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A problem of a nonconfocal suspended strip in an elliptical waveguide is analyzed by using a semianalytical approach, which is the so-called null-field boundary integral-equation method (BIEM). The null-field BIEM is proposed by introducing the idea of null field, degenerate kernels, and eigenfunction expansion to improve the conventional dual(More)
In this paper, a semi-analytical approach is proposed to solve natural frequencies and natural modes for circular plates with multiple circular holes by using the indirect formulation in conjunction with degenerate kernels and Fourier series. All the kernels in the indirect formulation are expanded into degenerate form. By uniformly collocating points on(More)
Keywords: Green's function Method of fundamental solutions Image method Trefftz method a b s t r a c t In this paper, the Green's function for the annular Laplace problem is first derived by using the image method which can be seen as a special case of method of fundamental solutions. Three cases, fixed–fixed, fixed–free and free–fixed boundary conditions(More)
In this paper, a semi-analytical approach is proposed to solve the scattering problem of flexural waves and to determine dynamic moment concentration factors (DMCFs) in an infinite thin plate with multiple circular holes. The null-field integral formulation is employed in conjunction with degenerate kernels, tensor transformation and Fourier series. In the(More)
Consider the over-determined system Fx = b where F ∈ R m×n , m ≥ n and rank (F) = r ≤ n, the effective condition number is defined by Cond eff = b σ r x , where the singular values of F are given as σmax = σ1 ≥ σ2 ≥ ... ≥ σr > 0 and σr+1 = ... = σn = 0. For the general perturbed system (A + ∆A)(x + ∆x) = b + ∆b involving both ∆A and ∆b, the new error bounds(More)
Spurious eigensolutions in the boundary integral equation (BIE) or boundary element method (BEM) for doubly-connected domain problems, the eccentric and annular membranes , are studied analytically and numerically in this paper. For the mathematical analysis, we employ the null-field integral equation, the degenerate kernels and the Fourier series to prove(More)