectric patches are employed for the design of a tunable, one-dimensional metamaterial. The configuration considered encompasses a beam undergoing longitudinal and transverse motion, and a periodic array of piezoelectric patches with electrodes connected to a resonant electric circuit. The resulting acousto-electrical system is characterized by an internal resonant behavior that occurs at the tuning frequency of the shunting circuits, and is analogous in its operation to other internally resonating systems previously proposed, with the addition of its simple tunability. The performance of the beam is characterized through the application of the transfer matrix approach, which evaluates the occurrence of bandgaps at the tuning frequencies and estimates wave attenuation within such bands. Moreover, a homogenization study is conducted to illustrate the internal resonant characteristics of the system within an analytical framework. Experiments performed on the considered beam structure validate the theoretical predictions and illustrate its internal resonant characteristics and the formation of the related bandgaps.

Vibration and Wave Propagation Control of Plates with Periodic Arrays of Shunted Piezoelectric Patches

Periodic arrays of shunted, piezoelectric patches are employed to control waves propagating over the surface of plate structures, and corresponding vibrations. The shunted, piezoelectric patches act as sources of impedance mismatch, which gives rise to interference phenomena resulting from the interaction between incident, reflected and transmitted waves. Periodically distributed mismatch zones, i.e., the piezo patches, produce frequency dependent, wave-dynamic characteristics, which include the generation of band gaps, or stop bands in the frequency domain. The extent of induced band gaps depends on the mismatch in impedance generated by each patch. The total impedance mismatch, in turn, is determined by the added mass and stiffness of each patch as well as the shunting electrical impedance. Proper selection of the shunting electric-circuit thus provides control over the attenuation capabilities of the piezo-plate structure, as well as the ability to adapt to changing excitation conditions. Control of wave-propagation attenuation and vibration reduction for plates with periodic, shunted, piezoelectric patches is demonstrated numerically, employing finite-element models of the considered structures.

A Perturbation Approach for Predicting Wave Propagation in One-Dimensional Nonlinear Periodic Structures

Wave propagation in one-dimensional nonlinear periodic structures is investigated through a novel perturbation analysis and accompanying numerical simulations. Several chain unit cells are considered featuring a sequence of masses connected by linear and cubic springs. Approximate closed-form, first-order dispersion relations capture the effect of nonlinearities on harmonic wave propagation. These relationships document amplitude-dependent behavior to include tunable dispersion curves and cutoff frequencies, which shift with wave amplitude. Numerical simulations verify the dispersion relations obtained from the perturbation analysis. The simulation of an infinite domain is accomplished by employing viscous-based perfectly matched layers appended to the chain ends. Numerically estimated wavenumbers show good agreement with the perturbation predictions. Several example chain unit cells demonstrate the manner in which nonlinearities in periodic systems may be exploited to achieve amplitude-dependent dispersion properties for the design of tunable acoustic devices.

Wave Propagation in Auxetic Tetrachiral Honeycombs

This paper describes a numerical and experimental investigation on the flexural wave propagation properties of a novel class of negative Poissons ratio honeycombs with tetrachiral topology. Tetrachiral honeycombs are structures defined by cylinders connected by four tangent ligaments, leading to a negative Poissons ratio (auxetic) behavior in the plane due to combined cylinder rotation and bending of the ribs. A Bloch wave approach is applied to the representative unit cell of the honeycomb to calculate the dispersion characteristics and phase constant surfaces varying the geometric parameters of the unit cell. The modal density of the tetrachiral lattice and of a sandwich panel having the tetrachiral as core is extracted from the integration of the phase constant surfaces, and compared with the experimental ones obtained from measurements using scanning laser vibrometers.