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.

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.

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 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.

Coupled Dynamic Instability Analysis of Thin-Walled Columns Subjected to Harmonic Axial Loading

2018 ◽  
Vol 10 (05) ◽  
pp. 1850051 ◽  
Author(s):  
Amit Yadav ◽  
Sarat Kumar Panda ◽  
Tanish Dey
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Cross Section ◽  
Dynamic Instability ◽  
Axial Loading ◽  
Mode Shapes ◽  
Instability Analysis ◽  
Aspect Ratios ◽  
Instability Regions ◽  
Thin Walled

This paper presents triply coupled vibrations and instability analysis of thin-walled columns having a non-symmetrical open cross-section. Vlasov’s theory is used to derive the governing differential equations for coupled flexural and torsional vibrations. A numerical method is presented to determine the exact natural frequencies and corresponding mode shapes in terms of real functions. Employing Galerkin’s method, the coupled partial differential equations are reduced to a set of coupled Mathieu type equations. Following Bolotin’s method, the principal instability regions of thin-walled column with a non-symmetrical cross-section having various boundary conditions are determined. Numerical examples are presented to examine the effect of different boundary conditions, aspect ratios, static and dynamic load factors on principal instability regions. The study of response and corresponding phase plot in stable and unstable regions are carried out to identify the dynamic instability behavior.

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 Slender Concrete-Filled Steel Tubular Columns with General Supports

2019 ◽  
Vol 19 (04) ◽  
pp. 1950045
Author(s):  
Youqin Huang ◽  
Jiyang Fu ◽  
Di Wu ◽  
Airong Liu ◽  
Wei Gao ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Dynamic Stability ◽  
Cross Sections ◽  
Dynamic Instability ◽  
Static Stability ◽  
Constant Component ◽  
Cross Sectional ◽  
Tubular Columns ◽  
New Findings ◽  
Cfst Columns

The static stability of slender concrete-filled steel tubular (CFST) columns has been explored thoroughly while few researches have been carried out on the dynamic stability of CFST columns even if all applied loadings are naturally time-dependent. This paper presents an analytical procedure for evaluating the dynamic stability of CFST columns of various composite cross-sections under general boundary conditions. This paper is featured by the following facts: (1) proportional damping is considered in derivation of the governing equations on the lateral parametric vibration of the CFST columns subject to axial excitation; (2) Bolotin’s method is used to determine the boundaries of the regions of dynamic instability for the CFST columns with general supports; (3) the relationship of static and dynamic stability, and the effects of boundary conditions and cross-sectional forms are uncovered. New findings of this investigation are (1) larger amplitude or constant component of excitation make it easier for the dynamic instabilities of the CFST columns to occur, while increasing the constant component of excitation reduces the critical value of frequency ratio for the dynamic instability to occur; (2) the dynamic stability analysis can determine the critical loads for both the static and dynamic instability of CFST columns, and the critical instability load decreases with increasing disturbance on the static load; (3) under the same consumptions of steel and concrete, the square columns have better performance of dynamic stability than the circular columns, but there is no definite conclusion on the effect of hollow size on the dynamic stability of double-skin columns.

Vibrations of Axially Moving Vertical Rectangular Plates in Contact with Fluid

2016 ◽  
Vol 16 (02) ◽  
pp. 1450092 ◽  
Author(s):  
Yan Qing Wang ◽  
Sen Wen Xue ◽  
Xiao Bo Huang ◽  
Wei Du
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Fluid Pressure ◽  
Added Mass ◽  
Vibration Characteristics ◽  
Rectangular Plates ◽  
Moving Plate ◽  
Bernoulli’S Equation ◽  
Aspect Ratios ◽  
Axially Moving

The vibration characteristics of an axially moving vertical plate immersed in fluid and subjected to a pretension are investigated, with a special consideration to natural frequencies, complex mode functions and critical speeds of the system. The classical thin plate theory is adopted for the formulation of the governing equation of motion of the vibrating plates. The effects of free surface waves, compressibility and viscidity of the fluid are neglected in the analysis. The velocity potential and Bernoulli’s equation are used to describe the fluid pressure acting on the moving plate. The effect of fluid on the vibrations of the plate may be regarded as equivalent to an added mass on the plate. The formulation of added mass is obtained from kinematic boundary conditions of the plate–fluid interfaces. The effects of some system parameters such as the moving speed, stiffness ratios, location and aspect ratios of the plate and the fluid-plate density ratios on the above-mentioned vibration characteristics of the plate–fluid system are investigated in detail. Various different boundary conditions are considered in the study.

scholarly journals Dynamic Stability of Bi-Directional Functionally Graded Porous Cylindrical Shells Embedded in an Elastic Foundation

2020 ◽  
Vol 10 (4) ◽  
pp. 1345 ◽  
Author(s):  
Farshid Allahkarami ◽  
Hasan Tohidi ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Boundary Conditions ◽  
Dynamic Stability ◽  
Elastic Foundation ◽  
Dynamic Instability ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Practical Applications ◽  
Energy Devices ◽  
Various Boundary Conditions

This paper investigates the dynamic buckling of bi-directional (BD) functionally graded (FG) porous cylindrical shells for various boundary conditions, where the FG material is modeled by means of power law functions with even and uneven porosity distributions of ceramic and metal phases. The third-order shear deformation theory (TSDT) is adopted to derive the governing equations of the problem via the Hamilton’s principle. The generalized differential quadrature (GDQ) method is applied together with the Bolotin scheme as numerical strategy to solve the problem, and to draw the dynamic instability region (DIR) of the structure. A large parametric study examines the effect of different boundary conditions at the extremities of the cylindrical shell, as well as the sensitivity of the dynamic stability to different thickness-to-radius ratios, length-to-radius ratios, transverse and longitudinal power indexes, porosity volume fractions, and elastic foundation constants. Based on results, the dynamic stability of BD-FG cylindrical shells can be controlled efficiently by selecting appropriate power indexes along the desired directions. Furthermore, the DIR is highly sensitive to the porosity distribution and to the extent of transverse and longitudinal power indexes. The numerical results could be of great interest for many practical applications, as civil, mechanical or aerospace engineering, as well as for energy devices or biomedical systems.

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