Department of Mechanical Engineering

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The present work deals with the parametric instability regions of a cantilever beam with tip mass subjected to time-varying magnetic field and axial force. The nonlinear temporal differential equation of motion having two frequency parametric excitations is solved using second-order method of multiple scales. The closed-form expressions for the parametric instability regions for three different resonance conditions are determined. The influence of magnetic filed, axial load, damping constant and mass ratio on the parametric instability regions are investigated. These results obtained from perturbation analysis are verified by solving the temporal equation of motion using fourth-order Runge-Kutta method. The instability regions obtained using this method is found to be in good agreement with the experimental result. © 2007 Elsevier Ltd. All rights reserved.

World University root node

Journal of Sound and Vibration

Parametric instability of a cantilever beam with magnetic field and periodic axial load

A stochastic finite-element-based prediction of the buckling of composite laminated plates, with and without cutouts, under axial compression and shear is presented. The solution for the buckling response is achieved by first evaluating the prebuckled-stress distribution from linear elastostatic analysis. Using this, the critical buckling load and its mode are evaluated by solving an eigenvalue problem. A layerwise plate model is used for both prebuckling and buckling analysis. The effect of prebuckling stresses on the critical buckling load is discussed. The influence of both circular and elliptical cutouts on the buckling strength of composite laminates is presented. The stochastic buckling analysis is done based on the mean-centered first-order perturbation technique. The mean and variance of the buckling strength of composite plates are validated with results available in the literature. Subsequently, the effect of uncertainty in the material properties, obtained from micromechanics-based approach, on the buckling strength of the laminated plates is studied. Results are presented for two-layered plates with different layups and boundary conditions. Copyright © 2007 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

AIAA Journal

Stochastic buckling analysis of laminated plates under shear and compression

Composite plates with cutouts are extensively used in many mechanical structures. The presence of a cutout complicates the stress distribution in the plate. In this study an attempt has been made to incorporate the effect of prebuckled stress on the stability analysis of moderately thick/very thick composite laminated plates with cutouts under in-plane compressive loading using a "Simple higher order shear deformation theory" based on four unknown displacement functions (u0, v0, wb, ws). The finite element method is employed to study the critical buckling load of laminated plates. The change in critical buckling response of both thick and thin rectangular symmetric laminates with respect to the fibre orientation angle has been studied. The interaction curves (between Nx and Ny for different parameters of the laminates) are studied in detail. © 2006 Elsevier Ltd. All rights reserved.

Composite Structures

Stability analysis of composite laminate with and without rectangular cutout under biaxial loading

In this paper, an automatic adaptation of equivalent single layer and layerwise models in any region of the domain is devised using a simple modeling error estimator. The interelement jumps are used to define the modeling error indicator. The proposed modeling error indicator is found to be robust and methodology is very effective in reducing the modeling error. An initially damaged laminate is analysed for adaptive selection of models. The concept of sublayers introduced is found to be very effective to control the modeling error. Copyright © 2007 by the American Institute of Aeronautics and Astronautics, Inc.

Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

Finite element based adaptive modeling for layered composite structures

A nonlinear finite element buckling analysis based on updated Lagrangian formulation is presented to study the compression behaviour of damaged laminated composite plates. A continuum damage mechanics based approach is used to study the coupled behaviour of instability and the associated damage developed in the laminated plates due to the applied compressive loading. The laminated plate is modeled as the sets of laminae bonded together by an elastic interface which is represented by a continuous distribution of matrix material. In this study, a composite laminated plate with and without an existing damage is also considered. A layerwise plate model is used to study the effect of the presence of existing static damage on the buckling strength of laminated plates. Further, the initiation and growth of the existing damage is also studied which may lead to catastrophic failure before the instability occurs.

A nonlinear finite element analysis of damaged laminated plates under uniaxial compression

Flight-test data of helicopters indicate that vibratory levels in the fuselage exhibit a wide spectrum of frequencies, including a few below the rotor revolutions per minute. It is well known that helicopter blades operate in a complex aerodynamic environment, involving time-varying heave, pitch, and pulsating oncoming flow. During operation, some sections of the rotor blade undergo dynamic stall once in a revolution. This paper attempts to understand the reason for the existence of several frequencies in the response of the fuselage and the possible cause for this observed phenomenon by analyzing the effects of dynamic stall and aeroelastic couplings on the response of 2-D airfoil. The ONERA dynamic stall model developed by Petot is modified by incorporating a higher-order rational approximation of Theodorsen's lift deficiency function. This improved model is shown to provide a better correlation with experimental stall data. The response characteristics of a 2-D airfoil undergoing pitching and plunging motion in a pulsating oncoming flow, simulating the response of a cross section of a helicopter rotor blade in forward flight are analyzed. This study shows significant difference in the response characteristics of the airfoil for unsteady (dynamic stall model) and quasi-steady aerodynamic models. It is observed that the nonlinear aerodynamics (dynamic stall effects) in association with aeroelastic couplings above a certain level lead to a bounded chaotic motion of the airfoil.

Chaotic response of an airfoil due to aeroelastic coupling and dynamic stall

The present work deals with the non-linear vibration of a harmonically excited single link roller-supported flexible Cartesian manipulator with a payload. The governing equation of motion of this system is developed using extended Hamilton's principle, which is reduced to the second-order temporal differential equation of motion, by using generalized Galerkin's method. This equation of motion contains both cubic non-linearities of geometric and inertial type in addition to linear forced and non-linear parametric excitation terms. Method of multiple scales is used to solve this non-linear equation and study the stability and bifurcations of the system. Influence of amplitude of the base excitation and mass ratio on the steady state response of the system is investigated for both simple and subharmonic resonance conditions. Critical bifurcation points are determined from the fixed-point responses and periodic, quasi-periodic responses are also found for different system parameters. The results obtained using the perturbation analysis are compared with the previously published experimental work and are found to be in good agreement. This work will be useful for the designer of a flexible manipulator. © 2007 Elsevier Ltd. All rights reserved.

International Journal of Non-Linear Mechanics

Non-linear dynamics of a flexible single link Cartesian manipulator

A novel physical chemical filtration process in a tundish for removal of inclusion particles from molten steel is proposed and analyzed. The considered inclusion particles are mainly composed of the minerals alumina (Al2O3) and spinel (MgAl2O4), which have an affinity to adhere (on contact) to an inclusion trap. An industrial tundish is considered and modified with a zigzag channel block insert installed across the molten steel flow so that when the molten steel flows through the zigzag channels, the inclusion particles are driven into contact with the channel surfaces by increased recirculation and turbulence. The inclusions will bond with the surfaces and be removed from the molten steel. The flow behavior in a fully three-dimensional model of such a tundish, with and without the incorporation of the zigzag channels, is then modeled and dynamically simulated. The flow patterns and particle trajectories are then computed and critically analyzed leading to the conclusion that the proposed filtering system is practically feasible. Copyright © 2007 Tech Science Press.

Fluid Dynamics and Materials Processing

Modeling the flow of molten steel in a tundish containing an inclusion filtering trap

In this paper we show that we can use a modified version of the h-p spectral element method proposed in [6,7,13,14] to sol ve elliptic problems with general boundary conditions to exponential accuracy on polygonal domains using nonconforming spectral element functions. A geometrical mesh is used in a neighbourhood of the corners. With this mesh we seek a solution which minimizes the sum of a weighted squared norm of the residuals in the partial differential equation and the squared norm of the residuals in the boundary conditions in fractional Sobolev spaces and enforce continuity by adding a term which measures the jump in the function and its derivatives at inter-element boundaries, in fractional Sobolev norms, to the functional being minimized. In the neighbourhood of the corners, modified polar coordinates are used and a global coordinate system elsewhere. A stability estimate is derived for the functional which is minimized based on the regularity estimate in [2]. We examine how to parallelize the method and show that the set of common boundary values consists of the values of the function at the corners of the polygonal domain. The method is faster than that proposed in [6,7,14] and the h-p finite element method and stronger error estimates are obtained. © Printed in India.

Fulltext

Proceedings of the Indian Academy of Sciences: Mathematical Sciences

Nonconforming h-p spectral element methods for elliptic problems

Due to their high strength to weight ratios, laminated composite materials have found extensive applications in the construction of mechanical, aerospace, marine and automotive structures. Predictions of the failure of composite structures and the maximum loads that the structures can withstand have become an important topic of research for reliability assurance. In particular, the first-ply failure analysis of laminated composite plates subjected to transverse loads has drawn close attention in recent years. Accurate prediction of failure of composite structures has become more challenging to designers in the presence of inherent scatter in the material properties. The objective of the present study is to improve the efficacy of composite material design by predicting the statistics of first-ply failure of orthotropic plates with random material properties under random loading. In the present study stochastic finite element solutions of probabilistic failure load of composite laminated plates are obtained with layer-wise plate theory and analytical solutions are found using Kirchhoff-Love plate theory. Tsai-Wu and Hoffman criteria have been adopted to predict the first-ply failure load and first-order perturbation technique has been used to evaluate the mean and variance of failure statistics. The capability of stochastic finite element in predicting the first-ply failure load statistics has been studied by comparing the results with analytical solutions. It has been found that the stochastic finite element has high accuracy for the cases considered. The present solutions are also compared with results available in the literature. Numerical results have been presented to illustrate the application of the developed procedure. © 2005 Elsevier Ltd. All rights reserved.