Effects of Geometric Imperfections on Large-Amplitude Vibrations of Rectangular Plates With Hysteresis Damping

1984 ◽  
Vol 51 (1) ◽  
pp. 216-220 ◽  
Author(s):  
David Hui
Keyword(s):  
Large Amplitude ◽  
Plate Thickness ◽  
Rectangular Plates ◽  
Structural Damping ◽  
Geometric Imperfections ◽  
Geometric Imperfection ◽  
Forcing Function ◽  
Initial Geometric Imperfections ◽  
Spatial Shape ◽  
Large Amplitude Vibrations

The present paper deals with the effects of initial geometric imperfections on large-amplitude vibrations of simply supported rectangular plates. The vibration mode, the geometric imperfection, and the forcing function are taken to be of the same spatial shape. It is found that geometric imperfections of the order of a fraction of the plate thickness may significantly raise the free linear vibration frequencies. Furthermore, contrary to the commonly accepted theory that large-amplitude vibrations of plates are of the hardening type, the presence of small geometric imperfections may cause the plate to exhibit a soft-spring behavior. The effects of hysteresis (structural) damping on the vibration amplitude are also examined.

Effects of Initial Geometric Imperfections on Parametric Instability of Rectangular Plates

2001 ◽  
Author(s):  
Lyne St-Georges ◽  
G. L. Ostiguy
Keyword(s):  
Lateral Displacement ◽  
Plate Thickness ◽  
Parametric Instability ◽  
Experimental Tests ◽  
Rectangular Plates ◽  
Rational Analysis ◽  
Geometric Imperfections ◽  
Simply Supported ◽  
Geometrical Imperfections ◽  
Initial Geometric Imperfections

Abstract The authors present a rational analysis of the effect of initial geometric imperfections on the dynamic behaviour of rectangular plates activated by a parametric excitation. This subject has been extensively investigated theoretically in the past, but no experimental data seems to be complete enough to validate the theory. The main objective of this investigation is to fill this void by performing experimental tests on geometrically imperfect plates, and to highlight the geometric imperfection’s influence on resonance’s curves. The study is carried out for an isotropic, elastic, homogeneous, and thin rectangular plate. The plate under investigation is subjected to the action of an in-plane force uniformly distributed along two opposite edges, is initially stress free and simply supported. Theoretical calculation and experimental tests are performed. In the theoretical approach, a dynamic version of the Von Kármán non-linear theory is used to evaluate the lateral displacement of the plate. The test rig used in the experimentation simulates simply supported edges and can accept plates with different aspect ratio. The test plates are pre-formed with lateral deflection or geometrical imperfections, in a shape corresponding to various vibration modes. Comparison between experimental and theoretical results reveals good agreement and allows the determination of the theory’s limitations. The theory used correctly describes the behaviour of the plate when imperfection amplitude is inferior to the plate thickness.

scholarly journals ANÁLISE NUMÉRICA DE PERFIS DE AÇO FORMADOS A FRIO EM SEÇÃO “I” CONSTITUÍDA POR DUPLO “U” SUBMETIDOS À COMPRESSÃO

2020 ◽  
Vol 12 (1) ◽  
pp. 95-110
Author(s):  
Gabriel Cintra Macedo ◽  
Wanderson Fernando Maia
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Plate Thickness ◽  
Experimental Studies ◽  
Structural Behavior ◽  
The Finite Element Method ◽  
Geometric Imperfections ◽  
Initial Geometric Imperfections ◽  
Normal Strength ◽  
Double Channel

Although the section “I”, in double channel, is widely used, there are few studies on its behavior. Therefore, this work aims to contribute to a greater mastery over the structural behavior of this built-up sections. A nonlinear numerical analysis was performed using the Finite Element Method in the Ansys program, using existing experimental studies as a comparative database. The effect of length, number of connections, plate thickness and the presence of geometric and material imperfections on the normal strength of the columns. For this analysis, it was essential to consider the initial geometric imperfections, because there was a considerable reduction in the normal strength of the columns, thus getting closer to the values obtained experimentally. With regard to normative procedures, values against security were found in most cases, showing the need to conduct further studies in the area for the development of more appropriate formulations.

Effects of Geometric Imperfections on Vibrations of Biaxially Compressed Rectangular Flat Plates

1983 ◽  
Vol 50 (4a) ◽  
pp. 750-756 ◽  
Author(s):  
David Hui ◽  
A. W. Leissa
Keyword(s):  
Plate Thickness ◽  
Biaxial Compression ◽  
Vibration Frequencies ◽  
Finite Deflections ◽  
Flat Plates ◽  
Geometric Imperfections ◽  
Geometric Imperfection ◽  
Simply Supported ◽  
Initial Geometric Imperfection

This paper deals with the effects of geometric imperfections on the vibration frequencies of simply supported flat plates under in-plane uniaxial or biaxial compression. The analysis is based on a solution of the nonlinear von Ka´rma´n equations for finite deflections, incorporating the influence of an initial geometric imperfection. It is found that significant increase in the vibration frequencies may occur for imperfection amplitude of the order of a fraction of the plate thickness, even in the absence of in-plane forces.

Influence of Geometric Imperfections and In-Plane Constraints on Nonlinear Vibrations of Simply Supported Cylindrical Panels

1984 ◽  
Vol 51 (2) ◽  
pp. 383-390 ◽  
Author(s):  
David Hui
Keyword(s):  
Shell Thickness ◽  
Nonlinear Vibrations ◽  
Vibration Mode ◽  
Vibration Frequencies ◽  
Linear Vibration ◽  
Geometric Imperfections ◽  
Simply Supported ◽  
Cylindrical Panels ◽  
Initial Geometric Imperfections ◽  
Large Amplitude Vibrations

This papers deals with the effects of initial geometric imperfections on large-amplitude vibrations of cylindrical panels simply supported along all four edges. In-plane movable and in-plane immovable boundary conditions are considered for each pair of parallel edges. Depending on whether the number of axial and circumferential half waves are odd or even, the presence of geometric imperfections (taken to be of the same shape as the vibration mode) of the order of the shell thickness may significantly raise or lower the linear vibration frequencies. In general, an increase (decrease) in the linear vibration frequency corresponds to a more pronounced soft-spring (hard-spring) behavior in nonlinear vibration.

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