Vibration and Post-buckling of In-Plane Loaded Rectangular Plates Using a Multiterm Galerkin’s Method

2002 ◽  
Vol 69 (5) ◽  
pp. 589-592 ◽  
Author(s):  
S. Ilanko
Keyword(s):  
Series Representation ◽  
Initial Imperfection ◽  
Normal Displacement ◽  
Rectangular Plates ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Edge Conditions ◽  
Post Buckling ◽  
The Difference ◽  
Shell Vibration

A procedure to calculate the natural frequencies of in-plane loaded, thin, slightly curved, simply supported rectangular plates is presented, with numerical results. This includes the solutions to von Karman’s static equilibrium equation and the linear shell vibration equation using Galerkin’s method. The compatibility equations are given in terms of Airy stress functions which satisfy the “shear free” and “constant normal displacement” in-plane edge conditions. This procedure is an extension to the method presented by Hui and Leissa, the difference being the use of a multiterm Fourier series representation for the initial imperfection, the static deflection and the vibratory modes.

Steady-state modelling method for matrix-reactance frequency converter with boost topology

2011 ◽  
Vol 60 (2) ◽  
pp. 137-148
Author(s):  
Igor Korotyeyev ◽  
Beata Zięba
Keyword(s):  
Fourier Series ◽  
Steady State ◽  
Differential Equations ◽  
Numerical Method ◽  
Frequency Converter ◽  
Double Fourier Series ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Modelling Method ◽  
Three Phase

Steady-state modelling method for matrix-reactance frequency converter with boost topologyThis paper presents a method intended for calculation of steady-state processes in AC/AC three-phase converters that are described by nonstationary periodical differential equations. The method is based on the extension of nonstationary differential equations and the use of Galerkin's method. The results of calculations are presented in the form of a double Fourier series. As an example, a three-phase matrix-reactance frequency converter (MRFC) with boost topology is considered and the results of computation are compared with a numerical method.

Galerkin’s method revisited and corrected in the problem of Jaworski and Dowell

2021 ◽  
Vol 155 ◽  
pp. 107604
Author(s):  
Isaac Elishakoff ◽  
Marco Amato ◽  
Alessandro Marzani
Keyword(s):  
Galerkin’S Method ◽  
Galerkin's Method

A characteristic type of instability in the large deflexions of elastic plates III. Curved rectangular plates in axial compression

1954 ◽  
Vol 222 (1148) ◽  
pp. 44-59 ◽  
Keyword(s):  
Axial Compression ◽  
Rectangular Plates ◽  
Bending Moments ◽  
Elastic Plates ◽  
Characteristic Type ◽  
Circular Tubes ◽  
Axis Parallel ◽  
Post Buckling ◽  
Thin Walled ◽  
The Stability

The analysis of part I is extended to deal with the case of free-edged rectangular plates having an initial curvature about an axis parallel to one pair of opposite edges and loaded by distributed bending moments applied to the straight edges and compressive forces applied to the curved edges. In particular, the stability and post-buckling behaviour of such plates subjected to the compressive forces alone is studied. The axially symmetrical buckling of thin-walled circular tubes in axial compression is also considered. Experimental plates are found to buckle at loads rather lower than those predicted.

Solution of the Moving Mass Problem Using Complex Eigenfunction Expansions

1999 ◽  
Author(s):  
Keh-Yang Lee ◽  
Anthony A. Renshaw
Keyword(s):  
Solution Technique ◽  
Distributed Parameter ◽  
Moving Mass ◽  
Eigenfunction Expansions ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Mass Problem ◽  
Linearly Independent ◽  
Large Numbers ◽  
Speed Accuracy

Abstract A new solution technique is developed for solving the moving mass problem for nonconservalive, linear, distributed parameter systems using complex eigenfunction expansions. Traditional Galerkin analysis of this problem using complex eigenfunctions fails in the limit of large numbers of terms because complex eigenfunctions are not linearly independent. This linear dependence problem is circumvented in the method proposed here by applying a modal constraint on the velocity of the distributed parameter system (Renshaw, 1997). This constraint is valid for all complete sets of eigenfunctions but must be applied with care for finite dimensional approximations of concentrated loads such as found in the moving mass problem. A set of real differential ordinary equations in time are derived which require exactly as much work to solve as Galerkin’s method with a set of real, linearly independent trial functions. Results indicate that the proposed method is competitive with traditional Galerkin’s method in terms of speed, accuracy and convergence.

Thermal post-buckling of laminated and isotropic rectangular plates with fixed edges: Comparison of experimental and numerical results

2012 ◽  
Vol 226 (10) ◽  
pp. 2393-2401 ◽  
Author(s):  
Marco Amabili ◽  
Mohammad Reza Sareban Tajahmadi
Keyword(s):  
Deformation Theory ◽  
Laboratory Experiments ◽  
Continuation Method ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Numerical Results ◽  
Rectangular Plates ◽  
Arc Length ◽  
Thermal Changes ◽  
Post Buckling

Post-buckling behaviors of laminated composite and isotropic rectangular plates subjected to various thermal changes are studied. Geometric imperfections are taken into account since they play a fundamental role. The plate is modeled using a nonlinear, higher order shear deformation theory. Plates with clamped edges are considered. A pseudo-arc length continuation method is used to obtain numerical results. Laboratory experiments have been performed in order to compare to the numerical calculations.

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