A m,n -bipartite graph is a bipartite graph such that one bipartition has m vertices and the other bipartition has n vertices. The tree dumbbell D n, a, b consists of the path Pn−a−b together with a independent vertices adjacent to one pendent vertex of Pn−a−b and b independent vertices adjacent to the other pendent vertex of Pn−a−b. In this paper, firstly, we show that, among m,n bipartite gra...

It is shown that in the Love-Kirchhoff plate theory, an edge wave can travel in a circular thin disk made of an isotropic elastic material. This disk edge wave turns out to be faster than the classic flexural acoustic wave in a straight-edged, semi-infinite, thin plate, a wave which it mimics when the curvature radius becomes very large compared to the wavelength.

We study Hamiltonians with point interactions in spaces of vectorvalued functions. Using some information from the theory of quantum graphs we describe a class of the operators which can be reduced to the direct sum of several one-dimensional problems. This class includes many “model” interactions, in particular, the so-called δ, δp, δ s, δ , and the Kirchhoff couplings. We apply this observati...

We study the mechanical response of elastic rods bent into open knots, focusing on the case of trefoil and cinquefoil topologies. The limit of a weak applied tensile force is studied both analytically and experimentally: the Kirchhoff equations with self-contact are solved by means of matched asymptotic expansions; predictions on both the geometrical and mechanical properties of the elastic equ...

We study Hamiltonians with point interactions in spaces of vectorvalued functions. Using some information from the theory of quantum graphs we describe a class of the operators which can be reduced to the direct sum of several one-dimensional problems. It shown that such reduction is closely connected with the invariance under channel permutations. Examples are provided by some “model” interact...

Abstract A balance law for material momentum in shells and plates is proposed. The implications of this the propagation defects, phase transformations, shocks are explored. developments presented using a purely mechanical theory Cosserat (or directed) shell specialized to cases Kirchhoff–Love linearly elastic plate theory. To explore connections literature on delamination adhesion, applied prob...

‎using nehari manifold methods and mountain pass theorem‎, ‎the existence of nontrivial and radially symmetric solutions for a class of $p$-kirchhoff-type system are established.

In this work, an attempt is done to apply the Kirchhoff plate theory find out vibrational analyses of a nanoplate incorporating surface irregularity effects. The effects on natural frequency vibration nanomaterials, especially for nanoplates, have not been investigated before, and most previous research carried regular nanoplates. Therefore, it must be emphasized that vibrations irregular are n...