P.K. Sinha

Active vibration control of composite sandwich beams with piezoelectric extension-bending and shear actuators

We have used quasi-static equations of piezoelectricity to derive a finite element formulation capable of modelling two different kinds of piezoelastically induced actuation in an adaptive composite sandwich beam. This formulation is made to couple certain piezoelectric constants to a transverse electric field to develop extension-bending actuation and shear-induced actuation. As an illustration, we present a sandwich model of three sublaminates: face/core/face. We develop a control scheme based on the linear quadratic regulator/independent modal space control (LQR/IMSC) method and use this to estimate the active stiffness and the active damping introduced by shear and extension-bending actuators. To assess the performance of each type of actuator, a dynamic response study is carried out in the modal domain. We observe that the shear actuator is more efficient in actively controlling the vibration than the extension-bending actuator for the same control effort.

Hygrothermal effects on the free vibration of laminated composite plates

Abstract Effects of moisture and temperature on the free vibration of laminated composite plates are investigated. The analysis is carried out by the finite element method with the quadratic isoparametric element, which takes transverse shear deformation into account. The analysis also accounts for lamina material properties at elevated moisture concentration and temperature. Results are presented showing the reduction in the natural frequency with the increase in uniform moisture concentration and temperature for symmetric and antisymmetric laminates with simply supported and clamped boundary conditions.

Hygrothermal effects on the buckling of laminated composite plates

Abstract The effects of moisture and temperature on the static instability of laminated composite plates are investigated. The analysis is carried out by the finite element method using a quadratic isoparametric element which takes transverse shear deformation into account. The conventional finite element formulation is modified to include hygrothermal effects. The stiffness matrix, geometric stiffness matrix due to residual stresses, geometric stiffness matrix due to applied in-plane loads and load vector of the element are derived based upon the principle of minimum potential energy. The analysis accounts for reduced lamina material properties at elevated moisture concentrations and temperatures. Critical loads are obtained for symmetric and anti-symmetric laminates with simply-supported and clamped boundary conditions at different moisture concentrations and temperatures. Their dependence on moisture and temperature is studied. The effects of aspect ratio and side-to-thickness ratio on the critical loads are also considered. Mode shapes are verified in a few cases for anti-symmetric cross-ply laminate.

Hygrothermal effects on the bending characteristics of laminated composite plates

Abstract Effects of moisture and temperature on the bending characteristics of laminated composite plates are investigated. The analysis is carried out by the finite element method using the quadratic isoparametric plate bending element which takes transverse shear deformation into account. The analysis also accounts for reduced lamina material properties at the elevated moisture concentration and temperature. Deflections and stress resultants are obtained for anti-symmetric cross-ply and angle-ply laminates for simply-supported and clamped boundary conditions at different moisture concentrations and temperatures, and their dependence on moisture and temperature is studied.

Microstructural studies of (PbLa)(ZrTi)O3 ceramics using complex impedance spectroscopy

Lanthanum modified lead zirconate titanate (PLZT:8∕60∕40) ceramics prepared by a sol-gel route showed a well-defined microstructure comprising of grains separated by boundaries. Complex impedance spectroscopy has provided a convincing evidence for the existence of both grain (bulk) and grain-boundary effects that were separated in the frequency domain in impedance spectrum. The impedance analysis further provided the value of relaxation frequency, which was a characteristic intrinsic property of the material and was independent of sample geometrical factors. Relaxation frequency calculated at different temperatures was used to evaluate bulk dielectric constant (eb), which was compared with the real part of the dielectric constant (e′). The temperature variation of the bulk electrical conductivity (σdc) indicated an evidence of Arrhenius-type thermally activated process showing a linear variation up to a temperature of 713°K and was predominantly governed by grain boundary conduction showing a plateau regi...

Bending and free vibration analysis of shear deformable laminated composite beams by finite element method

In the present investigation a higher-order shear deformation theory and the conventional first-order theory are used to develop a finite element method to analyse accurately the bending and free vibration behaviour of laminated composite beams, using nine-noded isoparametric elements. The higher-order theory assumes all the displacement components, u, v and w, which contain variation up to a cubic power of z. The effects of various parameters such as fibre orientation, stacking sequence, span-to-thickness ratio and support condition on the non-dimensionalised deflections, stresses and fundamental frequencies are investigated. Cases where only the higher-order theory is likely to yield accurate results are highlighted.

Non-linear coupled slosh dynamics of liquid-filled laminated composite containers: a two dimensional finite element approach

Abstract This paper brings into focus some of the interesting effects arising from the non-linear motion of the liquid free surface, due to sloshing, in a partially filled laminated composite container along with the associated coupling due to fluid–structure interaction effects. The finite element method based on two-dimensional fluid and structural elements is used for the numerical simulation of the problem. A numerical scheme is developed on the basis of a mixed Eulerian–Lagrangian approach, with velocity potential as the unknown nodal variable in the fluid domain and displacements as the unknowns in the structure domain. The FE formulation based on Galerkin weighted residual method along with an iterative solution procedure are explained in detail followed by a few numerical examples. Numerical results obtained by the present investigation for the rigid containers are first compared with the existing solutions to validate the code for non-linear sloshing without fluid–structure coupling. Thereafter the computational procedures are advanced to obtain the coupled interaction effect of non-linear sloshing in laminated composite containers.

Dynamic response analysis of a liquid-filled cylindrical tank with annular baffle

Abstract Baffles are generally used as damping devices in liquid storage tanks. The focus of the present paper is to study the influence of a baffle on the dynamic response of a partially liquid-filled cylindrical tank. A baffle is assumed here to have the shape of a thin annular circular plate. The natural frequencies of an inviscid and incompressible liquid are determined for varying positions and dimensions of a baffle attached normal to the tank wall. The flexibility of both the baffle and the tank are considered in studying the effects of liquid–baffle and liquid–tank interactions on the sloshing mode frequencies. Finite element codes are developed and are then used to analyze both the liquid domain and the structural domain (i.e., the tank and the baffle). The coupled vibration frequencies of the tank–baffle system are computed considering the effect of sloshing of liquid. The results obtained for a liquid-filled elastic tank without a baffle and a rigid tank with a rigid baffle are in good agreement with the available results. The slosh amplitude of liquid in a rigid tank with and without a rigid baffle is studied under translational base excitation. The effects of the tank wall and baffle flexibility on the slosh response are also investigated.

Bending, free vibration and impact response of thick laminated composite plates

In the present paper, the higher-order shear deformation theories (HST6, HST9, HST11, HST12) and the conventional first-order theory (FST) are employed to develop finite element analysis methods using eight-noded isoparametric elements to study the bending, free vibration and impact behaviour of laminated composite plates. The present results, based on higher-order theories, compare well with those existing in the literature. The effects of various parameters, such as span to thickness ratios, support conditions and stacking sequences on the laminate response are investigated. It is revealed that the first-order theory provides reasonably dependable results for natural frequencies, contact force, impact response and velocity profile of impactor for both thin and thick laminates. However, the higher-order theories are needed to compute stresses accurately in thick laminates.

Free vibration analysis of point-supported laminated composite doubly curved shells—A finite element approach

Abstract A finite element analysis for studying the free vibration behaviour of generalized doubly curved laminated composite shells is presented using eight-noded curved quadrilateral isoparametric finite elements. The formulation assumes first-order shear deformation theory for thin and shallow shells, and also considers the two principal radii of curvature and the radius of cross-curvature. Some of the results obtained are compared with those present in the existing literature. Several other numerical results are presented by varying fibre orientations, lamination schemes, support spacings, aspect ratio, lower height to higher height ratio (for conoids), the thickness to radius ratio and radii of curvature ratio (for elliptic and hyperbolic paraboloids), which are relevant to the doubly curved shells.