The dynamic fundamental solution and BEM formulation for laminated anisotropic Kirchhoff plates

Daros, C.H.

doi:10.1016/j.enganabound.2015.01.001

Cited by 9 publications

(1 citation statement)

References 19 publications

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“…Вопросы нестационарной динамики изотропных пластин затронуты в [8][9][10], ортотропных пластин, в том числе на упругом основании, -в статьях [11][12][13]. Стационарным и нестационарным колебаниям анизотропных и многослойных пластин посвящены статьи [14][15][16][17][18][19]. Исследования стационарного динамического поведения анизотропных пластин на упругих и инерционных основаниях представлены в публикациях [20][21][22].…”

Section: Introductionunclassified

A Fundamental Solution for an Anisotropic Plate on an Inertial Foundation

Serdyuk

Сердюк

Fedotenkov

2022

PSP

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The work is devoted to the construction of a new fundamental solution for a thin elastic anisotropic unbounded Kirchhoff plate on an inertial Winkler foundation. The fundamental solution is a function of the normal movement of two spatial coordinates and time in response to the impact of a single concentrated load, mathematically modeled by the Dirac delta function. The anisotropy model considered in this article has one plane of symmetry that geometrically coincides with the median plane of the plate and is characterized for the Kirchhoff plate model by six independent components of the tensor of elastic constants of the material. The problem statement includes the equations of motion of an anisotropic plate in displacements and initial conditions. The solution of the corresponding initial problem for the fundamental solution is constructed using integral Laplace transformations in time and two-dimensional integral Fourier transform in spatial coordinates. The inverse integral Laplace transform is found analytically with a preliminary analysis of the invertible function. The original fundamental Fourier solution is constructed using the numerical method of integrating rapidly oscillating functions. The parameters of numerical integration are calculated with a given accuracy when analyzing the quality of the desired functions by a continuous norm. For the constructed new fundamental solution, a numerical analysis of the nature of the propagation of nonstationary disturbances is carried out, and the influence of the parameters of the inertial Winkler foundation on the behavior of the normal deflection of an anisotropic plate in time at the point of action of the delta function is investigated. The asymmetric nature of unsteady plate oscillations consistent with the model of the elastic medium under consideration is demonstrated. The constructed fundamental solution makes it possible to investigate the nonstationary normal deflection of an anisotropic plate on an inertial basis under the action of arbitrary loads using an integral operator of the convolution type in spatial coordinates and time. In addition, the fundamental solution has versatility with respect to the properties of the plate materials and the parameters of the foundation, namely: isotropic, transversally isotropic and orthotropic materials can act as the plate material. In this case, the foundation may be inertialess or absent altogether.

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Section: Introductionunclassified