Values Of Taper Constant Research Articles

Vibration of Visco-Elastic Parallelogram Plate with Thickness Variation Linearly in one Direction and Parabolic in another Direction

The main objective of the present investigation is to study the vibration of visco-elastic parallelogram plate whose thickness varies bi-directionally. It is assumed that the plate is clamped on all the four edges and that the thickness varies linearly in one direction and parabolically in another direction. Using the separation of variables method and Rayleigh-Ritz technique with a two-term deflection function, the governing differential equation has been solved for vibration of visco-elastic parallelogram plate. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The assumption of small deflection is made. Visco-elastic of the plate is taken of the “Kelvin Type”. Time period and deflection function at different point for the first two modes of vibration are calculated for various values of taper constant, aspect ratio and skew angle and results are presented in tabular form. Alloy “Duralumin” is considered for all the material constants used in numerical calculations.

Forced vibrations of non-homogeneous rectangular plate of linearly varying thickness

An analysis is presented of the forced vibrations of non-homogeneous rectangular plate of variable thickness on the basis of classical plate theory. The non-homogeneity of the plate material is assumed to arise due to the variation in density which is assumed to vary linearly. The thickness of the plate also varies linearly. Approximate formulae are proposed for estimating the maximum deflection of a rectangular plate subject to a uniformly distributed harmonic lateral load. Maximum deflection for the different values of the fundamental frequency of vibration is computed for a simply supported-free-simply supported-free plate for various values of taper constant, non-homogeneity constant and aspect ratios. Results are presented in graphical form.

Vibration of Visco-elastic Orthotropic Parallelogram Plate with Linear Thickness Variation in Both Directions

A simple model presented here for vibration of a visco-elastic, orthotropic parallelogram plate with linear thickness variation in both directions. Using the separation of variables method, the governing differential equation has been solved for the vibration of a visco-elastic, orthotropic parallelogram plate having clamped boundary conditions on all four of the edges. An approximate but convenient frequency equation is derived by using the Rayleigh-Ritz technique with a two-term deflection function. The time period and deflection function at different points for the first two modes of vibration are calculated for various values of taper constants, aspect ratio and skew angle.

Analysis of Plate Vibration under Exponentially Varying Thermal Condition

A mathematical model is developed to assist the design engineers by analyzing the vibration response of non-homogeneous orthotropic rectangular plate under exponentially varying thermal condition. Plate thickness varies parabolically in both directions. Using Rayleigh Ritz approach, frequency parameter and two term deflection function is calculated for diverse values of taper constants. For the best comprehension of the vibration analysis, results are depicted graphically.

Study the Thermal Gradient Effect on Frequencies of a Trapezoidal Plate of Linearly Varying Thickness

In this paper, effect of thermal gradient on vibration of trapezoidal plate of varying thickness is studied. Thermal effect and thickness variation is taken as linearly in x-direction. Rayleigh Ritz technique is used to calculate the fundamental frequencies. The frequencies corresponding to the first two modes of vibrations are obtained for a trapezoidal plate for different values of taper constant, thermal gradient and aspect ratio. Results are presented in graphical form.

Effect of thermal gradient on vibration of non-homogeneous visco-elastic elliptic plate of variable thickness

An analysis and numerical results are presented for free transverse vibrations of non-homogeneous visco-elastic elliptic plate whose temperature and thickness spatial variations both are parabolic along a line through plate centre. The variation in density is assumed as parabolic along a line through plate centre, which raise non-homogeneity of the plate materials and make problem interesting as introducing variation in non-homogeneity of the material mass density reduce the problem practical importance in comparison to homogenous plate. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The governing differential equation of motion has been solved by Galerkin’s technique. Deflection, time period and logarithmic decrement corresponding to the first two modes of vibrations of a clamped non-homogeneous visco-elastic elliptic plate for various values of taper constant, thermal constants, non-homogeneity constant and aspect ratio are obtained and shown graphically.

Vibration of Clamped Visco‐Elastic Rectangular Plate with Parabolic Thickness Variations

Most of the machines and engineering structures experience vibration and their design generally requires consideration for their dynamic behavior. Due to this, the study of vibration, as it deals with the vibratory behavior of bodies, is acquiring increasingly importance in several engineering applications, nuclear reactor technology and aeronautical field etc. Most of the work has been done in the field of elastic and non‐elastic behavior of the bodies but a very little work is done in the field of visco‐elastic bodies with varying thickness. The analysis presented here is to study the effect of taper constants on free vibration of a clamped visco‐elastic rectangular plate with parabolically varying thickness. The two‐dimensional thickness variation is taken as the Cartesian product of parabolic variations along the two concurrent edges of the plate. Using Rayleigh‐Ritz method, frequency equation derives. Logarithmic decrement, time period and deflection for the first two modes of vibration are calculated for various values of taper constants and aspect ratio.

Vibration of visco-elastic rectangular plate with linearly thickness variations in both directions

The analysis presented here is to study the effect of linear thickness variations in both directions on vibration of visco-elastic rectangular plate having clamped boundary conditions on all the four edges. Using the separation of variables method, the governing differential equation has been solved for vibration of visco-elastic rectangular plate. An approximate but quite convenient frequency equation is derived by using Rayleigh–Ritz technique with a two-term deflection function. Logarithmic decrement, time period and deflection at different points for the first two modes of vibration are calculated for various values of taper constants and aspect ratio.

Vibrational characteristics of annular plates and rings of radially varying thinkness

In this paper, annular plates having thickness variation are studied by deriving the equations of motion on the basis of the Mindlin plate theory. The Chebyshev collocation method is employed to solve the differential equation governing the transverse motion of such plates. The dimensionless frequencies are evaluated for different values of taper constant (α), thickness ratio (hu). radii ratio (e) and power (n). The results of an experimental investigation are also presented, and the agreement between these findings and the predicted values in theory is remarkably good. As a result of this study, it is found that the effects of rotatory inertia and transverse shear deformation reduce the natural frequencies for all boundary conditions and for all values ofn. ho, ∈, a ands (mode number). This study also showed that the natural frequencies of annular plates with thickness expressed by the nth power function are higher than those by the (n−1)th power function for positive values of α, and vice versa for negative values ofe for all three boundary conditions. Moreover, there is a proof that the natural frequencies of annular plates tend to be higher as the taper constant decrease and/or as the radii ratio increase for all three boundary conditions and for all values ofn, s andho.

Natural frequencies of a linearly tapered non-homogeneous isotropic elastic circular plate resting on an elastic foundation

An analysis is presented here for the design of engineering systems where composite materials and non-uniform structures are used. A simple model for free vibrations of a non-homogeneous isotropic elastic circular plate of linearly varying thickness resting on an elastic foundation is considered. The governing differential equation of motion is solved by the Frobenius method. The frequencies, deflections and moments corresponding to the first five modes of vibration are computed for clamped and simply supported edge conditions for various values of taper constant, non-homogeneity parameter and foundation modulus.

Buckling and vibrations of polar orthotropic annular plates on elastic foundation subjected to hydrostatic peripheral loading

An analysis is presented of the effect of hydrostatic peripheral loading and that of an elastic foundation on the natural frequencies of free axisymmetric vibrations and critical buckling parameter of linearly varying thickness annular plates exhibiting polar orthotropic characteristics, on the basis of classical plate theory. The numerical solution of the governing differential equation derived by using Hamilton's energy principle is obtained by the spline technique method for three different boundary conditions: inner and outer both clamped; inner clamped and outer simply supported; inner free and outer clamped. Transverse displacements, moments in normalized form for a particular set of plate parameters and buckling loads in compression for different values of taper constant, foundation modulus and rigidity ratios have been computed for the first two modes of vibration. The numerical results are compared with exact values and with the results of other authors. The close agreement of the values illustrates the versatility of this simple and elegant method, provided the number of nodal points is taken appropriately.

Natural frequencies of a non homogeneous isotropic elastic infinite plate of variable thickness resting on elastic foundation

The dynamic free response of a nonhomogeneous isotropic elastic infinite plate of parabolically varying thickness resting on an elastic foundation has been studied. The frequencies, deflections and moments corresponding to the first five modes of vibration have been computed for the two combinations of boundary conditions, clamped-clamped (C-C) and clamped-simply supported (C-SS) and various values of taper constant, nonhomogeneity parameter and foundation modulus by applying the method of Frobenius for the solution of the governing differential equation of motion.

Thermal effect on frequencies of an orthotropic rectangular plate of linearly varying thickness

An analysis is presented here of the effect of a constant thermal gradient on free axisymmetric vibrations of an orthotropic elastic rectangular plate of linearly varying thickness. The governing differential equation of motion is solved by Frobenius' method. The frequencies corresponding to the first two modes of vibrations are obtained for an orthotropic rectangular plate with different combinations of boundary conditions for various values of taper constant and the temperature gradient.

Axisymmetric vibrations of annular plates of variable thickness

Free axisymmetric vibrations of annular plates of variable thickness have been studied on the basis of the classical theory of plates. The Chebyshev collocation method has been employed to solve the differential equation governing the transverse motion of such plates. The displacement of the plate element is expressed as a Chebyshev polynomial in terms of the radial co-ordinate. Frequencies and mode shapes have been computed for different values of taper constant and radii ratio, for the first two modes of vibration of a plate with a linearly varying thickness, treated as an example.

Quintic splines in vibrations of nonuniform annular plates

Free axisymmetric vibrations of annular plates of non-uniform thickness have been studied on the basis of classical theory of plates. The fourth order differential equation governing the transverse motion is solved using the quintic spline interpolation technique. Characteristic equations for plates of linearly varying thickness have been obtained for three combinations of boundary conditions at the inner and outer boundaries. Frequencies, mode shapes and moments have been computed for different values of taper constant and radii ratio, for the first two modes of vibration.

Axisymmetric vibrations of circular plates of linearly varying thickness

Free axisymmetric vibrations of circular plates of linearly varying thickness have been studied on the basis of classical theory of plates. The differential equation governing the motion of such plates have been solved by Frobenius method. The transverse displacement has been expressed as an infinite power series in the radial coordinate. Frequency parameters have been computed for the first three modes of vibration for clamped as well as simply supported circular plates corresponding to different values of taper constant.

Effect of Transverse Shear and Rotatory Inertia on Vibrations of an Infinite Strip of Variable Thickness

Free vibrations of an infinite strip of parabolically varying thickness have been studied on the basis of shear theory of plates. The differential equations governing the motion of such strips have been solved by Frobenius method of series solution. Transverse deflection as well as rotation in the strip elements are obtained as infinite series. Frequency parameters are calculated for different values of taper constant and thickness to breadth ratio for two combinations of boundary conditions.