scholarly journals Dynamic Stability of Euler Beams under Axial Unsteady Wind Force

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
You-Qin Huang ◽  
Han-Wen Lu ◽  
Ji-Yang Fu ◽  
Ai-Rong Liu ◽  
Ming Gu
Keyword(s):  
Dynamic Stability ◽  
Dynamic Instability ◽  
Time History ◽  
Wind Load ◽  
Frequency Equation ◽  
Unstable State ◽  
Wind Force ◽  
Eigenvalue Method ◽  
Load Component ◽  
Instability Regions

Dynamic instability of beams in complex structures caused by unsteady wind load has occurred more frequently. However, studies on the parametric resonance of beams are generally limited to harmonic loads, while arbitrary dynamic load is rarely involved. The critical frequency equation for simply supported Euler beams with uniform section under arbitrary axial dynamic forces is firstly derived in this paper based on the Mathieu-Hill equation. Dynamic instability regions with high precision are then calculated by a presented eigenvalue method. Further, the dynamically unstable state of beams under the wind force with any mean or fluctuating component is determined by load normalization, and the wind-induced parametric resonant response is computed by the Runge-Kutta approach. Finally, a measured wind load time-history is input into the dynamic system to indicate that the proposed methods are effective. This study presents a new method to determine the wind-induced dynamic stability of Euler beams. The beam would become dynamically unstable provided that the parametric point, denoting the relation between load properties and structural frequency, is located in the instability region, no matter whether the wind load component is large or not.

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.

scholarly journals Structural Damping Effects on Dynamic Instability of Subtangentially Loaded and Shear Deformable Beck’s Columns

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Dong-Ju Min ◽  
Jaegyun Park ◽  
Sang-Ho Yeon ◽  
Moon-Young Kim
Keyword(s):  
Dynamic Instability ◽  
Time History ◽  
Linear Instability ◽  
Frequency Equation ◽  
Structural Damping ◽  
Damping Coefficients ◽  
Instability Theory ◽  
History Analysis ◽  
Stability Maps ◽  
Parametric Studies

A frequency equation of externally and internally damped and shear-flexible cantilever columns subjected to a subtangentially follower force is analytically derived in a dimensionless form with relation to the linear instability theory of Beck’s columns. Some parametric studies are then performed with variation of two damping coefficients under the assumption of Rayleigh damping. Based on the analysis results, it is demonstrated that three damping cases in association with flutter loads of Beck’s columns can be selected including one case representative of structural damping. Finally, stability maps of shear-flexible and damped Beck’s columns are constructed for the three damping cases and discussed in the practical range of damping coefficients and shear parameters. In addition, flutter loads and time history analysis results are presented using dimensionless FE analysis and compared with exact solutions.

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.

scholarly journals On the Dynamic Stability of a Reinforced Concrete Plate, Taking into Account the Material Creep

2018 ◽  
Vol 196 ◽  
pp. 01025
Author(s):  
Elena Kosheleva
Keyword(s):  
Differential Equation ◽  
Reinforced Concrete ◽  
Dynamic Stability ◽  
Critical Frequency ◽  
Dynamic Instability ◽  
Frequency Equation ◽  
Concrete Plate ◽  
Material Creep ◽  
Linear Differential ◽  
Separated Variables

The problem of the dynamic stability of a reinforced concrete plate armoured in two directions parallel to its edges is considered. To describe the viscoelastic properties of concrete, an integral dependence was adopted with an exponential kernel. The use of this dependence led to a linear differential equation of plate vibration. In addition to the creep of concrete, the work of the reinforcement was taken into account. The solution of the differential equation of vibrations of a plate in the form of a series with separated variables is considered, which satisfies the plate fastening conditions. Differential equations are obtained for the time function by the Bubnov-Galerkin method. The task was to find the main areas of dynamic instability. For this, the critical frequency equation was obtained. The influence of the coefficients entering into the equation of critical frequencies on the position of the main regions of dynamic instability is investigated.

Dynamic Stability of Rotating FG-CNTRC Cylindrical Shells under Combined Static and Periodic Axial Loads

2018 ◽  
Vol 18 (12) ◽  
pp. 1850151 ◽  
Author(s):  
Yasin Heydarpour ◽  
Parviz Malekzadeh
Keyword(s):  
Dynamic Stability ◽  
Volume Fraction ◽  
Dynamic Instability ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Mechanical Stresses ◽  
Functionally Graded ◽  
Coriolis Acceleration ◽  
Axial Forces ◽  
Instability Regions

The dynamic stability behavior of rotating functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells under combined static and periodic axial forces is investigated. The governing equations are derived based on the first-order shear deformation theory (FSDT) of shells. The initial mechanical stresses due to the steady state rotation of the shell are evaluated by solving the dynamic equilibrium equations. The equations of motion under different boundary conditions are discretized in the spatial domain and transformed into a system of Mathieu–Hill type equations using the differential quadrature method (DQM) together with the trigonometric series. The influences of both the initial mechanical stresses and Coriolis acceleration are considered. Then, the parametric resonance is analyzed and the dynamic instability regions are determined by employing the Bolotin’s first approximation. After validating the approach, the effects of rotational speed, Coriolis acceleration, carbon nanotubes (CNTs) distribution in the thickness direction, CNTs volume fraction, length and thickness-to-mean radius ratios on the principal dynamic instability regions are examined in detail.

scholarly journals PARAMETRIC RESONANCE CHARACTERISTICS OF ANGLE-PLY TWISTED CURVED PANELS

2008 ◽  
Vol 08 (01) ◽  
pp. 61-76 ◽  
Author(s):  
S. K. SAHU ◽  
A. V. ASHA
Keyword(s):  
Shear Deformation ◽  
Dynamic Stability ◽  
Dynamic Instability ◽  
Excitation Frequency ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
First Order ◽  
Cylindrical Panels ◽  
Instability Regions ◽  
Curved Panels

The present study deals with the dynamic stability of laminated composite pre-twisted cantilever panels. The effects of various parameters on the principal instability regions are studied using Bolotin's approach and finite element method. The first-order shear deformation theory is used to model the twisted curved panels, considering the effects of transverse shear deformation and rotary inertia. The results on the dynamic stability studies of the laminated composite pre-twisted panels suggest that the onset of instability occurs earlier and the width of dynamic instability regions increase with introduction of twist in the panel. The instability occurs later for square than rectangular twisted panels. The onset of instability occurs later for pre-twisted cylindrical panels than the flat panels due to addition of curvature. However, the spherical pre-twisted panels show small increase of nondimensional excitation frequency.

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.

Study on Wear-Preventing of Needle Valve in Fuel Injection System Mounted on DME Engine

2011 ◽  
Vol 228-229 ◽  
pp. 1057-1062
Author(s):  
Xin Rong Wen ◽  
Guang De Zhang ◽  
Wei Hua Wang ◽  
Xie Lu ◽  
Sun Jing
Keyword(s):  
Dynamic Stability ◽  
Structural Design ◽  
Fuel Injection ◽  
Dynamic Instability ◽  
Calculation Model ◽  
The Other ◽  
Injection System ◽  
Needle Valve ◽  
Fuel Injection System ◽  
Theoretical Support

The purpose of this paper is to provide theoretical support for the structural design to prevent the wear of needle. The actual wear of the orientation part of the needle in scrapped needles was researched. The presented results showed that the main reason to the wear of the orientation part of needle was the dynamic instability and the abrasives enter into the surface of orientation part which increases the wear, and that the calculation model of dynamic stability was proposed to prevent the wear of needle. This model was a pressure rod, one end of which was fixed, the other was free, and the two ends were pressed on axial force which changes with time. Besides, the classic formula of dynamic stability of pressure rod was changed rationally, so as to correspond with the calculation model. It will play a part in preventing the wear of needle.

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