Green’s Functions of Multi-Layered Plane Media with Arbitrary Boundary Conditions and Its Application on the Analysis of the Meander Line Slow-Wave Structure

A method was proposed for solving the dyadic Green’s functions (DGF) and scalar Green’s functions (SGF) of multi-layered plane media in this paper. The DGF and SGF were expressed in matrix form, where the variables of the boundary conditions (BCs) can be separated in matrix form. The obtained DGF and SGF are in explicit form and suitable for arbitrary boundary conditions, owing to the matrix form expression and the separable variables of the BCs. The Green’s functions with typical BCs were obtained, and the dispersion characteristic of the meander line slow-wave structure (ML-SWS) is analyzed based on the proposed DGF. The relative error between the theoretical results and the simulated ones with different relative permittivity is under 3%, which demonstrates that the proposed DGF is suitable for electromagnetic analysis to complicated structure including the ML-SWS.

Fundamental solutions and Hadamard states for a scalar field with arbitrary boundary conditions on an asymptotically AdS spacetimes

We consider the Klein-Gordon operator on an n-dimensional asymptotically anti-de Sitter spacetime (M,g) together with arbitrary boundary conditions encoded by a self-adjoint pseudodifferential operator on ∂M of order up to 2. Using techniques from b-calculus and a propagation of singularities theorem, we prove that there exist advanced and retarded fundamental solutions, characterizing in addition their structural and microlocal properties. We apply this result to the problem of constructing Hadamard two-point distributions. These are bi-distributions which are weak bi-solutions of the underlying equations of motion with a prescribed form of their wavefront set and whose anti-symmetric part is proportional to the difference between the advanced and the retarded fundamental solutions. In particular, under a suitable restriction of the class of admissible boundary conditions and setting to zero the mass, we prove their existence extending to the case under scrutiny a deformation argument which is typically used on globally hyperbolic spacetimes with empty boundary.

Free vibration analysis of three-layer thin cylindrical shell with variable thickness two-dimensional FGM middle layer under arbitrary boundary conditions

In this paper, a unified method is developed to analyze free vibrations of the three-layer functionally graded cylindrical shell with non-uniform thickness. The middle layer is composed of two-dimensional functionally gradient materials (2D-FGMs), whose thickness is set as a function of smooth continuity. Four sets of artificial springs are assigned at the ends of the shells to satisfy the arbitrary boundary conditions. The Sanders’ shell theory is used to obtain the strain and curvature-displacement relations. Furthermore, the Chebyshev polynomials are selected as the admissible function to improve computational efficiency, and the equation of motion is derived by the Rayleigh–Ritz method. The effects of spring stiffness, volume fraction indexes, configuration on of shell, and the change in thickness of the middle layer on the modal characteristics of the new structural shell are also analyzed.