Guided waves dispersion analysis for prestressed viscoelastic waveguides by means of the SAFE method

Abstract

a b s t r a c tThe work focuses on the effect of a general state of initial stress on the dispersion behavior of guided waves in viscoelastic waveguides. To this purpose, an extension of the Semi Analytical Finite Element (SAFE) method is proposed to formulate the wave equation and to extract the waves modal properties in viscoelastic prestressed waveguides. The wave equation is derived in linearized incremental form within an updated Lagrangian framework, where the prestressed configuration is considered to be slightly deviated from the corresponding unstressed one. Next, by using the SAFE method and the Boltzmann superposition principle, a linear algebraic system of equations is obtained in the complex wavenumber-frequency domain. Dispersive guided waves wavelengths, phase velocity, group velocity and attenuation, are extracted by solving a polynomial eigenvalue problem. A modal formula for the wave energy velocity calculation, that exploits the wave equation SAFE matrices only, is proposed. Such formula is based on the linearized incremental form of the Poynting theorem obtained by manipulating the energy balance principle expressed in material description.Numerical examples on a hysteretic 113A standard rail profile and on an ASME 1-1/2 Schedule 160 steel pipe, considering various states of initial stress and applied loadings, are presented to show the effect of prestress on the dispersive properties of mechanical waves in viscoelastic waveguides.

Simulation of elastic guided waves interacting with defects in arbitrarily long structures using the Scaled Boundary Finite Element Method

“…Substituting (11) into (9) one obtains the eigenvalue problem −Zψ = λψ (15) or in matrix notation −Z = (16) where the columns of are the eigenvectors and denotes the diagonal matrix with the eigenvalues being the elements on the diagonal. It is well known that the same eigenvalue problem [64][65][66] or similar formulations [36][37][38] can be used to compute the wavenumbers and mode shapes of propagating modes in the waveguide, and thus obtain the dispersion curves. Z is a Hamiltonian matrix; if λ is an eigenvalue, so are −λ, λ and −λ.…”

“…In the context of ultrasonic guided waves in solids, the concept of discretizing the cross-section only is often referred to as Semi-Analytical Finite Element (SAFE) Method [36][37][38], which uses the same quadratic eigenvalue problem as the TLM. It has been extended by discretizing a two-dimensional cross-section with standard Finite Elements in order to describe more general three-dimensional waveguides.…”

A Numerical Study on the Excitation of Guided Waves in Rectangular Plates Using Multiple Point Sources

“…Numerical solutions are attractive due to the flexibility of dealing with arbitrary geometry and complex boundary conditions. SAFE is one of the most popular numerical techniques for calculating the eigenmodes of guided waves in an arbitrary cross-sectional waveguide [13][14][15][16][17][18][19][20]. SAFE introduces analytical modal solutions into the wave equation, and requires only the cross-sectional area of the waveguide to be meshed.…”

Guided wave propagation in metallic and resin plates loaded with water on single surface

“…Recently, SAFE calculations considering leaky media have become feasible by introducing absorbing layers and perfectly matched layers surrounding the leaky media or by expressing the outer open domain with the boundary element method [7][8][9][10][11]. SAFE calculations for leaky Lamb waves were formulated based on the characteristic that waves leaking into fluids propagate as plane harmonic waves with the sound speed of the fluids [1].…”