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Critical Points of Kirchhoff-Routh-Type Functions
2021For $2\le N\in \N$ and $\G_i\in \R\setminus\{0\}$ we proof that functions of the form $$ H_\G (p_1,\dots, p_N) = \sum_{i\ne j} \G_i\G_j G(p_i,p_j) + \sum_{i=1}^N \G_i^2 R(p_i) , $$ admit critical points under various circumstances. The $p_i$ will either belong to an open, bounded subset $\gO\subset \R^d$ with smooth boundary for $d \ge 3$ or to a ...
Fiernkranz, Tim +1 more
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Properties of minimizers for the fractional Kirchhoff energy functional
Journal of Mathematical Physics, 2023In this paper, we are concerned with a fractional Kirchhoff equation with a general coercive potential. First, we consider some existence and nonexistence of L2-constraint minimizers for related constrained minimization problems. Most importantly, by constructing appropriate trial functions for some delicate energy estimates and studying decay ...
Lintao Liu +3 more
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Dynamic characterisation of functionally graded imperfect Kirchhoff microplates
Composite Structures, 2017This paper aims at thorough investigation of the nonlinear forced vibration characteristics of functionally graded imperfect microplates. To this end, the modified couple stress (MCS) theory together with the Mori-Tanaka homogenisation technique is employed in order to take into account the size-dependent behaviour and the through-thickness variable ...
Ghayesh, M. +3 more
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Mediterranean Journal of Mathematics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xincai Zhu, Changjian Wang, Yanfang Xue
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xincai Zhu, Changjian Wang, Yanfang Xue
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Some analytical solutions of functionally graded Kirchhoff plates
Composites Part B: Engineering, 2015Abstract The elastostatic problem of a functionally graded K irchhoff plate, with no kinematic constraints on the boundary, under constant distributions of transverse loads per unit area and of boundary bending couples is investigated. Closed-form expressions are provided for displacements, bending–twisting curvatures and moments of an isotropic ...
Apuzzo A. +2 more
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The quasiconvex envelope of the Saint Venant–Kirchhoff stored energy function
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1995We give an explicit expression for the quasiconvex envelope of the Saint Venant–Kirchhoff stored energy function in terms of the singular values. This envelope is also the convex, polyconvex and rank 1 convex envelope of the Saint Venant–Kirchhoff stored energy function.
Le Dret, Hervé, Raoult, Annie
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Exact solutions of isotropic viscoelastic functionally graded Kirchhoff plates
Composite Structures, 2014Abstract Viscoelastic equilibrium problems of K irchhoff plates can be solved in a closed form only under special geometric assumptions, loading conditions and kinematic constraints on the boundary. A new solution procedure, based on a correspondence principle between a linearly elastic, homogeneous and orthotropic S aint -V enant beam under ...
BARRETTA, RAFFAELE, Luciano R.
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Generalized functions and Kirchhoff formulas
Aeroacoustics Conference, 1996The theory of generalized functions was developed by L. Schwartz in the forties. It has had a major impact in many areas of mathematics, physics, and engineering. In particular, the solution of many of the problems of wave propagation in acoustics can be simplified by using generalized function theory.
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Multi-image, reverse time, and Kirchhoff migrations with compact Green’s functions
GEOPHYSICS, 2023Using compact representations of Green’s functions we derive a common framework for reverse time migration (RTM) and Kirchhoff migration. These compact Green’s functions (CGFs) are 3D volumes containing traveltimes and amplitudes for the N most representative events in the upcoming/downgoing decomposed 4D wavefields originating from a point source ...
Carlos Cunha +7 more
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2d Kirchhoff Migration for Receiver Function
Chinese Journal of Geophysics, 2007AbstractWe extend seismic reflection Kirchhoff migration to receiver function study, to adapt to lateral velocity variation and improve the precision and resolution of receiver function migration. Model experiment shows that Kirchhoff migration can implement effective image of converted phases, remove the fictitious image, in contrast to ray‐based ...
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