Displaying similar documents to “On the stationary vibrations of a rectangular plate subjected to stress prescribed partially at the circumference.”

Vibrations of Composite Laminated Circular Panels and Shells of Revolution with General Elastic Boundary Conditions via Fourier-Ritz Method

Qingshan Wang, Dongyan Shi, Fuzhen Pang, Qian Liang (2016)

Curved and Layered Structures

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A Fourier-Ritz method for predicting the free vibration of composite laminated circular panels and shells of revolution subjected to various combinations of classical and non-classical boundary conditions is presented in this paper. A modified Fourier series approach in conjunction with a Ritz technique is employed to derive the formulation based on the first-order shear deformation theory. The general boundary condition can be achieved by the boundary spring technique in which three...

A modified Fourier solution for vibration analysis of moderately thick laminated annular sector plates with general boundary conditions, internal radial line and circumferential arc supports

Fuzhen Pang, Haichao Li, Xuhong Miao, Xueren Wang (2017)

Curved and Layered Structures

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In this paper, a modified Fourier solution based on the first-order shear deformation theory is developed for the free vibration problem of moderately thick composite laminated annular sector plates with general boundary conditions, internal radial line and circumferential arc supports. In this solution approach, regardless of boundary conditions, the displacement and rotation components of the sector plate are written in the form of the trigonometric series expansion in which several...

On the Mixed Modulus of Smoothness and a Class of Double Fourier Series

Krasniqi, Xhevat Z. (2013)

Mathematica Balkanica New Series

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MSC 2010: 42A32; 42A20 In this paper we have defined a new class of double numerical sequences. If the coefficients of a double cosine or sine trigonometric series belong to the such classes, then it is verified that they are Fourier series or equivalently their sums are integrable functions. In addition, we obtain an estimate for the mixed modulus of smoothness of a double sine Fourier series whose coefficients belong to the new class of sequences mention above. ...

On the analysis of elastic layers by a Fourier series, Green's function approach

Giorgio Novati (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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The plane strain elastic analysis of a homogeneous and isotropic layer of constant thickness, is formulated using Fourier series expansions in the direction parallel to the layer and suitable Green's functions in the transversal direction. For each frequency the unknown distributions of the Fourier coefficients relevant to the symmetric or skew-symmetric problems are governed by one-dimensional equations which can be solved exactly. The proposed method is used to critically discuss the...

Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

V.V. Zozulya (2017)

Curved and Layered Structures

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New models for micropolar plane curved rods have been developed. 2-D theory is developed from general 2-D equations of linear micropolar elasticity using a special curvilinear system of coordinates related to the middle line of the rod and special hypothesis based on assumptions that take into account the fact that the rod is thin.High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First stress...