Research Advances in the Dynamic Stability Behavior of Plates and Shells: 1987–2005—Part I: Conservative Systems

2007 ◽  
Vol 60 (2) ◽  
pp. 65-75 ◽  
Author(s):  
S. K. Sahu ◽  
P. K. Datta
Keyword(s):  
Dynamic Stability ◽  
Parametric Excitation ◽  
Dynamic Instability ◽  
Three Dimensional ◽  
Plate And Shell ◽  
Plates And Shells ◽  
Instability Regions ◽  
Nonconservative Loading ◽  
Stability Of Structures

This paper reviews most of the recent research done in the field of dynamic stability/dynamic instability/parametric excitation/parametric resonance characteristics of structures with special attention to parametric excitation of plate and shell structures. The solution of dynamic stability problems involves derivation of the equation of motion, discretization, and determination of dynamic instability regions of the structures. The purpose of this study is to review most of the recent research on dynamic stability in terms of the geometry (plates, cylindrical, spherical, and conical shells), type of loading (uniaxial uniform, patch, point loading …), boundary conditions (SSSS, SCSC, CCCC …), method of analysis (exact, finite strip, finite difference, finite element, differential quadrature, and experimental …), method of determination of dynamic instability regions (Lyapunovian, perturbation, and Floquet’s methods), order of theory being applied (thin, thick, three-dimensional, nonlinear …), shell theory used (Sanders’, Love’s and Donnell’s), materials of structures (homogeneous, bimodulus, composite, FGM …), and the various complicating effects such as geometrical discontinuity, elastic support, added mass, fluid structure interactions, nonconservative loading and twisting, etc. The important effects on dynamic stability of structures under periodic loading have been identified and influences of various important parameters are discussed. A review of the subject for nonconservative systems in detail will be presented in Part 2. This review paper cites 156 references.

Dynamic Instability of Delaminated Composite Plates under Parametric Excitation

2006 ◽  
Vol 326-328 ◽  
pp. 1765-1768 ◽  
Author(s):  
Meng Kao Yeh ◽  
Kuei Chang Tung
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parametric Excitation ◽  
Composite Plate ◽  
Dynamic Instability ◽  
Composite Plates ◽  
Modal Parameters ◽  
The Finite Element Method ◽  
Electromagnetic Device ◽  
Instability Regions

The dynamic instability behavior of delaminated composite plates under transverse excitations was investigated experimentally and analytically. An electromagnetic device, acting like a spring with alternating stiffness, was used to parametrically excite the delaminated composite plates transversely. An analytical method, combined with the finite element method, was used to determine the instability regions of the delaminated composite plates based on the modal parameters of the composite plate and the position, the stiffness of the electromagnetic device. The delamination size and position of composite plates were varied to assess their effects on the excitation frequencies of simple and combination resonances in instability regions. The experimental results were found to agree with the analytical ones.

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).

The method of caustics for the determination of normal loads acting on surfaces of elastic bodies

1980 ◽  
Vol 15 (1) ◽  
pp. 37-41 ◽  
Author(s):  
P S Theocaris ◽  
N I Ioakimidis
Keyword(s):  
Three Dimensional ◽  
Contact Problems ◽  
Two Dimensional ◽  
Concentrated Force ◽  
Elastic Bodies ◽  
Plate And Shell ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Quantities Of Interest

The optical method of caustics constitutes an efficient experimental technique for the determination of quantities of interest in elasticity problems. Up to now, this method has been applied only to two-dimensional elasticity problems (including plate and shell problems). In this paper, the method of caustics is extended to the case of three-dimensional elasticity problems. The particular problems of a concentrated force and a uniformly distributed loading acting normally on a half-space (on a circular region) are treated in detail. Experimentally obtained caustics for the first of these problems were seen to be in satisfactory agreement with the corresponding theoretical forms. The treatment of various, more complicated, three-dimensional elasticity problems, including contact problems, by the method of caustics is also possible.

Dynamic Stability of Woven Fiber Laminated Composite Shallow Shells in Hygrothermal Environment

2017 ◽  
Vol 17 (08) ◽  
pp. 1750084 ◽  
Author(s):  
M. Biswal ◽  
S. K. Sahu ◽  
A. V. Asha
Keyword(s):  
Dynamic Stability ◽  
Degrees Of Freedom ◽  
Dynamic Instability ◽  
Shear Deformation Theory ◽  
Shell Element ◽  
Load Factor ◽  
Element Formulation ◽  
Shallow Shells ◽  
Instability Regions ◽  
Hygrothermal Environment

The dynamic stability of bidirectional woven fiber laminated glass/epoxy composite shallow shells subjected to harmonic in-plane loading in hygrothermal environment is considered. An eight-noded isoparametric shell element with five degrees of freedom is used in the analysis. In the present finite element formulation, a composite doubly curved shell model based on first-order shear deformation theory (FSDT) is used for the dynamic stability analysis of shell panels subjected to hygrothermal loading. A program is developed using MATLAB for the parametric study on the dynamic stability of shell panels under the hygrothermal field. The effects of various parameters like static load factor, curvature, shallowness, temperature, moisture, stacking sequence and boundary conditions on the dynamic instability regions of woven fiber glass/epoxy shell panels are investigated. The location of dynamic instability regions is shown to affect significantly due to presence of the hygrothermal field.

DYNAMIC STABILITY OF LAMINATED COMPOSITE PLATES WITH PIEZOELECTRIC LAYERS SUBJECTED TO PERIODIC IN-PLANE LOAD

2011 ◽  
Vol 11 (02) ◽  
pp. 297-311 ◽  
Author(s):  
S. PRADYUMNA ◽  
ABHISHEK GUPTA
Keyword(s):  
Dynamic Stability ◽  
Dynamic Instability ◽  
Plate Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Load Parameter ◽  
Control Voltage ◽  
Laminated Composite Plates ◽  
Piezoelectric Layers ◽  
Instability Regions

In this paper, the dynamic stability characteristics of laminated composite plates with piezoelectric layers subjected to periodic in-plane load are studied. The finite element method is employed using a modified first-order shear deformation plate theory (MFSDT). The formulation includes the effects of transverse shear, in-plane, and rotary inertia. The boundaries of dynamic instability regions are obtained using Bolotin's approach. The structural system is considered to be undamped. The correctness of the formulation is established by comparing the authors' results with those available in the published literature. The effects of control voltage, static buckling load parameter, number of stacking layers, and thickness of plate on the principal and second instability regions are investigated for cross-ply laminated composite plate.

Dynamic Instability of a Cylindrical Shell Structure Subjected to Horizontal and Vertical Excitations Simultaneously

2004 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Taisuke Nosaka ◽  
Tomohiro Ito
Keyword(s):  
Cylindrical Shell ◽  
Dynamic Stability ◽  
Parametric Excitation ◽  
Dynamic Instability ◽  
Simulation Analysis ◽  
Seismic Analysis ◽  
Shell Structures ◽  
Analysis Method ◽  
Water Tanks ◽  
Vertical Excitations

Many structures such as support columns such as those for elevated expressways and towers tend to become larger and more flexible recently, thus the buckling or collapse of these structures is considered to easily occur than ever due to huge earthquakes. Actually, in the Hyogo-ken Nambu earthquake in Japan, buckling phenomena of tall support columns were observed every-where. Therefore, the evaluation technology on the dynamic stability is very important in order to ensure the seismic design reliability for these structures. The authors have ever studied the effects of the horizontal and vertical simultaneous excitations on the above-mentioned buckling phenomena of support columns experimentally. More-over, they also investigated the fundamental phenomena of the dynamic stability of the support columns subjected to the horizontal and vertical excitations simultaneously by numerical simulations using an analytical model where the support column is treated as a tall elastic cantilever beam. The purpose of this paper is on the dynamic instability, that is dynamic buckling, of a cylindrical shell structures such as those for elevated expressways, towers, containment vessels, LNG tanks and water tanks in various industrial plants so on subjected to horizontal and vertical excitations simultaneously. The coupled motion of equation with horizontal and vertical excitations simultaneously for these cylindrical shell structures is derived in this paper, and this modeling is shown to become a Mathieu type’s parametric excitation. The numerical simulation analysis is carried out for a cylindrical shell model with an attached mass on its tip. Comparing with the classical seismic analysis method, this proposed dynamic instability analysis method shows the larger deformation in horizontal direction due to the parametric excitation of the vertical seismic wave. As the results, the structures are apt to lose the structural stability more due to the coupling effects between the horizontal and vertical seismic simultaneous loadings.

Formulæ and Methods of Calculation of the Strength of Plate and Shell Structures in Aeroplane Construction

1936 ◽  
Vol 40 (311) ◽  
pp. 769-788 ◽  
Author(s):  
O. S. Heck ◽  
H. Ebner
Keyword(s):  
Present Report ◽  
Relevant Literature ◽  
Shell Structures ◽  
Structural Elements ◽  
Thin Walled Structures ◽  
Methods Of Calculation ◽  
Plate And Shell ◽  
Plates And Shells ◽  
Detailed List

The object of the present report is to make a general survey of the simple formulas and methods of calculation for the determination of the strength of thin-walled structures (plate and shell structures) which are increasing in importance in aeroplane construction, and to facilitate the study of original papers by adding a detailed list of relevant literature. an essential characteristic of the sheet metal covered structures in question is, that the metal skin in addition to the stiffening elements participates in the transmission of force. structures in which the metal sheet serves merely as a covering but which is not loaded in accordance with its strength, do not come within the scope of the present considerations. non-stiffened and stiffened plates and shells, mostly of very small wall-thickness (about 0.5 to 1.2 mm.) may be regarded as structural elements in plate and shell structures (especially shell fuselages, “ monocoques ” and wings).

Dynamic Instability of Laminated-Composite and Sandwich Plates Using a New Inverse Trigonometric Zigzag Theory

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Rosalin Sahoo ◽  
B. N. Singh
Keyword(s):  
Stability Analysis ◽  
Boundary Conditions ◽  
Dynamic Stability ◽  
Dynamic Instability ◽  
Excitation Frequency ◽  
Laminated Composite ◽  
Sandwich Plates ◽  
Load Amplitude ◽  
Instability Regions ◽  
Zigzag Theory

A structure with periodic dynamic load may lead to dynamic instability due to parametric resonance. In the present work, the dynamic stability analysis of laminated composite and sandwich plate due to in-plane periodic loads is studied based on recently developed inverse trigonometric zigzag theory (ITZZT). Transverse shear stress continuity at layer interfaces along with traction-free boundary conditions on the plate surfaces is satisfied by the model obviating the need of shear correction factor. An efficient C0 continuous, eight noded isoparametric element with seven field variable is employed for the dynamic stability analysis of laminated composite and sandwich plates. The boundaries of instability regions are determined using Bolotin's approach and the first instability zone is presented either in the nondimensional load amplitude–excitation frequency plane or load amplitude–load frequency plane. The influences of various parameters such as degrees of orthotropy, span-thickness ratios, boundary conditions, static load factors, and thickness ratios on the dynamic instability regions (DIRs) are studied by solving a number of problems. The evaluated results are validated with the available results in the literature based on different deformation theories. The efficiency of the present model is ascertained by the improved accuracy of predicted results at the cost of less computational involvement.

Dynamic Instability of Stiffened Plates with Cutout Subjected to In-Plane Uniform Edge Loadings

2003 ◽  
Vol 03 (03) ◽  
pp. 391-403 ◽  
Author(s):  
A. K. L. Srivastava ◽  
P. K. Datta ◽  
A. H. Sheikh
Keyword(s):  
Boundary Conditions ◽  
Dynamic Stability ◽  
Dynamic Instability ◽  
Plate Theory ◽  
Stiffened Plates ◽  
Numerical Examples ◽  
Different Boundary Conditions ◽  
Reissner Plate ◽  
Aspect Ratios ◽  
Instability Regions

This paper is concerned with the dynamic stability of stiffened plates with cutout subjected to harmonic in-plane edge loadings. The plate is modelled using the Mindlin–Reissner plate theory and the method of Hill's infinite determinants is applied to analyze the dynamic instability regions. Stiffened plates with cutout possessing different boundary conditions, aspect ratios, and cutout sizes considering and neglecting in-plane displacements have been analyzed for dynamic instability. The boundaries of the instability regions, including those of the principal one, are computed and presented graphically. These results are given in a non-dimensional form and illustrated by means of numerical examples.

Parametric Excitation of Pre-Stressed Graphene Sheets under Magnetic Field: Nonlinear Vibration and Dynamic Instability

2019 ◽  
Vol 19 (11) ◽  
pp. 1950135
Author(s):  
Majid Ghadiri ◽  
S. Hamed S. Hosseini
Keyword(s):  
Magnetic Field ◽  
Parametric Excitation ◽  
Dynamic Instability ◽  
Equation Of Motion ◽  
Multiple Time Scales ◽  
Graphene Sheets ◽  
Multiple Time ◽  
Unstable Solutions ◽  
Instability Regions ◽  
Voigt Model

Motivated by the lack of sufficient accuracy in investigation of nonlinear dynamics of graphene sheets (GS), nonlinear dynamic instability and frequency response of the pre-stressed single layered GS (SLGS) are investigated in the present paper. To achieve this aim, in the first step, SLGS embedded on a visco-Pasternak foundation is modeled while it is under an initial stress and subjected to a parametric axial force and magnetic field. Then, based on Eringen’s theory, nonlinear von Karman relations and Kelvin–Voigt model, the nonlinear governing equation of motion is derived. In the next step, Galerkin technique and multiple time scales method are employed to analyze and solve the equation of motion. Emphasizing the effect of parametric excitation, for considering the instability regions, bifurcation points are discussed. As a result, a parametric study is conducted to show the importance of damping coefficient and parametric excitation in dynamic instability of the system. Numerical examples are also treated which show various discontinuous bifurcations. Also, infinitely stable and unstable solutions are addressed.

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