scholarly journals Geometrically nonlinear transverse vibrations of Bernoulli-Euler beams carrying a finite number of masses and taking into account their rotatory inertia

2017 ◽  
Vol 199 ◽  
pp. 489-494 ◽  
Author(s):  
Adri Ahmed ◽  
Benamar Rhali
Keyword(s):  
Finite Number ◽  
Geometrically Nonlinear ◽  
Rotatory Inertia ◽  
Transverse Vibrations

A Finite Element Analysis of the Harmonic Response of Damped Five-Layer Plates

1985 ◽  
Vol 199 (4) ◽  
pp. 311-317
Author(s):  
E Ioannides ◽  
P Grootenhuis
Keyword(s):  
Finite Element ◽  
Solution Procedure ◽  
Rotatory Inertia ◽  
Element Analysis ◽  
Harmonic Response ◽  
Harmonic Vibrations ◽  
Transverse Vibrations ◽  
Strain Behaviour ◽  
Vibrating Plates ◽  
Viscoelastic Layers

Solutions have been obtained for the harmonic vibrations of five-layer plates by means of a finite element method. This method is an extension of a previously developed analysis for three-layer plates. The five-layer plates contain two constrained viscoelastic layers which provide the damping. The degenerate case when the thickness of the middle elastic layer becomes zero and the plate is reduced to a four-layer one has also been included in the solution procedure. Moreover, the method allows for the study of both torsional and transverse vibrations of five (or four)-layer beams treated as vibrating plates with a large aspect ratio. As in the case of three-layer plates, triangular finite elements are used to allow for a greater variety of shapes. In the analysis damping is introduced by replacing the real moduli of the viscoelastic material by complex equivalent moduli which account for the phase difference between strain and stress. The present method allows for the non-linear stress-strain behaviour of the viscoelastic layers, the effects of the rotatory inertia and the extension within the viscoelastic layers. The finite element computations have been verified by comparison with experimental results for four-layer and five-layer beams in transverse and torsional vibrations and a five-layer square plate in transverse vibration.

Upper and Lower Bounds of Frequencies for Cantilever Bars of Variable Cross Sections

1966 ◽  
Vol 33 (4) ◽  
pp. 948-950 ◽  
Author(s):  
J. H. Gaines ◽  
Enrico Volterra
Keyword(s):  
Lower Bounds ◽  
Cross Sections ◽  
Transverse Shear ◽  
Natural Frequencies ◽  
Numerical Results ◽  
Upper And Lower Bounds ◽  
Variable Cross ◽  
Tabular Form ◽  
Rotatory Inertia ◽  
Transverse Vibrations

Upper and lower bounds of frequencies of transverse vibrations of cantilever bars of variable cross sections are presented, taking into account the effects of transverse shear and of rotatory inertia. Numerical results for the first four natural frequencies are presented in tabular form for different inertia characteristics of the bars.

scholarly journals Nonlinear Dynamic Analysis of Plates Stiffened by Parallel Beams with Deformable Connection

2014 ◽  
Vol 2014 ◽  
pp. 1-22 ◽  
Author(s):  
J. A. Dourakopoulos ◽  
E. J. Sapountzakis
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Practical Interest ◽  
Geometrically Nonlinear ◽  
Analog Equation Method ◽  
Transverse Vibrations ◽  
Proposed Model ◽  
Great Practical Interest ◽  
Analog Equation

In this paper a general solution to the geometrically nonlinear dynamic analysis of plates stiffened by arbitrarily placed parallel beams of arbitrary doubly symmetric cross-section, subjected to dynamic loading, is presented. The plate-beam structure is assumed to undergo moderate large deflections and the nonlinear analysis is carried out by retaining nonlinear terms in the kinematical relations. According to the proposed model, the arbitrarily placed parallel stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, making the hypothesis that the plate and the beams can slip in all directions of the connection without separation and taking into account the arising tractions in all directions at the fictitious interfaces. These tractions are integrated with respect to each half of the interface width resulting in two interface lines, along which the loading of the beams and the additional loading of the plate are defined. Six boundary value problems are formulated and solved using the analog equation method (AEM), a BEM-based method. Both free and forced transverse vibrations are considered and numerical examples with great practical interest are presented demonstrating the effectiveness, wherever possible, the accuracy, and the range of applications of the proposed method.

Criteria and Methods for Reliable Three-Dimensional Image Reconstruction

1974 ◽  
Vol 32 ◽  
pp. 330-331
Author(s):  
R. A. Crowther
Keyword(s):  
Image Reconstruction ◽  
Finite Number ◽  
Density Distribution ◽  
Electron Micrographs ◽  
Mathematical Problem ◽  
Three Dimensional ◽  
Ideal Case ◽  
Dimensional Image ◽  
General Object ◽  
The Ideal

The reconstruction of a three-dimensional image of a specimen from a set of electron micrographs reduces, under certain assumptions about the imaging process in the microscope, to the mathematical problem of reconstructing a density distribution from a set of its plane projections.In the absence of noise we can formulate a purely geometrical criterion, which, for a general object, fixes the resolution attainable from a given finite number of views in terms of the size of the object. For simplicity we take the ideal case of projections collected by a series of m equally spaced tilts about a single axis.

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