Effects of Geometric Imperfections on Frequency-Load Interaction of Biaxially Compressed Antisymmetric Angle Ply Rectangular Plates

1985 ◽  
Vol 52 (1) ◽  
pp. 155-162 ◽  
Author(s):  
David Hui
Keyword(s):  
Biaxial Loading ◽  
Composite Plates ◽  
Laminated Plates ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Geometric Imperfections ◽  
Simply Supported ◽  
Interaction Curves

The present paper deals with the influence of small geometric imperfections on the vibration frequencies of rectangular, simply supported, angle ply, thin composite plates subjected to inplane uniaxial or biaxial compressive preload. Depending on the amount of preload, the frequencies of laminated plates with different imperfection shapes may be significantly higher than those for perfect plates, especially in a certain range of fiber angles. Interaction curves between frequency and applied preload are plotted for various fiber angles and imperfection amplitudes for both the uniaxial and equal biaxial loading cases.

BUCKLING AND VIBRATION OF STEPPED, SYMMETRIC CROSS-PLY LAMINATED RECTANGULAR PLATES

2001 ◽  
Vol 01 (03) ◽  
pp. 385-408 ◽  
Author(s):  
Y. XIANG ◽  
J. N. REDDY
Keyword(s):  
Solution Method ◽  
Natural Frequencies ◽  
Laminated Plates ◽  
The Other ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Buckling Loads ◽  
Simply Supported ◽  
Step Thickness ◽  
Thickness Variations

This paper presents the exact buckling loads and vibration frequencies of multi-stepped symmetric cross-ply laminated rectangular plates having two opposite edges simply supported while the other two edges may have any combination of free, simply supported, and clamped conditions. An analytical method that uses the Lévy solution method and the domain decomposition technique is proposed to determine the buckling loads and natural frequencies of stepped laminated plates. Buckling and vibration solutions are obtained for symmetric cross-ply laminated rectangular plates having two-, three- and four-step thickness variations.

Transient Response of Laminated Plates Subject to Close Proximity Explosions

1999 ◽  
Author(s):  
John M. Coggin ◽  
Jeffrey M. K. Chock ◽  
Rakesh K. Kapania ◽  
Eric R. Johnson
Keyword(s):  
Transient Response ◽  
Composite Plates ◽  
Laminated Plates ◽  
Blast Load ◽  
The Novel ◽  
Element Mesh ◽  
Simply Supported ◽  
First Order ◽  
Close Proximity ◽  
Load Types

Abstract We study the transient response of simply supported composite plates subject to close proximity explosions. Many studies are currently availiable in which the blast load is applied uniformly across the plate; and is described by step, N-pulse, or Friedlander equations. The novel aspect considered here is the case for which the blast pressure is due to a close proximity explosion, and is therefore taken to be both spatially and temporally varying. Two methods for calculating blast pressures are developed for arbitrary blast size and distance. A FORTAN program is described that automates the application of an arbitrary blast load to a generic finite element mesh. Modal superposition and NASTRAN solution procedures are verified for several load types and stacking sequences. Results are obtained within the framework of classical and first order plate theories for a variety of parameters including; stacking sequence, blast size, blast distance, and blast calculation method.

scholarly journals Vibration of Skew Sandwich Plates With Laminated Facings

1997 ◽  
Author(s):  
C. M. Wang ◽  
K. K. Ang ◽  
C. Wang
Keyword(s):  
Ritz Method ◽  
Composite Plates ◽  
Sandwich Plates ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Edge Conditions ◽  
System Vibration ◽  
Special Case ◽  
Length Limitation ◽  
Good Agreement

A Rayleigh-Ritz analysis is presented for the free vibration of skew sandwich plates composed of an orthotropic core and laminated facings. By proposing a set of Ritz functions consisting of the product of mathematically complete polynomial functions and the the boundary equations raised to appropriate powers, the Rayleigh-Ritz method can be automated to handle such composite plates with any combination of edge conditions. For convenience and better accurarcy, the Ritz formulation was derived in the skew coordinate system. Vibration frequencies of rectangular plates (a special case of skew plates) obtained via this method have been found to be in good agreement with previous researchers results. Owing to length limitation, only sample vibration frequencies for skew sandwich plates are presented.

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.

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.

Nonlinear Vibrations of Rectangular Plates With Different Boundary Conditions: Theory and Experiments

2005 ◽  
Author(s):  
M. Amabili ◽  
C. Augenti
Keyword(s):  
Boundary Condition ◽  
Good Accuracy ◽  
Continuation Method ◽  
Laser System ◽  
Normal Displacement ◽  
Vibration Modes ◽  
Rectangular Plates ◽  
Geometric Imperfections ◽  
Simply Supported ◽  
Actual Geometry

Large-amplitude vibrations of rectangular plates subjected to harmonic excitation are investigated. The von Ka´rma´n nonlinear strain-displacement relationships are used to describe the geometric nonlinearity. A specific boundary condition, with restrained normal displacement at the plate edges and fully free in-plane displacements, not previously considered, has been introduced as a consequence that it is very close to the experimental boundary condition. Results for this boundary condition are compared to nonlinear results previously obtained for: (i) simply supported plates with immovable edges; (ii) simply supported plates with movable edges, and (iii) fully clamped plates. The nonlinear equations of motion are studied by using a code based on arclength continuation method. A thin rectangular stainless-steel plate has been inserted in a metal frame; this constraint is approximated with good accuracy by the newly introduced boundary condition. The plate inserted into the frame has been measured with a 3D laser system in order to reconstruct the actual geometry and identify geometric imperfections (out-of-planarity). The plate has been experimentally tested in laboratory for both the first and second vibration modes for several excitation magnitudes in order to characterize the nonlinearity of the plate with imperfections. Numerical results are able to follow experimental results with good accuracy for both vibration modes and for different excitation levels once the geometric imperfection is introduced in the model. Effects of geometric imperfections on the trend of nonlinearity and on natural frequencies are shown; convergence of the solution with the number of generalized coordinates is numerically verified.

Exact Solutions for the Free Vibrations and Buckling of Rectangular Plates With Linearly Varying In-Plane Loading

2001 ◽  
Author(s):  
Arthur W. Leissa ◽  
Jae-Hoon Kang
Keyword(s):  
Solution Procedure ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Transverse Displacement ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Buckling Loads ◽  
Simply Supported ◽  
Edge Conditions ◽  
Elastically Supported

Abstract An exact solution procedure is formulated for the free vibration and buckling analysis of rectangular plates having two opposite edges simply supported when these edges are subjected to linearly varying normal stresses. The other two edges may be clamped, simply supported or free, or they may be elastically supported. The transverse displacement (w) is assumed as sinusoidal in the direction of loading (x), and a power series is assumed in the lateral (y) direction (i.e., the method of Frobenius). Applying the boundary conditions yields the eigenvalue problem of finding the roots of a fourth order characteristic determinant. Care must be exercised to obtain adequate convergence for accurate vibration frequencies and buckling loads, as is demonstrated by two convergence tables. Some interesting and useful results for vibration frequencies and buckling loads, and their mode shapes, are presented for a variety of edge conditions and in-plane loadings, especially pure in-plane moments.

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.

scholarly journals An Elasticity Solution for Vibration Analysis of Laminated Plates with Functionally Graded Core Reinforced by Multi-walled Carbon Nanotubes

2017 ◽  
Vol 61 (4) ◽  
pp. 309 ◽  
Author(s):  
Vahid Tahouneh
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Mass Density ◽  
Functionally Graded ◽  
Laminated Plates ◽  
Rectangular Plates ◽  
Multiwalled Carbon ◽  
Simply Supported ◽  
Pasternak Model ◽  
Multi Walled Carbon Nanotubes

In the present work, vibration characteristics of functionally graded (FG) sandwich rectangular plates reinforced by multiwalled carbon nanotubes (MWCNTs) resting on Pasternak foundation are presented. The response of the elastic medium is formulated by the Winkler/Pasternak model. Modified Halpin-Tsai equation is used to evaluate the Young’s modulus of the MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The mass density and Poisson’s ratio of the MWCNT/phenolic composite are considered based on the rule of mixtures. The proposed sandwich rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the sandwich plates are investigated.

scholarly journals Hygrothermo-mechanical behaviour of layered composite plates

2002 ◽  
Vol 24 (3) ◽  
pp. 142-150
Author(s):  
Tran Ich Thinh
Keyword(s):  
Finite Element ◽  
Mechanical Behaviour ◽  
Composite Plates ◽  
Layered Composite ◽  
Rectangular Plates ◽  
Fe Method ◽  
Third Order ◽  
Numerical Examples ◽  
Simply Supported ◽  
Displacement Theory

In this paper, a hygrothermo-mechanical behaviour of simply supported, composite layered rectangular plates is presented. The analysis is based on use of the Finite Element (FE) method and the full third-order displacement theory. Numerical examples are presented for symmetrically in-axis (0° /90° /90° /0°) and off-axis ( 45° / - 45° / -45° / 45°) layered rectangular plates.

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