We present a short and self-contained proof of Jin’s theorem about the piecewise syndeticity of difference sets which is entirely elementary, in the sense that no use is made of nonstandard analysis, ergodic theory, measure theory, ultrafilters, or other advanced tools. An explicit bound to the number of shifts that are needed to cover a thick set is provided. Precisely, we prove the following:...

A general process for optimization of a sandwich panel to minimize the effects of air blast loading is presented here. The panel geometry consists of two metal face plates with a crushable honeycomb or other type of core. Optimization is necessary as there is strong coupling between the several variables and the physics, which makes parametric studies relatively ineffective. Virtual testing is ...

A novel multi-functional plate-like lamination that combines a thermal energy storage capability with a structural capability is described. The lamination consists of a paraffin impregnated porous graphitic core (the energy storage volume) encapsulated between rigid graphite/epoxy composite plates and ribs to form a twodimensional box structure. Heat storage is via solidliquid phase transition ...

A three-dimensional mixed variational principle is used to derive a Kth-order two-dimensional linear theory for an anisotropic homogeneous piezoelectric (PZT) plate. Themechanical displacements, the electric potential, the inplane components of the stress tensor, and the in-plane components of the electric displacement are expressed as a Ž nite series of orderK in the thickness coordinate by ta...

the buckling analysis of annular composite plates reinforced by carbon nanotubes subjected to compressive and torsional loads are studied in this paper. the mori-tanaka method is employed to calculate the effective elastic modulus of composites having aligned oriented straight cnts. the effects of cnts volume fractions, orientation angles, boundary conditions and geometric ratio of plate are di...

In this paper, we report a method to increase the open-circuit voltage VOC of an organic solar cell by inserting an interfacial layer between the donor and acceptor layers to form a cascade-type energy band structure. We demonstrate its feasibility using a recently reported asymmetric pentacene derivative, tetraceno 2,3-b thiophene TT as a donor material, C60 as an acceptor material, and copper...

in this paper the nonlinear bending analysis of thick functionally graded plates subjected to mechanical loading is studied. the formulation is derived based on the third-order shear deformation plate theory and von kármán type non-linearity. young’s modulus is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. the principle of virtual wo...

  Free vibration of sandwich plates with temperature dependent functionally graded (FG) face sheets in various thermal environments is investigated. The material properties of FG face sheets are assumed to be temperature-dependent and vary continuously through the thickness according to a power-law distribution in terms of the volume fractions of the constituents. Also, the material properties ...

Two series of experiments are performed to investigate the dynamic response of various essential components of a class of sandwich structures, under high-rate inertial loads. One consists of dynamic inertia tests and the other involves dynamic impact tests. A split Hopkinson bar apparatus is modified and used for these experiments. First, the energy-absorbing characteristics of the plate materi...