Based on a non classical plate theory, an analytical model is proposed for the first time to analyze free vibration problem of partially cracked thin isotropic submerged plate in the presence of thermal environment. The governing equation for the cracked plate is derived using the Kirchhoff’s thin plate theory and the modified couple stress theory. The crack terms are formulated using simplifie...

Elaborating on a Maxwellian representation of longitudinal wave propagation in a viscothermal fluid, a general nonlocal macroscopic theory of sound propagation in homogeneous porous media saturated with a viscothermal fluid has been recently proposed. The present paper validates this new nonlocal Maxwellian theory by showing that, in the case of the propagation in straight circular tubes, it is...

The article addresses the mathematical modeling of folding a thin elastic sheet along prescribed curved arc. A rigorous model reduction from general hyperelastic material description is carried out under appropriate scaling conditions on energy and geometric properties arc in dependence small thickness. resulting two-dimensional piecewise nonlinear Kirchhoff plate bending with continuity condit...

Normalized mutual power of radiation, active and reactive, has been analyzed in this paper. The sound source is an annular plate, clamped to a planar, rigid and infinite baffle. The plate’s vibrations are axisymmetric and sinusoidal with respect to time. A Kirchhoff-Love’s model of a perfectly elastic plate has been used. First, the integral formulas for the mutual sound power have been present...

The fundamental relationship between matrices over the rational numbers and a newly defined type of graph, a Kirchhoff graph, is discussed. For a given matrix, a Kirchhoff graph for that matrix represents the orthogonal complementarity of the null and row spaces of the matrix. A number of basic results are proven, and then a relatively complicated Kirchhoff graph is constructed for a matrix tha...

In this paper, we study Kirchhoff type problems on a bounded domain. We consider the cases that the nonlinearity is superlinear near zero but asymptotically 4-linear at infinity, and the nonlinearity is asymptotically linear near zero but 4-superlinear at infinity. By computing the relevant critical groups, we obtain nontrivial solutions via Morse theory.

In this article, we consider the multiplicity of positive solutions for a class of Kirchhoff type problems with concave and convex nonlinearities. Under appropriate assumptions, we prove that the problem has at least two positive solutions, moreover, one of which is a positive ground state solution. Our approach is mainly based on the Nehari manifold, Ekeland variational principle and the theor...

The diffraction theory of Kirchhoff is applied to the semi-infinite aperture of a black half-screen. The derivative of the spherical Green's function is taken into account without any approximation. The uniformly evaluated scattering integral is compared with the physical optics solution. It is shown that the non-omitted term causes the existence of fictitious diffracted waves.