Matteo Mazzotti

A coupled SAFE-2.5D BEM approach for the dispersion analysis of damped leaky guided waves in embedded waveguides of arbitrary cross-section

The paper presents a Semi-Analytical Finite Element (SAFE) formulation coupled with a 2.5D Boundary Element Method (BEM) for the computation of the dispersion properties of viscoelastic waveguides with arbitrary cross-section and embedded in unbounded isotropic viscoelastic media. Attenuation of guided modes is described through the imaginary component of the axial wavenumber, which accounts for material damping, introduced via linear viscoelastic constitutive relations, as well as energy loss due to radiation of bulk waves in the surrounding media. Energy radiation is accounted in the SAFE model by introducing an equivalent dynamic stiffness matrix for the surrounding medium, which is derived from a regularized 2.5D boundary element formulation. The resulting dispersive wave equation is configured as a nonlinear eigenvalue problem in the complex axial wavenumber. The eigenvalue problem is reduced to a linear one inside a chosen contour in the complex plane of the axial wavenumber by using a contour integral method. Poles of leaky and evanescent modes are obtained by choosing appropriately the phase of the wavenumbers normal to the interface in compliance with the nature of the waves in the surrounding medium. Finally, the obtained eigensolutions are post-processed to compute the energy velocity and the radiated wavefield in the surrounding domain. The reliability of the method is first validated on existing results for waveguides of circular cross sections embedded in elastic and viscoelastic media. Next, the potential of the proposed numerical framework is shown by computing the dispersion properties for a square steel bar embedded in grout and for an H-shaped steel pile embedded in soil.

Dispersion analysis of leaky guided waves in fluid-loaded waveguides of generic shape.

A fully coupled 2.5D formulation is proposed to compute the dispersive parameters of waveguides with arbitrary cross-section immersed in infinite inviscid fluids. The discretization of the waveguide is performed by means of a Semi-Analytical Finite Element (SAFE) approach, whereas a 2.5D BEM formulation is used to model the impedance of the surrounding infinite fluid. The kernels of the boundary integrals contain the fundamental solutions of the space Fourier-transformed Helmholtz equation, which governs the wave propagation process in the fluid domain. Numerical difficulties related to the evaluation of singular integrals are avoided by using a regularization procedure. To improve the numerical stability of the discretized boundary integral equations for the external Helmholtz problem, the so called CHIEF method is used. The discrete wave equation results in a nonlinear eigenvalue problem in the complex axial wavenumbers that is solved at the frequencies of interest by means of a contour integral algorithm. In order to separate physical from non-physical solutions and to fulfill the requirement of holomorphicity of the dynamic stiffness matrix inside the complex wavenumber contour, the phase of the radial bulk wavenumber is uniquely defined by enforcing the Snell-Descartes law at the fluid-waveguide interface. Three numerical applications are presented. The computed dispersion curves for a circular bar immersed in oil are in agreement with those extracted using the Global Matrix Method. Novel results are presented for viscoelastic steel bars of square and L-shaped cross-section immersed in water.

Band structure analysis of leaky Bloch waves in 2D phononic crystal plates

HighlightsA hybrid finite element‐plane wave expansion method is proposed.Phononic crystal plates in contact with acoustic half‐spaces are considered.Complex Bloch wavenumbers are obtained from a nonlinear eigenvalue problem.Attenuation band diagrams are shown for 1D and 2D phononic crystal plates. &NA; A hybrid Finite Element‐Plane Wave Expansion method is presented for the band structure analysis of phononic crystal plates with two dimensional lattice that are in contact with acoustic half‐spaces. The method enables the computation of both real (propagative) and imaginary (attenuation) components of the Bloch wavenumber at any given frequency. Three numerical applications are presented: a benchmark dispersion analysis for an oil‐loaded Titanium isotropic plate, the band structure analysis of a water‐loaded Tungsten slab with square cylindrical cavities and a phononic crystal plate composed of Aurum cylinders embedded in an epoxy matrix.

Ultrasonic leaky guided waves in fluid-coupled generic waveguides: hybrid finite-boundary element dispersion analysis and experimental validation

A numerical procedure is presented for the computation of dispersive parameters in elastic mechanical waveguides of generic cross-section immersed in non-viscous fluids. The method uses a semi-analytical finite element formulation to describe the solid waveguide, while a two-and-a-half dimensional boundary element method is used to represent the unbounded surrounding fluid. Leaky and trapped guided wave modes are found on the appropriate Riemann sheets by enforcing the generalized Snell–Descartes law along the fluid-structure interface and solving a nonlinear eigenvalue problem. The method is validated experimentally by extracting the frequency-real wavenumber dispersion curves of a rectangular bar and a thin angle aluminum bar via a two-dimensional Fast Fourier Transform. In both cases, a very good agreement is observed between the numerical and the experimental solutions.

A 2.5D boundary element formulation for modeling damped waves in arbitrary cross-section waveguides and cavities

A regularized 2.5D Boundary Element Method (BEM) is proposed to predict the dispersion properties of damped stress guided waves in waveguides and cavities of arbitrary cross-section. The wave attenuation, induced by material damping, is introduced using linear viscoelastic constitutive relations and described in a spatial manner by the imaginary component of the axial wavenumber. The discretized dispersive wave equation results in a nonlinear eigenvalue problem, which is solved obtaining complex axial wavenumbers for a fixed frequency using a contour integral algorithm. Due to the singular characteristics and the multivalued feature of the wave equation, the requirement of holomorphicity inside the contour region over the complex wavenumber plane is fulfilled by the introduction of the Sommerfeld branch cuts and by the choice of the permissible Riemann sheets. A post processing analysis is developed for the extraction of the energy velocity of propagative guided waves. The reliability of the method is demonstrated by comparing the results obtained for a rail and a bar with square cross-section with those obtained from a 2.5D Finite Element formulation also known in literature as Semi Analytical Finite Element (SAFE) method. Next, to show the potential of the proposed numerical framework, dispersion properties are predicted for surface waves propagating along cylindrical cavities of arbitrary cross-section. It is demonstrated that the attenuation of surface waves approaches asymptotically the attenuation of Rayleigh waves.

Experimental Observation of a Large Low-Frequency Band Gap in a Polymer Waveguide

The quest for large and low frequency band gaps is one of the principal objectives pursued in a number of engineering applications, ranging from noise absorption to vibration control, to seismic wave abatement. For this purpose, a plethora of complex architectures (including multi-phase materials) and multi-physics approaches have been proposed in the past, often involving difficulties in their practical realization. To address this issue, in this work we propose an easy-to-manufacture design able to open large, low frequency complete Lamb band gaps exploiting a suitable arrangement of masses and stiffnesses produced by cavities in a monolithic material. The performance of the designed structure is evaluated by numerical simulations and confirmed by Scanning Laser Doppler Vibrometer (SLDV) measurements on an isotropic polyvinyl chloride plate in which a square ring region of cross-like cavities is fabricated. The full wave field reconstruction clearly confirms the ability of even a limited number of unit cell rows of the proposed design to efficiently attenuate Lamb waves. In addition, numerical simulations show that the structure allows to shift of the central frequency of the BG through geometrical modifications. The design may be of interest for applications in which large BGs at low frequencies are required.

Computation of leaky guided waves dispersion spectrum using vibroacoustic analyses and the Matrix Pencil Method: a validation study for immersed rectangular waveguides.

The paper aims at validating a recently proposed Semi Analytical Finite Element (SAFE) formulation coupled with a 2.5D Boundary Element Method (2.5D BEM) for the extraction of dispersion data in immersed waveguides of generic cross-section. To this end, three-dimensional vibroacoustic analyses are carried out on two waveguides of square and rectangular cross-section immersed in water using the commercial Finite Element software Abaqus/Explicit. Real wavenumber and attenuation dispersive data are extracted by means of a modified Matrix Pencil Method. It is demonstrated that the results obtained using the two techniques are in very good agreement.

Boundary condition identification for a grid model by experimental and numerical dynamic analysis

There is a growing need to characterize unknown foundations and assess substructures in existing bridges. It is becoming an important issue for the serviceability and safety of bridges as well as for the possibility of partial reuse of existing infrastructures. Within this broader contest, this paper investigates the possibility of identifying, locating and quantifying changes of boundary conditions, by leveraging a simply supported grid structure with a composite deck. Multi-reference impact tests are operated for the grid model and modification of one supporting bearing is done by replacing a steel cylindrical roller with a roller of compliant material. Impact based modal analysis provide global modal parameters such as damped natural frequencies, mode shapes and flexibility matrix that are used as indicators of boundary condition changes. An updating process combining a hybrid optimization algorithm and the finite element software suit ABAQUS is presented in this paper. The updated ABAQUS model of the grid that simulates the supporting bearing with springs is used to detect and quantify the change of the boundary conditions.

Virtual Laboratory for Leveraging Technology for Bridges and Constructed Systems

The writers are exploring the development of an innovative and adaptive resource for highway bridge owners, managers, engineers as well as technicians from non-destructive testing (NDT) and structural health monitoring (SHM) industries and the public. The primary objective is an official Federal Highway Administration (FHWA) website offering guidance and training on how technology tools may be selected and applied with sufficient depth to generate reliable and actionable information. Currently a large number of technology tools in the realm of “information, communication, computing and data technology,” “software for modelling and analysis of multi-physics phenomena and civil engineering systems,” “sensing, imaging and non-destructive probing,” and, “uncertainty and risk analysis and decision-making” are available for off-the-shelf purchase or applications by consultants. However, there are very few institutions that offer an ability for an integrative leveraging of such tools and the resulting data in conjunction with engineering heuristics for meaningful, feasible and effective solutions to infrastructure performance problems.

An investigation on wireless sensors for asset management and health monitoring of civil structures

Application of wireless sensors and sensor networks for Structural Health Monitoring has been investigated for a long time. Key limitations for practical use are energy requirements, connectivity, and integration with existing systems. Current sensors and sensor networks mainly rely on wired connectivity for communication and external power source for energy. This paper presents a suite of wireless sensors that are low-cost, maintenance free, rugged, and have long service life. The majority of the sensors considered were designed by transforming existing, proven, and robust wired sensors into wireless units. In this study, the wireless sensors were tested in laboratory conditions for calibration and evaluation along with wired sensors. The experimental results were also compared to theoretical results. The tests mostly show satisfactory performance of the wireless units. This work is part of a broader Federal Highway Administration sponsored project intended to ultimately validate a wireless sensing system on a real, operating structure to account for all the uncertainties, environmental conditions and operational variability that are encountered in the field.