On Wave Modes With Zero Group Velocity in an Elastic Layer

1984 ◽  
Vol 51 (3) ◽  
pp. 652-656 ◽  
Author(s):  
J. L. Tassoulas ◽  
T. R. Akylas
Keyword(s):  
Group Velocity ◽  
Frequency Spectrum ◽  
Elastic Layer ◽  
Harmonic Wave ◽  
Circular Disk ◽  
Free Surfaces ◽  
Time Harmonic ◽  
Free Vibration Frequency ◽  
Zero Group ◽  
Wave Modes

A study is made of time-harmonic wave modes in an elastic layer in plane strain with traction-free surfaces. It is demonstrated that, at points of the Rayleigh-Lamb frequency spectrum where the group velocity vanishes, there exist nonseparable time-harmonic modes in which the amplitudes of the displacements vary linearly in the direction along the layer. These modes are used to explain the terrace-like structure of the free-vibration frequency spectrum of a circular disk.

Topological sensitivity analysis revisited for time-harmonic wave scattering problems. Part I: the free space case

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Frédérique Le Louër ◽  
María-Luisa Rapún
Keyword(s):  
Free Space ◽  
Order Term ◽  
Harmonic Wave ◽  
Dirichlet Condition ◽  
Point Sources ◽  
Neumann Condition ◽  
Scattering Problems ◽  
Content Type ◽  
Time Harmonic ◽  
Topological Gradient

PurposeIn this paper, the authors revisit the computation of closed-form expressions of the topological indicator function for a one step imaging algorithm of two- and three-dimensional sound-soft (Dirichlet condition), sound-hard (Neumann condition) and isotropic inclusions (transmission conditions) in the free space.Design/methodology/approachFrom the addition theorem for translated harmonics, explicit expressions of the scattered waves by infinitesimal circular (and spherical) holes subject to an incident plane wave or a compactly supported distribution of point sources are available. Then the authors derive the first-order term in the asymptotic expansion of the Dirichlet and Neumann traces and their surface derivatives on the boundary of the singular medium perturbation.FindingsAs the shape gradient of shape functionals are expressed in terms of boundary integrals involving the boundary traces of the state and the associated adjoint field, then the topological gradient formulae follow readily.Originality/valueThe authors exhibit singular perturbation asymptotics that can be reused in the derivation of the topological gradient function that generates initial guesses in the iterated numerical solution of any shape optimization problem or imaging problems relying on time-harmonic acoustic wave propagation.

Dependence of the Frequency Spectrum of a Circular Disk on Poisson’s Ratio

1957 ◽  
Vol 24 (1) ◽  
pp. 53-54
Author(s):  
R. L. Sharma
Keyword(s):  
Frequency Spectrum ◽  
Poisson’S Ratio ◽  
Circular Disk ◽  
Intermediate Frequency ◽  
Poisson's Ratio ◽  
Axially Symmetric ◽  
Frequency Range ◽  
Flexural Vibrations ◽  
Circular Disks

Abstract The results of computations of frequencies of axially symmetric flexural vibrations of circular disks are given for an intermediate frequency range and for several values of Poisson’s ratio.

scholarly journals Fatigue crack detection in pipes with multiple mode nonlinear guided waves

2018 ◽  
Vol 18 (1) ◽  
pp. 180-192 ◽  
Author(s):  
Ruiqi Guan ◽  
Ye Lu ◽  
Kai Wang ◽  
Zhongqing Su
Keyword(s):  
Fatigue Crack ◽  
Crack Detection ◽  
Guided Waves ◽  
Second Harmonic ◽  
Experimental Testing ◽  
Harmonic Wave ◽  
Guided Wave ◽  
Element Analysis ◽  
Fatigue Crack Detection ◽  
Wave Modes

This study elaborates fundamental differences in fatigue crack detection using nonlinear guided waves between plate and pipe structures and provides an effective approach for analysing nonlinearity in pipe structures. For this purpose, guided wave propagation and interaction with microcrack in a pipe structure, which introduced a contact acoustic nonlinearity, was analysed through a finite element analysis in which the material nonlinearity was also included. To validate the simulation results, experimental testing was performed using piezoelectric transducers to generate guided waves in a specimen with a fatigue crack. Both methods revealed that the second harmonic wave generated by the breathing behaviour of the microcrack in a pipe had multiple wave modes, unlike the plate scenario using nonlinear guided waves. Therefore, a proper index which considered all the generated wave modes due to the microcrack was developed to quantify the nonlinearity, facilitating the identification of microscale damage and further assessment of the severity of the damage in pipe structures.

Sign in / Sign up

Export Citation Format

Share Document