Hypernormal Form at Cubic of a Rectangular Symmetric Cross-Ply Laminated Composite Plate

2012 ◽  
Vol 581-582 ◽  
pp. 641-644
Author(s):  
Wen Yuan Jia ◽  
Jing Li ◽  
Bin He
Keyword(s):  
Normal Form ◽  
Mechanical Model ◽  
Composite Plate ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Laminated Composite ◽  
Laminated Plates ◽  
Laminated Composite Plate ◽  
Averaged Equations ◽  
Lie Brackets

Based on wings flutter on flying aircraft in this paper, the authors study the mechanical model of the rectangular symmetric cross-ply composite laminated plates. Frist, the method of multiple scales is employed to obtain the four-dimensional averaged equations of the model. Then, the method of new grading function and multiple Lie brackets is utilized to obtain the hypernormal form (simplest normal form, unique normal form) at cubic of above averaged equations.

Hypernormal Form at Cubic of Honeycomb Sandwich Plate Dynamics Model

2013 ◽  
Vol 437 ◽  
pp. 81-84 ◽  
Author(s):  
Xin Li ◽  
Jing Li ◽  
Bin He
Keyword(s):  
Normal Form ◽  
Sandwich Plate ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Dynamics Model ◽  
Average Equation ◽  
Honeycomb Sandwich ◽  
Honeycomb Sandwich Plate ◽  
Lie Brackets ◽  
Plate Dynamics

Honeycomb sandwich plate have been widly applied in industry design in recent years. In this paper, we study the cubic hypernormal form (the simplest normal form and the unique normal form) for honeycomb sandwich plate dynamics model with the help of Maple symbolic computation. Firstly, we get the average equation of four dimensional cartesian form by using the method of multiple scales perturbation analysis. Based on the method combined new grading function with multiple Lie brackets, we obtain the hypernormal form of cubic truncated. The results will further enrich the research for dynamics of honeycomb sandwich plate model, and is also the basis for higher order normal form research.

DEGENERATE BIFURCATION ANALYSIS ON A PARAMETRICALLY AND EXTERNALLY EXCITED MECHANICAL SYSTEM

2001 ◽  
Vol 11 (03) ◽  
pp. 689-709 ◽  
Author(s):  
WEI ZHANG ◽  
PEI YU
Keyword(s):  
Normal Form ◽  
Mechanical System ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Main Attention ◽  
Zero Eigenvalue ◽  
Normal Form Theory ◽  
Local Bifurcations ◽  
Averaged Equations ◽  
Form Theory

A general parametrically and externally excited mechanical system is considered. The main attention is focused on the dynamical properties of local bifurcations as well as global bifurcations including homoclinic and heteroclinic bifurcations. In particular, degenerate bifurcations of codimension 3 are studied in detail. The original mechanical system is first transformed to averaged equations using the method of multiple scales. With the aid of normal form theory, the explicit expressions of the normal form associated with a double-zero eigenvalue and Z2-symmetry for the averaged equations are obtained. Based on the normal form, it has been shown that a parametrically and externally excited mechanical system can exhibit homoclinic and heteroclinic bifurcations, multiple limit cycles, and jumping phenomena in amplitude modulated oscillations. Numerical simulations are also given to verify the good analytical predictions.

Laminated Composite Plate Theory With Improved In-Plane Responses

1986 ◽  
Vol 53 (3) ◽  
pp. 661-666 ◽  
Author(s):  
H. Murakami
Keyword(s):  
Variational Principle ◽  
Composite Plate ◽  
Plate Theory ◽  
Laminated Composite ◽  
Laminated Plates ◽  
Thickness Variation ◽  
Laminated Plate ◽  
Laminated Composite Plate ◽  
Cylindrical Bending ◽  
Shear Deformable

In order to improve the accuracy of the in-plane response of the shear, deformable laminated composite plate theory, a new laminated plate theory has been developed based upon a new variational principle proposed by Reissner (1984). The improvement is achieved by including a zigzag-shaped C0 function to approximate the thickness variation of in-plane displacements. The accuracy of this theory is examined by applying it to a problem of cylindrical bending of laminated plates which has been solved exactly by Pagano (1969). The comparison of the in-plane response with the exact solutions for symmetric three-ply and five-ply layers has demonstrated that the new theory predicts the in-plane response very accurately even for small span-to-depth ratios.

Nonlinear Oscillations of an Antisymmetric Cross-Ply Laminated Composite Thin Rectangular Plate Under Parametric Excitation

2003 ◽  
Author(s):  
Min Ye ◽  
Yanhong Sun ◽  
Qian Ding ◽  
Wei Zhang
Keyword(s):  
Steady State ◽  
Parametric Excitation ◽  
Composite Plate ◽  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Laminated Composite ◽  
Governing Equations ◽  
Laminated Composite Plate ◽  
Nonlinear Responses ◽  
Averaged Equations

In this paper, nonlinear dynamics of a simply supported antisymmetric cross-ply laminated composite thin rectangular plate under parametric excitation is investigated. The governing equations of motion for the antisymmetric cross-ply laminated composite plate are derived by using von Karman type plate equation. The geometric nonlinearity and nonlinear damping are included in the governing equations of motion. A two-degree-of-freedom parametrically excited nonlinear system including the quadratic and cubic nonlinear terms is obtained by using the Galerkin method. Based on the Fourier expansion and the temporal rescaling, an asymptotic perturbation method is utilized to obtained four-dimensional nonlinear averaged equations on the amplitude and the phase of nonlinear oscillations of the antisymmetric cross-ply laminated composite plate for the first time. Based on the averaged equations, the steady state nonlinear responses and their stabilities are determined by using numerical approach. The relations between the steady state nonlinear responses and the amplitude and frequency of parametric excitation are obtained. Under the certain conditions, the antisymmetric cross-ply laminated composite plate may have two steady state nonzero solutions in which the jumping phenomenon occurs.

scholarly journals Stress analysis of infinite laminated composite plate with elliptical cutout under different in plane loadings in hygrothermal environment

2021 ◽  
Vol 8 (1) ◽  
pp. 1-12
Author(s):  
Ashok Magar ◽  
Achchhe Lal
Keyword(s):  
Stress Concentration ◽  
Stress Distribution ◽  
Composite Plate ◽  
Volume Fraction ◽  
Elliptical Hole ◽  
Laminated Composite ◽  
Laminated Composite Plate ◽  
Concentration Changes ◽  
Hygrothermal Environment ◽  
Plate Analysis

Abstract This paper presents the solution of stress distribution around elliptical cutout in an infinite laminated composite plate. Analysis is done for in plane loading under hygrothermal environment. The formulation to obtain stresses around elliptical hole is based on Muskhelishvili’s complex variable method. The effect of fibre angle, type of in plane loading, volume fraction of fibre, change in temperature, fibre materials, stacking sequence and environmental conditions on stress distribution around elliptical hole is presented. The study revealed, these factors have significant effect on stress concentration in hygrothermal environment and stress concentration changes are significant with change in temperature.

scholarly journals Experimental and Numerical Analyses on the Buckling Characteristics of Woven Flax/Epoxy Laminated Composite Plate under Axial Compression

Polymers ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 995
Author(s):  
Venkatachalam Gopalan ◽  
Vimalanand Suthenthiraveerappa ◽  
Jefferson Stanley David ◽  
Jeyanthi Subramanian ◽  
A. Raja Annamalai ◽  
...  
Keyword(s):  
Environmental Sustainability ◽  
Composite Plate ◽  
Compressive Load ◽  
Laminated Composite ◽  
Green Composite ◽  
Laminated Composite Plate ◽  
Axial Compressive Load ◽  
Number Of Layers ◽  
Structural Applications ◽  
Ply Orientation

The evolution of a sustainable green composite in various loadbearing structural applications tends to reduce pollution, which in turn enhances environmental sustainability. This work is an attempt to promote a sustainable green composite in buckling loadbearing structural applications. In order to use the green composite in various structural applications, the knowledge on its structural stability is a must. As the structural instability leads to the buckling of the composite structure when it is under an axial compressive load, the work on its buckling characteristics is important. In this work, the buckling characteristics of a woven flax/bio epoxy (WFBE) laminated composite plate are investigated experimentally and numerically when subjected to an axial compressive load. In order to accomplish the optimization study on the buckling characteristics of the composite plate among various structural criterions such as number of layers, the width of the plate and the ply orientation, the optimization tool “response surface methodology” (RSM) is used in this work. The validation of the developed finite element model in Analysis System (ANSYS) version 16 is carried out by comparing the critical buckling loads obtained from the experimental test and numerical simulation for three out of twenty samples. A comparison is then made between the numerical results obtained through ANSYS16 and the results generated using the regression equation. It is concluded that the buckling strength of the composite escalates with the number of layers, the change in width and the ply orientation. It is also noted that the weaving model of the fabric powers the buckling behavior of the composite. This work explores the feasibility of the use of the developed green composite in various buckling loadbearing structural applications. Due to the compromised buckling characteristics of the green composite with the synthetic composite, it has the capability of replacing many synthetic composites, which in turn enhances the sustainability of the environment.

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