Department of Mechanical Engineering

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Coupled electro-thermo-elastic equations applicable for the analysis of smart structures have been derived from first principles. Using the equations and applying layer-by-layer finite element model, the induced potential and mechanical deformations in the piezo and non-piezo core material have been obtained for various cases of actuation and sensing of a smart beam under external mechanical load and actuation potential. The present study clearly brings out the essential difference between sensing and actuation. It is also brought out that the interaction between polarisation and electric field in the piezo continuum leads to non-linear distributed body force and non-symmetric stress tensor. These non-linear effects are found to have significant influence on the deformation of a smart beam under actuation. Shape control studies of multi-patch smart beam have also been investigated.

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

Actuation, sensing and shape control of a smart beam using a general electro-thermo-elastic formulation

Accurate computation of the critical response quantities for laminated composite structures has become essential, especially from the design and design certification point of view. Worst case scenario analysis (corresponding to the load envelope) of the structure require computation of local quantities of interest. In such a situation, control of both modelling error and discretisation error for the quantities of interest is required. In this study, for a fixed plate model, a novel adaptive procedure is presented, based on a posteriori estimation of the error in the quantity of interest. This focussed adaptive procedure involves prediction of the desired optimal mesh sizes in the neighborhood of the region of interest and away from the region of interest, based on an a priori estimate of the error in the quantity of interest. The final desired mesh is obtained in one shot. It is found that the error estimator, for the quantity of interest is reasonably robust. Further, the adaptive procedure is very effective in controlling the local error to within the specified tolerances. © 2003 Elsevier Science Ltd. All rights reserved.

Computers and Structures

Focussed adaptivity for laminated plates

Coupled electro-thermo-elastic equations applicable for the analysis of smart structures have been derived from first principles. Using the equations and applying layer-by-layer finite element model, the induced potential and mechanical deformations in the piezo and non-piezo core material have been obtained for various cases of actuation and sensing of a smart beam under external mechanical load and actuation potential. The present study clearly brings out the essential difference between sensing and actuation. It is also brought out that the interaction between polarisation and electric field in the piezo continuum leads to non-linear distributed body force and nonsymmetric stress tensor. These non-linear effects are found to have significant influence on the deformation of a smart beam under actuation. Shape control studies of multi-patch smart beam have also been investigated. © 2003 The American Institute of Aeronautics and Astronautics Inc. All rights reserved.

44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

This paper presents a comprehensive description of the physical interactions in a piezoelectric material used in development of smart structures. The governing electro-thermo-elastic equations for the analysis of smart structures have been developed from the fundamental laws of conservation and thermodynamic principles. A brief description of the application of smart technology to rotorcraft is also presented.

Proceedings of SPIE - The International Society for Optical Engineering

A general approach to modeling and analysis of smart structures

The problem of vibration reduction in helicopter fuselages using the concept of active control of structural response is addressed. When the large size of the coupled gearbox-flexible fuselage system dynamics is considered, first a balanced-realization-based order reduction is employed to reduce the size of the problem. Then using the reduced-order model, a closed-loop controller is designed to minimize the vibratory levels in the fuselage with the constraint that the controller ensures stability of the original full-order system. The controller design is based on the concept of disturbance rejection by the internal model principle. When a four-block representation of the problem and doubly coprime factorization theory is employed, a stable controller is designed for this multi-input/multi-output control problem. It is observed that this controller yields a closed-loop transfer function, which rejects the external disturbance not only at the desired frequency but also in its neighborhood. In addition, contrary to open-loop control, the present technique of closed-loop control reduces the vibratory levels both in the fuselage and the gearbox. The influence of sensor locations on vibration minimization has also been highlighted.

Journal of Guidance, Control, and Dynamics

Order reduction and closed-loop vibration control in helicopter fuselages

The local and global quality of various smoothening based a-posteriori error estimators is tested in this paper, for symmetric laminated composite plates subjected to transverse loads. Smoothening based on strain recovery and displacement-field recovery is studied here. Effect of ply orientation, laminate thickness, boundary conditions, mesh topology, and plate model is studied for a rectangular plate. It is observed that for interior patches of elements, both the estimators based on strain or displacement smoothening are reliable. For element patches at the boundary of the domain, all estimators tend to be unreliable (especially for angle-ply laminates). However, the strain recovery based estimator is clearly more robust for element patches at the boundary, as compared to displacement-recovery based error estimators. Globally, all the estimators tested here were found to be very robust. © 2002 Elsevier Science Ltd. All rights reserved.

Local quality of smoothening based a-posteriori error estimators for laminated plates under transverse loading

Coupled electro-thermo-elastic equations applicable for the analysis of smart structures have been derived. These governing equations have been used to obtain the deformation of a smart beam under the action of external mechanical load and an electric potential. The results of the present study have been compared with those available in literature. The present study brings out the essential difference between sensing and actuation phenomena by solving for the electric potential and the deformation variables in the piezo material.

Electro-thermo-elastic formulation and analysis of a smart beam

Analysis of heterogeneous media, with rapidly oscillating material coefficients, is computationally intense and complex. Thus many averaging and multi-scale schemes have been developed to analyze the composite materials at the macroscopic and microscopic level, each of which may predict different results depending upon the assumptions made. The type of averaging will influence the quality of the computed solution quantities. The present work is an attempt to quantify the accuracy of various techniques with respect to the desired solution quantities (eg, displacements, strains, stresses). It has been shown that the microscopic and macroscopic behaviour essentially depends on the size, shape and properties of fibers as well as on their spatial distribution within the matrix. Severe errors in critical values of response quantities (eg, stresses) can be obtained for all the averaging methods.

Journal of the Institution of Engineers (India): Aerospace Engineering Journal

A comparative study of averaging schemes for periodic heterogeneous media

In this paper an effort has been made to model and damp a rotating flexible beam with a rotary joint. In this work bending of flexible beam is considered using Euler-Bernoulli beam theory. To model a flexible beam, which is essentially a continuous system, it is discretized by using finite element method. After finding the expression for displacement at any point using finite element method, the dynamic equations of motion are derived using Lagrangian formulation. Time response results are obtained for undamped and viscous damped systems. Finally flexible beam is modelled as -a typical laminated composite beam made up of number of layers of passive damping coating and a magnetostrictive material. A combined passive and active damping strategy in hybrid mode using combination of layers of ferromagnetic (passive) and smart (active) magnetostrictive (Terfenol-D) materials is proposed.

Hybrid damping of smart flexible rotating beam

The flow field generated by the diffraction of a shock wave from the open end of a shock tube is studied using the Particle Image Velocimetry (PJV). In particular, we examine the evolution of the compressible vortex ring as it travels from the tube exit. The shock Mach number was varied from about 1. 2 to 1. 5. The vorticity field associated with the vortex ring and its core are calculated from the measured velocity field. During initial formation and propagation, a jet like flow exists behind the vortex ring. The vortex ring detachment from the tailing jet, commonly referred to" pinch-off" is described in terms of a non-dimensional parameter. Far field microphone measurements show that the pressure signal consists of two pressure pulses of significant intensity corresponding to the spherically expanding shock wave and the incipient formation of the vortex ring at the tube exit Vortex generated sound is also identified in the signal with high frequency pressure fluctuations.