S. K. Sahu

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

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 ….), the method of determination of dynamic instability regions (Lyapunovian, perturbation and Floquet’s methods ), order of theory being applied (thin, thick, 3D, 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, non-conservative 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. Review on the subject for non-conservative systems in detail will be presented in Part-2.

Parametric Resonance Characteristics of Laminated Composite Doubly Curved Shells Subjected to Non-Uniform Loading

The parametric resonance characteristics of laminated composite doubly curved panels subjected to various in-plane static and periodic compressive edge loadings, including partial and concentrated edge loading are studied using finite element analysis. The first order shear deformation theory is used to model the doubly curved panels, considering the effects of transverse shear deformation and rotary inertia. The theory used is the extension of dynamic, shear deformable theory according to the Sander’s first approximation for doubly curved laminated shells, which can be reduced to Love’s and Donnell’s theories by means of tracers. The effects of number of layers, static load factor, side to thickness ratio, shallowness ratio, boundary conditions, degree of orthotropy, ply orientations and various load parameters on the principal instability regions of doubly curved panels are studied in detail using Bolotin’s method. Quantitative results are presented to show the effects of shell geometry, lamination details and load parameters on the stability boundaries. Results of plates and cylindrical shells are also presented as special cases and are compared with those available in the literature.

Dynamic instability of laminated composite rectangular plates subjected to non-uniform harmonic in-plane edge loading

Abstract The dynamic instability behaviour of isotropic, cross-ply and angle-ply laminated composite plates under combined uniaxial and harmonically varying in-plane point or patch loads is investigated using finite element analysis. The first-order shear deformation theory is used to model the composite laminates, considering the effects of transverse shear deformation and rotary inertia. The effects of various geometrical parameters, boundary conditions, lamination and load parameters on the principal dynamic instability regions of composite plates are studied in detail. The preferential orientations depending on the instability regions for simply supported patch and point loaded plates have been suggested for angle-ply plates. The dynamic instability region has been influenced by the restraint provided at the edges.

STABILITY OF LAMINATED COMPOSITE PRETWISTED CANTILEVER PANELS

This article deals with the stability analysis of angle-ply laminated composite twisted panels using the finite element method. Here, a eight-noded isoparametric quadratic shell element is used to develop the finite element procedure. To investigate the vibration and stability behavior of twisted panels, the effect of various geometrical parameters like angle of twist, aspect ratio, lamination parameters, shallowness ratio, etc. are studied. The influence of various parameters on the vibration and stability characteristics of twisted panels have been examined. Numerical results are presented to show the effects of pretwist angles, geometry, and lamination details on the stability characteristics of twisted plates.

PARAMETRIC RESONANCE CHARACTERISTICS OF ANGLE-PLY TWISTED 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 Bolotins 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.

Effects of Loading Speed on the Failure Behaviour of FRP Composites

Purpose – The objective of the present work is to ascertain the failure modes under different loading speeds along with change in percentage of constituents of FRP composites.Design/methodology/approach – This involves experimental investigation of FRP composites with woven roving fibers and matrix. Different types of composites, i.e. glass: epoxy, glass: polyester and (carbon+glass): epoxy are used in the investigation with change in percentage of constituents. The variability of fiber content of the composite is in the range of 0.55‐0.65 weight fractions. The matrix dominated property, like inter laminar shear strength (ILSS) has been studied by three point bend test using INSTRON 1195 material testing machine with increasing five cross head velocities.Findings – The variation of ILSS of laminates of FRP composites is significant for low loading speed and is not so prominent for high speed. The variation of ILSS are observed to be dependent on the type and amount of constituents present in the composite...

Parametric Resonance Characteristics of Laminated Composite Curved Shell Panels in a Hygrothermal Environment

The present study deals with the parametric resonance behaviour of laminated composite curved shell panels in a hygrothermal environment using Bolotin’s approach. A simple laminated model is developed using first order shear deformation theory (FSDT) for the vibration and dynamic stability analysis of laminated composite shells subjected to hygrothermal conditions. A computer program based on the finite element method (FEM) in a MATLAB environment is developed to perform all necessary computations. Quantitative results are presented to show the effects of curvature, ply-orientations, degree of orthotropy and geometry of laminates on the parametric instability of composite curved shell panels for different temperature and moisture concentrations. The excitation frequencies of laminated composite panels decrease with the increase of temperature and moisture due to reduction of stiffness for all laminates.