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Splines in vibration analysis of non-homogeneous circular plates of quadratic thickness

Singh Robin, Dhiman Neeraj, Tamsir Mohammad

Journal of Applied Analysis

2022

Vol. 28, nr 2

263--273

Mathematical model to account for non-homogeneity of plate material is designed, keeping in mind all the physical aspects, and analyzed by applying quintic spline technique for the first time. This method has been applied earlier for other geometry of plates which shows its utility. Accuracy and versatility of the technique are established by comparing with the well-known existing results. Effect of quadratic thickness variation, an exponential variation of non-homogeneity in the radial direction, and variation in density; for the three different outer edge conditions namely clamped, simply supported and free have been computed using MATLAB for the first three modes of vibration. For all the three edge conditions, normalized transverse displacements for a specific plate have been presentedwhich shows the shiftness of nodal radii with the effect of taperness.

A study on vibration of tapered non-homogeneous rectangular plate with structural parameters

Kaur N., Singhal A., Khanna A.

International Journal of Applied Mechanics and Engineering

2018

Vol. 23, no. 4

873--884

Effects of structural parameters on the vibration of a tapered non-homogeneous rectangular plate with different combinations of boundary conditions are discussed. Tapering in the plate is assumed to be sinusoidal in the x-direction. Here, temperature variation and non-homogeneity in the plate material are also considered sinusoidal in the x-direction. The Rayleigh-Ritz method is used to calculate the frequency parameter for the first two modes of vibration for different values of the structural parameters, i.e. the taper parameter, thermal gradient, aspect ratio and non-homogeneity constant. Results are obtained for three boundary conditions, i.e. clamped boundary (C-C-C-C), simply supported boundary (SS-SS-SS-SS) and clamped-simply supported boundary (CSS-C-SS). Numerical values of the frequency parameter are given in a compact tabular form.

Charge-density-wav features in tunnel spectra of high-T superconductors

Ekino T., Gabovich A. M., Li M. S., Pękała M., Szymczak H., Voitenko A. I.

Metrology and Measurement Systems

2008

Vol. 15, nr 2

145-151

Tunnel conductance G(V) was calculated for junctions between a normal metal and a spatially inhomogeneous superconductor with a dielectric gap on the nested sections of the Fermi surface or between two such superconductors. The dielectric gapping was considered to be a consequence of the charge density wave (CDW) appearance. Spatial averaging was carried out over domains with randomly varying parameters of the CDW superconductor (CDWS). The calculated G(V)s demonstrate a smooth transformation from patterns with a pronounced dip-hump structure (DHS) at low temperature, T, into those with a pseudogap depletion of the electron density of states at higher T within the range of actual critical temperatures of the CDWS domains. Thus, it is shown that both the DHS and the pseudogap have the same origin. This circumstance provides a new insight into the problem and explains the peculiar features of G(V) for Bi2Sr2CaCu2O8+δ and related high-Tc cuprates. At the same time, the approach, being quite general, can be applied to other CDWSs which belong to various other classes of materials.