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.

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.

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 INITIAL GEOMETRIC IMPERFECTIONS AKIBAT TEKUK SINGLE CURVATURE MOMENT PADA BALOK BAJA SEDERHANA

2020 ◽  
Vol 2 (3) ◽  
pp. 183-193
Author(s):  
Erlina Yanuarini ◽  
Yanuar Setiawan ◽  
Tri Widya Swastika
Keyword(s):  
Boundary Condition ◽  
Steel Beams ◽  
Steel Beam ◽  
Geometric Imperfections ◽  
Geometric Imperfection ◽  
Total Displacement ◽  
Initial Geometric Imperfection ◽  
Single Moment ◽  
Initial Geometric Imperfections ◽  
The Moment

ABSTRACTSteel beams are susceptible to initial geometric imperfections due to improper fabrication and installation processes. Consequently, long steel beams without stiffening are prone to bending due to lateral torsion. The purpose of this study is to determine the effect of variations in the initial geometric imperfections of Single Curvature-Moment (SCM) on the moment, total displacement, displacement in the X direction (U1), displacement in the Y direction (U2), and twist. This study used an RH profile with a compact wing and body. The boundary condition used is a simple beam with an initial geometric imperfection due to single moment-curvature (SCM) bending. The variations used are the initial geometric imperfections values of SCM 0 mm (without initial geometric imperfections), SR5 (with initial geometric imperfections of 5 mm), and SR10 (with initial geometric imperfections of 10 mm). Initial geometric imperfections of SCM in steel beam decreased moment capacities up to more than 2% in elastic conditions and 12% in plastic states. This SR10 beam is also a beam that has a displacement of the X-axis (U1 = -203,960 mm), a displacement of the Y-axis (U2 = -255,615 mm), and the most significant twist (28,179 °).Keywords: buckle, initial geometric imperfections, Single Curvature-MomentABSTRAKBalok baja rentan mengalami initial geometric imperfections akibat proses pabrikasi maupun pemasangan yang kurang tepat. Sementara balok baja yang panjang tanpa pengaku rentan mengalami tekuk akibat torsi lateral. Tujuan dari penelitian ini adalah untuk menentukan dampak variasi besarnya initial geometric imperfections Single Curvature-Moment (SCM) terhadap momen, displacement total, displacement arah X (U1), displacement arah Y (U2), dan twist. Penelitian ini menggunakan profil RH dengan sayap dan badan yang kompak. Boundary condition yang digunakan adalah balok sederhana dengan initial geometric imperfections akibat tekuk single momen curvature (SCM). Variasi yang digunakan adalah besarnya nilai initial geometric imperfections SCM 0 mm (tanpa initial geometric imperfections), SR5 (dengan initial geometric imperfections 5 mm), dan SR10 (dengan initial geometric imperfections 10 mm). Dari hasil penelitian diketahui bahwa pada kondisi elastis, leleh, maupun plastis, balok dengan initial geometric imperfections SCM menunjukkan penurunan kapasistas momen mengalami penurunan hingga mencapai lebih dari 2% pada kondisi elastis dan 12% pada kondisi plastis. Balok SR10 juga merupakan balok yang memiliki displacement arah sumbu X (U1=-203,960 mm), displacement arah sumbuY(U2=-255,615 mm), dan twist yang paling paling besar (28,179°).Kata kunci: tekuk, initial geometric imperfections, Single Curvature Moment

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.

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.

Determination of collapse moment of different angled pipe bends with initial geometric imperfection subjected to in-plane bending moments

2021 ◽  
pp. 095440622199640
Author(s):  
Manish Kumar ◽  
Pronab Roy ◽  
Kallol Khan
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Circular Cross Section ◽  
Initial Imperfection ◽  
Bend Angle ◽  
Bending Moments ◽  
Element Analysis ◽  
Geometric Imperfection ◽  
Initial Geometric Imperfection

From the recent literature, it is revealed that pipe bend geometry deviates from the circular cross-section due to pipe bending process for any bend angle, and this deviation in the cross-section is defined as the initial geometric imperfection. This paper focuses on the determination of collapse moment of different angled pipe bends incorporated with initial geometric imperfection subjected to in-plane closing and opening bending moments. The three-dimensional finite element analysis is accounted for geometric as well as material nonlinearities. Python scripting is implemented for modeling the pipe bends with initial geometry imperfection. The twice-elastic-slope method is adopted to determine the collapse moments. From the results, it is observed that initial imperfection has significant impact on the collapse moment of pipe bends. It can be concluded that the effect of initial imperfection decreases with the decrease in bend angle from 150∘ to 45∘. Based on the finite element results, a simple collapse moment equation is proposed to predict the collapse moment for more accurate cross-section of the different angled pipe bends.

Elastic Averaging in Flexure Mechanisms: A Muliti-Beam Parallelogram Flexure Case-Study

2006 ◽  
Author(s):  
Shorya Awtar ◽  
Edip Sevincer
Keyword(s):  
Mechanism Design ◽  
Parametric Model ◽  
Nonlinear Load ◽  
Geometric Imperfections ◽  
Geometric Imperfection ◽  
Flexure Mechanism ◽  
Important Concern ◽  
Proposed Model ◽  
Geometric Arrangements

Over-constraint is an important concern in mechanism design because it can lead to a loss in desired mobility. In distributed-compliance flexure mechanisms, this problem is alleviated due to the phenomenon of elastic averaging, thus enabling performance-enhancing geometric arrangements that are otherwise unrealizable. The principle of elastic averaging is illustrated in this paper by means of a multi-beam parallelogram flexure mechanism. In a lumped-compliance configuration, this mechanism is prone to over-constraint in the presence of nominal manufacturing and assembly errors. However, with an increasing degree of distributed-compliance, the mechanism is shown to become more tolerant to such geometric imperfections. The nonlinear load-stiffening and elasto-kinematic effects in the constituent beams have an important role to play in the over-constraint and elastic averaging characteristics of this mechanism. Therefore, a parametric model that incorporates these nonlinearities is utilized in predicting the influence of a representative geometric imperfection on the primary motion stiffness of the mechanism. The proposed model utilizes a beam generalization so that varying degrees of distributed compliance are captured using a single geometric parameter.

scholarly journals State space approach with FEM for the determination of structural behaviour of composite plates

2017 ◽  
Vol 8 (4) ◽  
pp. 468-483
Author(s):  
Asad Shukri Albostami ◽  
Zhangjian Wu ◽  
Zhenmin Zou
Keyword(s):  
Plate Thickness ◽  
Composite Plates ◽  
Thickness Direction ◽  
Middle Plane ◽  
Structural Behaviour ◽  
State Space Approach ◽  
Content Type ◽  
Simply Supported ◽  
Space Approach

Purpose An analytical investigation has been carried out for a simply supported rectangular plate with two different loading conditions by using 3D state space approach (SSA). Also, the accurate location of the neutral plane (N.P.) through the thickness of the plate can be identified: the N.P. is shifted away from the middle plane according to the loading condition. The paper aims to discuss these issues. Design/methodology/approach SSA and finite element method are used for the determination of structural behaviour of simply supported orthotropic composite plates under different types of loading. The numerical results from a finite element model developed in ABAQUS. Findings The effect of the plate thickness on displacements and stresses is described quantitatively. It is found that the N.P. of the plate, identified according to the values of the in-plane stresses through the thickness direction, is shifted away from the middle plane. Further investigation shows that the position of the N.P. is loading dependant. Originality/value This paper describe the effect of the plate thickness on displacements and stresses quantitatively by using an exact solution called SSA. Also, it is found that the N.P. of the plate, identified according to the values of the in-plane stresses through the thickness direction, is shifted away from the middle plane. Further investigation shows that the position of the N.P. is loading dependant.

Analysis of Nonlinear Buckling of a Long-Span Elliptic Paraboloid Suspended Dome Structure

2013 ◽  
Vol 639-640 ◽  
pp. 191-197 ◽  
Author(s):  
Zheng Rong Jiang ◽  
Kai Rong Shi ◽  
Xiao Nan Gao ◽  
Qing Jun Chen
Keyword(s):  
Single Layer ◽  
Buckling Mode ◽  
Nonlinear Buckling ◽  
Elliptic Paraboloid ◽  
Geometric Imperfection ◽  
Long Span ◽  
Initial Geometric Imperfection ◽  
Dome Structure ◽  
Unsymmetrical Loading ◽  
The Stability

The suspended dome structure, which is a new kind of hybrid spatial one composed of the upper single layer latticed shell and the lower cable-strut system, generally has smaller rise-to-span ratio, thus the overall stability is one of the key factors to the design of the structure. The nonlinear buckling behavior of an elliptic paraboloid suspended dome structure of span 110m80m is investigated by introducing geometric nonlinearity, initial geometric imperfection, material elastic-plasticity and half-span distribution of live loads. The study shows that the coefficient of stable bearing capacity usually is not minimal when the initial geometric imperfection configuration is taken as the first order buckling mode. The unsymmetrical loading distribution and the material nonlinearity might have significant effects on the coefficient. The structure is sensitive to the changes of initial geometric imperfection, and the consistent mode imperfection method is not fully applicable to the stability analysis of suspended dome structure.

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