Flexural wave scattering by varying-thickness annular inclusions on infinite thin plates

Multiple scattering of flexural waves on Mindlin plates with circular scatterers

“…This over‐determined system of equations can be solved by the least‐square method based on the generalized inverse matrix. Making the system of equations over‐determined in this way has been found to work well in the previous works [30–34] to avoid ill‐conditioning of the equations. In passing, however, it should be mentioned here that when the wave function expansions are applied to multiple scattering problems, a more standard approach is to express the expansions of the scattered fields by the other ( j ≠ i ) scatterers in Equation (17) in the single local coordinates around the i th scatterer using Graf's addition theorem [35].…”

“…In order to determine the unknown expansion coefficients , , , the numerical collocation technique, which was used in the previous works [30–34], is also employed here. Namely, the infinite series in Equation (25) are truncated with a finite number of terms, i.e., the infinite sums for are replaced by those for , where the integer parameter n max is set large enough to achieve sufficient accuracy.…”

“…Similar formulation has been applied by Wang et al. [31] to analyze the multiple scattering of flexural waves by annular inclusions.…”

Flexural waves in a periodic non-uniform Euler-Bernoulli beam: Analysis for arbitrary contour profiles and applications to wave control

“…They belong to a kind of burgeoning artificial composites usually consisting of multiple elements, and can exhibit some novel properties beyond those of conventional materials. PCs and metamaterials have been successfully adopted to control flexural waves [1][2][3][4][5][6][7][8][9][10][11][12][13], e.g., prohibiting their propagation based on the Bragg scattering [1][2][3]8,12] or the local resonances [7,10], localizing vibrations by a point defect [6], manipulating the phase difference with the aid of metasurface [11,13], cloaking of hidden objects by a specific distribution of material parameters [5], focusing energy via a particular gradient-index (GRIN) PC [4,9], and so forth.…”