Low-frequency Lamb wave mixing for fatigue damage evaluation using phase-reversal approach

Bending edge wave on a functionally graded fluid‐saturated porous magneto‐electro‐elastic plate

“…This shows that for MEE fluid-saturated porous plate, the cut-off frequency strictly depends upon the porosity parameter 𝜙 𝑝 , and the grading function. But if the porosity 𝜙 𝑝 = 0, then the cut-off frequency for the MEE plate is obtained from Equation (38) and is given by,…”

“…In recent years, Hughes et al [35,36] examined the features of fundamental edge wave mode numerically and experimentally. Some other experimental studies towards the detection of damages with the help of edge wave in thin elastic structures were done by Zhu et al [37,38], Wilde et al [39,40], and Chu and Courtney [41].…”

“…Some other experimental studies towards the detection of damages with the help of edge wave in thin elastic structures were done by Zhu et al. [37, 38], Wilde et al. [39, 40], and Chu and Courtney [41].…”

“…𝑁 1 = μ − χ𝑐 + M𝑐 − 𝑔(𝑛)𝜈 𝑠 ( μ𝑠 − χ𝑠 𝑐 ), 𝑁 2 = 1 − χ𝑐 − 𝑔(𝑛)𝜈 𝑠 (1 − χ𝑠 𝑐 ) and 𝑁 4 = 2 − μ − 𝑔(𝑛)𝜈 𝑠 (2 − μ𝑠 ) + 𝑔(𝑛) χ𝑠 𝑐 𝜈 𝑠 − χ𝑐 . Therefore, Equation (38) will exist if χ𝑐 ≠ 1 and 𝑁 2 ≠ 0.Case-IIThe proposed model can be decreased in the case of the bending edge wave on the isotropic plate together with the Winkler foundation model by considering the materials parameter used in the proposed model as follows: 𝑆 1 = 𝐸 1−𝜈 2 , 𝜙 𝑝 = 0, 𝐺 = 0, 𝑓 𝑥 2 𝑓 𝑥 3 (𝑛) = 2, 𝑁 1 = μ = 𝜈 (Poisson ratio), 𝑁 2 = 1, 𝑁 3 = 0, 𝑁 4 = (2 − μ), 𝜈 𝑠 = 0, 𝜏 𝑐 = 0, χ𝑐 = 0, M𝑐 = 0, 𝜎 0 = 0, 𝐷 = 2 𝜌 𝑠 = 𝜌 and neglecting the inertia term, the dispersion relation Equation(38) reduces to the form (with dimension), Variation of cut-off frequency for different foundation constant and grading index, (a) and (b) corresponding to Equations (40) and(41).…”

Mixing of Non-Collinear Lamb Wave Pulses in Plates with Material Nonlinearity

“…In the finite element simulations, the material nonlinearities and field equations can be modelled by considering the third-order terms of Murnaghan’s strain energy function [ 24 , 25 , 26 ]. Assuming the reference configuration is X and the current configuration of material is x , the displacement vector u is and the displacement gradient tensor F is where is the displacement gradient and I is the identity tensor.…”