Bending and Vibrations of a Thick Plate with Consideration of Bimoments

Abstract

The paper is dedicated to the development of the theory of orthotropic thick plates with consideration of internal forces, moments and bimoments. The equations of motion of a plate are described by two systems of six equations. New equations of motion of the plate and the boundary conditions relative to displacements, forces, moments, and bimoments are given. As an example, the problems of free and forced oscillations of a thick plate are considered under the effect of sinusoidal periodic load. The problem is solved by Finite Difference Method. Eigenfrequencies of the plate are determined, numeric maximum values of displacements, forces and moments of the plate are obtained depending on the frequency of external force. It is shown that when the value of the frequency of external effect approaches the eigenfrequency, there occurs an increase in displacement, force and moment values; that testifies a gradual transition of the motion of plate points into the resonant mode.

To the Solution of Three-Dimensional Problems of Oscillations in the Theory of Elasticity in Thick Plates of Variable Thickness

“…It should be noted that the equations of motion for the bimoment theory of plates of constant thickness developed in [13] [14] [15] [16] could be obtained from the constructed systems of equations. It could be shown that to obtain numerical results with satisfactory accuracy, it is sufficient to take into account eight terms of the series (4).…”

Effect of sulfuric acid solution on thermal conductivity and impact strength of epoxy resin reinforced by silicon dioxide powder

“…Thus causing a decrease in the value of thermal conductivity [13,14]. We note in Fig.5 The thermal conductivity starts to decrease with increasing immersion time this is because the process of immersion in chemical acid may cause, break down the chemical bonds and slip because this acid solution attacks the polymer strongly due to positive ions (H +) works to form a bond With the ends of the polymer chains and negative ions (SO 4 -) attack and weakness the interstitial area and therefore this acid has caused a disruption of the transfer of the phonons, which are responsible for the transfer of heat [15,16]. Table 3 shows the practical results of the Impact strength values for samples reinforced by silicon dioxide before and after immersion in sulfuric acid.…”

Dynamic methods of spatial calculation of structures based on a plate model

“…This article proposes a method for calculating the structures for seismic resistance on the basis of a continuum plate model developed in the framework of the bimoment theory [8][9][10][11][12][13][14][15][16][17], taking into account the spatial stress-strain state. If to consider the law of nonlinearity of displacements distribution in the cross-sections of the plate, then in addition to tensile and shear forces, bending and torsional moments, there appear the additional force factors, called the bimoments.…”