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A numerical method is presented in this paper for the free vibration analysis of circular and elliptical first order shear deformable plates. In this method, the ellipse is mapped into a circle and then the circular geometry of the plate is mapped using parabolic interpolation function of natural coordinates and eight nodal points of prescribed coordinates. The displacement fields are defined by a set of relatively very high order interpolation functions and for the displacement degrees of freedom a set of nodal points are defined separate from those of the geometric interpolation. Numerical results for the fully clamped elliptical plate are obtained and compared with the available data from the literature. Additional results for the simply 1‐supported complete elliptical plate and the annular elliptical plates subjected to various boundary conditions are presented and discussed.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

A bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view is given. The bibliography at the end of the paper contains 1,726 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1996‐1999.

This paper gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The bibliography at the end of the paper contains more than 1330 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1999–2002.

Ferrofluid lubrication of a porous secant shaped slider bearing was analysed considering slip velocity at the interface of film and porous regions. Expressions for various bearing characteristics were obtained. Computed values of dimensionless load capacity of the bearing, friction force on the moving slider, coefficient of friction and the position of the centre of pressure were displayed in a tabular form. The load capacity, friction and coefficient of friction decreased when the slip parameter increased. But, the load capacity as well as friction decreased and the coefficient of friction increased when the permeability parameter increased. The position of the centre of pressure was not significantly altered when the slip parameter increased. But, it slowly moved towards the inlet when the permeability parameter increased.

This paper aims to improve upon the performance of magnetic fluid‐based squeeze film between transversely rough curved annular plates by embarking on a comparative study of the geometrical structure of the curved annular plates.

The objectives are met by mathematically modeling a magnetic fluid‐based squeeze film between transversely rough curved annular plates. The standard method is to solve the associated Reynolds' equation with appropriate boundary conditions by describing the random roughness through a stochastic random variable with non‐zero mean, variance and skewness. Results for bearing performance characteristics such as pressure distribution and load‐carrying capacity are numerically computed. In order to analyze the quantitative effect of the roughness, different geometrical structures of surfaces have been considered and the results are compared.

Certainly, the performance of the bearing with the magnetic fluid lubricant is comparatively better than the conventional lubricant. The findings indicate that although the effect of roughness is adverse in general, the adverse effect introduced by roughness and aspect ratio can be compensated for, to a considerable extent, by the positive effect of magnetization parameter in the case of negatively skewed roughness by choosing the curvature parameters properly.

From the industry point of view, this investigation will be definitely useful for improving the performance of the squeeze film based on magnetic fluid between transversely rough curved annular plates by minimizing the effect of roughness. Furthermore, it offers an additional degree of freedom from a design point of view in the form of the geometrical structure of the surfaces.

The paper presents significant information as it compares shapes and offers suggestions for the best improved performance from a bearing's longevity point of view. This study presents an approach for the enhanced performance of the magnetic fluid‐based squeeze film between transversely rough curved annular plates.

The analysis of squeeze‐film performances between curved annular plates with an electrically conducting fluid in the presence of a transverse magnetic field is presented in this study. The magneto‐hydrodynamic (MHD) Reynolds‐type equation for squeezing‐film curved annular disks is derived using the continuity equation and the MHD motion equations. A closed‐form solution for the squeezing film pressure is obtained, and applied to predict the MHD squeeze‐film characteristics. According to the results obtained, the presence of applied magnetic fields signifies an increase in the MHD squeeze‐film pressure. Compared with the classical non‐conducting‐lubricant case, the magnetic‐field effect characterized by the Hartmann number provides an enhancement to the MHD load‐carrying capacity and the response time, especially for larger values of the curved shape parameter or smaller values of inner‐outer radius ratio of the curved annular disks.

The purpose of this research is to extract the natural frequencies of a circular plate containing a central hole reinforced with boron nitride nanotubes (BNNTs) and containing piezoelectric layers.

A unit cell shall be taken into account for the simulation of BNNT's volume fraction. A rectangular micromechanical model is used to obtain the mechanical properties of unit cell of piezoelectric fiber-reinforced composite (PFRC). The three-dimensional (3D) elasticity method is presented to provide the relationship between displacements and stresses. The one-dimensional differential quadrature method (1D-DQM) and the state-space methodology are combined to create the semi-analytical technique. The state-space approach is utilized to implement an analytical resolution in the thickness direction, and 1D-DQM is used to implement an approximation solution in the radial direction. The composite consists of a polyvinylidene fluoride (PVDF) matrix and BNNTs as reinforcement.

A study on the PFRC is carried, likewise, the coefficients of its properties are obtained using a micro-electromechanical model known as the rectangular model. To implement the DQM, the plate was radially divided into sample points, each with eight state variables. The boundary situation and DQM are used to discretize the state-space equations, and the top and bottom application surface conditions are used to determine the natural frequencies of the plate. The model's convergence is assessed. Additionally, the dimensionless frequency is compared to earlier works and ABAQUS simulation in order to validate the model. Finally, the effects of the thickness, lateral wavenumber, boundary conditions and BNNT volume fraction on the annular plate's free vibration are investigated. The important achievements are that increasing the volume fraction of BNNTs increases the natural frequency.

The micromechanical “XY rectangle” model in PFRC along with the three-dimensional elasticity model is used in this literature to assess how the piezoelectric capabilities of BNNTs affect the free vibration of polymer-based composite annular plates under various boundary conditions.

The purpose of this paper is to study and analyse the behaviour of a magnetic fluid-based squeeze film between rotating transversely rough porous annular plates, taking the elastic deformation into consideration.

The stochastic film thickness characterizing the roughness is considered to be asymmetric with non-zero mean and variance and skewness while a magnetic fluid is taken as the lubricant. The associated stochastically averaged Reynolds-type equation is solved with appropriate boundary conditions to obtain the pressure distribution, which in turn is used to derive the expression for the load-carrying capacity.

It is observed that the roughness of the bearing surfaces affects the performance adversely, although the bearing registers an improved performance owing to the magnetic fluid lubricant. Also, it is seen that the deformation causes reduced load-carrying capacity. The bearing can support a load even in the absence of flow, unlike the case of conventional lubricants.

The originality of the paper lies in the fact that the negative effect of porosity, deformation and standard deviation can be minimized to some extent by the positive effect of the magnetic fluid lubricant in the case of negatively skewed roughness by suitably choosing the rotational inertia and aspect ratio. This effect becomes sharper when negative variance occurs.

This paper aims to study the effects of surface roughness on the characteristics of squeeze film lubrication between curved annular plates.

The modified Reynolds type equation governing the fluid film pressure is derived. The stochastic method for rough surfaces developed by Christensen is to derive stochastic type equation and has been solved for two types of one‐dimensional roughness patterns. Closed form expressions of mean squeeze film pressure and mean load carrying capacity are obtained.

The bearing characteristics are computed for various values of roughness parameter. It is found that the effect of radial (circumferential) roughness pattern is to shift the point of maximum pressure towards the inlet (outlet) edge and also observe that the mean load‐carrying capacity increases (decreases) for the circumferential (radial) roughness pattern compared with the corresponding smooth case, for both concave and convex pad geometries.

The analysis is useful in obtaining suitable mathematical model of physical problems. The one which we have considered here is the idealized form of functioning of bearings in general. Analysis of finer models requires pure numerical schemes, for which the present model is a base.

Findings of the present paper have applications in machine elements like clutch plates and collar bearings.

Inclusions of surface roughness effect on the characteristics of bearings are original contributions in tribology.