Parametric Resonance of Stiffened Rectangular Plates

1972 ◽  
Vol 39 (1) ◽  
pp. 217-226 ◽  
Author(s):  
R. C. Duffield ◽  
N. Willems
Keyword(s):  
Parametric Resonance ◽  
Parametric Instability ◽  
Stiffened Plates ◽  
Rectangular Plates ◽  
Stiffened Plate ◽  
Discrete Elements ◽  
Periodic Force ◽  
Simply Supported ◽  
Dynamic Forces ◽  
Instability Regions

This investigation is concerned with the onset of parametric instability of a simply supported stiffened rectangular plate subjected to in-plane sinusoidal dynamic forces. An analytical analysis is developed for the stiffened plate with the stiffeners treated as discrete elements. The results show that the location and size of the stiffeners have a significant effect on the location and contour of the boundaries of the parametric instability regions when compared with those of a flat unstiffened plate. Experimental verification is obtained for stiffened plates with a single centrally located stiffener transverse to an in-plane periodic force acting on two opposite edges.

Buckling of Transverse Stiffened Plates Under Shear

1947 ◽  
Vol 14 (4) ◽  
pp. A269-A274
Author(s):  
Tsun Kuei Wang
Keyword(s):  
Finite Length ◽  
Stiffened Plates ◽  
Rectangular Plates ◽  
Simply Supported

Abstract This paper presents an analysis of buckling of simply supported rectangular plates reinforced by any number of transverse stiffeners and subjected to shearing forces uniformly distributed along the edges. Two cases are considered: (a) The case of a plate with a finite length; (b) one in which the length is infinite. The critical shearing stresses in both cases are expressed in similar forms, that is, τcrd2Ept2=-π4384(1-ν2)drbΩ in Equation (13), and τcrd2Ept2=π224(1-ν2)K in Equation (24), respectively. Design curves are drawn as shown in Figs. 2, 3, and 5.

Dynamic Stability of Simply Supported Beams With Multi-Harmonic Parametric Excitation

2020 ◽  
pp. 2150027
Author(s):  
Chao Xu ◽  
Zhengzhong Wang ◽  
Baohui Li
Keyword(s):  
Parametric Resonance ◽  
Parametric Excitation ◽  
Dynamic Instability ◽  
Elastic Structures ◽  
Simply Supported ◽  
Response Characteristics ◽  
Positive Effects ◽  
Excited Vibration ◽  
Mdof Systems ◽  
Instability Regions

Determination of the regions of dynamic instability has been an important issue for elastic structures. Under the extreme climate, the external load acting on structures is becoming more and more complicated, which can induce dynamic instability of elastic structures. In this study, we explore the dynamic instability and response characteristics of simply supported beams under multi-harmonic parametric excitation. A numerical approach for determining the instability regions under multi-harmonic parametric excitation is developed here by examining the eigenvalues of characteristic exponents of the monodromy matrix based on the Floquet theorem, and the fourth-order Runge–Kutta method is used to calculate the dynamic responses. The accuracy of the method is verified by the comparison with classical approximate boundary formulas of dynamic instability regions. The numerical results reveal that Bolotin’s approximate formulas are only applicable to the low-order instability regions with a small value of the excitation parameter of simple parametric resonance. Multi-harmonic parametric excitation can significantly change the dynamic instability regions, it may cause parametric resonance on beams for longitudinal complex periodic loads. The influence of frequency and number of multiply harmonics on the parametrically excited vibration of the beam is explored. High-order harmonics with low-frequency have positive effects on the stable response characteristics for multi-harmonic parametric excitation. This paper provides a new perspective for the vibration suppression of parametric excitation. The developed procedure can be used for multi-degree-of-freedom (MDOF) systems under complex excitation (e.g. tsunami waves and strong winds).

VIBRATION AND DYNAMIC INSTABILITY OF STIFFENED PLATES SUBJECTED TO IN-PLANE HARMONIC EDGE LOADING

2002 ◽  
Vol 02 (02) ◽  
pp. 185-206 ◽  
Author(s):  
A. K. L. SRIVASTAVA ◽  
P. K. DATTA ◽  
A. H. SHEIKH
Keyword(s):  
Dynamic Instability ◽  
Stiffened Plates ◽  
Stiffened Plate ◽  
Element Analysis ◽  
Aspect Ratios ◽  
Stiffness Properties ◽  
Edge Loading ◽  
Instability Regions ◽  
Varying Mass ◽  
Good Agreement

The vibration and dynamic instability behavior of a stiffened plate subjected to uniform in-plane edge loading is studied using finite element analysis. The method of Hill's infinite determinants is applied to analyze the dynamic instability regions. Rectangular stiffened plates possessing different boundary conditions, aspect ratios, varying mass and stiffness properties and varying number of stiffeners have been analyzed for dynamic instability. The results are obtained considering the bending displacements of the plate and the stiffener. Eccentricity of the stiffeners give rise to axial and bending displacement in the middle plane of the plate. The results show that the principal instability regions have a significant effect considering and neglecting in-plane displacements. Comparison with published results indicates good agreement.

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.

A Parametric Approach for the Stress Analysis of Orthogonally Stiffened Rectangular Plates

1983 ◽  
Vol 105 (4) ◽  
pp. 363-368 ◽  
Author(s):  
R. J. Dohrmann ◽  
J. N. Wu ◽  
R. E. Beckett
Keyword(s):  
Stress Analysis ◽  
Orthotropic Plate ◽  
Plate Thickness ◽  
Normal Pressure ◽  
Rectangular Plates ◽  
Maximum Deflection ◽  
Stiffened Plate ◽  
Parametric Approach ◽  
Simply Supported ◽  
Plate Geometry

This report describes a parametric approach for the stress analysis of orthogonally stiffened rectangular plates. The analysis assumes that the deflection of an orthogonally stiffened plate is approximated by a homogeneous orthotropic plate of a uniform thickness. Polynomial expressions for maximum deflection for two sets of boundary conditions (all edges clamped and two edges clamped–two edges simply supported) are presented in terms of plate geometry and loading (normal pressure and in-plane forces). A method for computing the stress is presented that permits stresses in the actual orthogonally stiffened plate (that generally does not have a uniform plate thickness) to be determined.

Nonlinear Modal Interactions of a Parametrically Excited Composite Column

2017 ◽  
Author(s):  
Jerzy Warminski ◽  
Andrzej Teter
Keyword(s):  
Parametric Resonance ◽  
Dynamic Properties ◽  
Parametric Instability ◽  
Local Mode ◽  
Modal Interactions ◽  
Periodic Force ◽  
Composite Column ◽  
General Arrangement ◽  
Composite Configuration ◽  
Modes Coupling

Nonlinear dynamics of a composite column loaded by axial periodic force is presented in the paper. The simply supported channel column is made of several layers of a laminate with an general arrangement, leading to mechanical deformation couplings. A reduced model of the column is represented by a set of nonlinear equations which includes geometric nonlinear terms and parametric excitation. For the selected configuration of the composite structure parametric instability zones and vibration modes coupling occur. In contrast to isotropic materials, a modification of the reinforcing fibres layout results in a change of structure dynamic properties and a location of parametric resonance zones. Furthermore, buckling phenomenon may occur through various scenarios, by the global or local mode activation. The effect of the composite configuration on the principal parametric resonance zones is presented.

Parametric Instability of a Leipholz Column Under Periodic Excitation

1999 ◽  
Author(s):  
Bongsu Kang ◽  
Chin An Tan
Keyword(s):  
Boundary Conditions ◽  
Axial Load ◽  
Parametric Instability ◽  
Periodic Excitation ◽  
Combination Resonance ◽  
Simply Supported ◽  
Free Boundary Conditions ◽  
Difference Type ◽  
Instability Regions ◽  
The Difference

Abstract In this paper, the parametric instability of a Leipholz column under four boundary conditions is studied. The distributed, follower-type axial load is assumed to be uniform and periodic. Instability regions are obtained and the existence of combination resonance of sum and difference types is discussed for each set of boundary conditions. It is found that combination resonance of sum type exists in all the cases of boundary conditions considered, but the difference type exists only in the cases of clamped-simply supported and clamped-free boundary conditions. The combination resonance is shown to be as important as the simple parametric resonance. Results, when compared to a column under a periodic end load, show that the instability characteristics of these two columns are considerably different.

Stability Analysis of the Stiffened Plate with Rids under the Longitudinal Loads

2011 ◽  
Vol 243-249 ◽  
pp. 279-283
Author(s):  
Yu Zhang
Keyword(s):  
Potential Energy ◽  
Boundary Conditions ◽  
Critical Loads ◽  
Minimum Condition ◽  
Stiffened Plates ◽  
Stiffened Plate ◽  
Simply Supported ◽  
Total Potential ◽  
The Stability ◽  
Work Done

The stiffened plate with rids was considered as a whole structure. Using energy method the stability of stiffened plates with rids under the longitudinal forces was analyzed. Calculating the potential energy of deformation of plate and that of rids and the work done by the neutral plane forces of plate when the plates were buckled, the formulas of critical loads of the stiffened plate with rids under longitudinal forces were derived from the minimum condition of total potential energy. Using the formulas in this paper engineers can easily calculate the critical loads of the stiffened plate with rids under the boundary conditions: the opposite sides are fixed and the other opposite sides are simply supported, four sides are simply supported. The formula of critical loads of the stiffened plate with rids under other boundary conditions can be derived using the method in this paper.

Vibration of Centrally Stiffened Rectangular Plate

1961 ◽  
Vol 65 (610) ◽  
pp. 695-697 ◽  
Author(s):  
C. L. Kirk
Keyword(s):  
Orthotropic Plate ◽  
Natural Frequencies ◽  
Flexural Vibration ◽  
Empirical Method ◽  
Rectangular Plates ◽  
Stiffened Plate ◽  
Simply Supported ◽  
Stiffening Ribs ◽  
Square Plate ◽  
Semi Empirical

Natural frequencies of free flexural vibration of rectangular plates may, in many cases, be considerably increased by attaching to the plate one or more elastic stiffening ribs parallel to one edge, or by casting or machining the plate and stiffeners integrally.Hoppmann has determined by a semi-empirical method the natural frequencies of an integrally stiffened simply-supported square plate, using the concept of a homogeneous orthotropic plate of uniform thickness having elastic compliances which are equivalent to those of the stiffened plate. Filippov has obtained the exact solution for the fundamental frequency of a simply-supported square plate having a number of equally spaced stiffeners and has considered the effect of point loads applied to the stiffeners in a direction perpendicular to the plane of the plate.

Vibration of Stiffened Rectangular Plates

1964 ◽  
Vol 68 (648) ◽  
pp. 850-851
Author(s):  
K. T. Sundara Raja Iyengar ◽  
K. S. Jagadish
Keyword(s):  
The Other ◽  
Spring Constant ◽  
Stiffened Plates ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Rayleigh Method ◽  
Free Edges

The vibrations of stiffened plates have been considered by Kirk and Mahalingam. Kirk has treated plates with several stiffeners and also a plate with a single stiffener. For plates with several stiffeners he uses the Rayleigh Method as employed by Warburton. The calculated frequencies have been shown to compare favourably with the experimental frequencies when the stiffness has been taken as ef3/3 for a stiffener. While considering the plate with a single stiffener he has replaced the stiffener by a line of massless springs the spring constant of which is determined on the basis of certain approximations. The Rayleigh method has then been applied to solve the simplified problem. A plate with two opposite edges free and the other two simply supported with a central stiffener parallel to the free edges has also been considered by Kirk.

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