scholarly journals Vibration Analysis of Rectangular Plates with One or More Guided Edges via Bicubic B-Spline Method

2005 ◽  
Vol 12 (5) ◽  
pp. 363-376 ◽  
Author(s):  
W.J. Si ◽  
K.Y. Lam ◽  
S.W. Gong
Keyword(s):  
Vibration Analysis ◽  
Plate Theory ◽  
Spline Interpolation ◽  
Accurate Method ◽  
Spline Functions ◽  
Rectangular Plates ◽  
B Spline ◽  
Thin Plate Theory ◽  
Edge Conditions ◽  
New Type

A simple and accurate method is proposed for the vibration analysis of rectangular plates with one or more guided edges, in which bicubic B-spline interpolation in combination with a new type of basis cubic B-spline functions is used to approximate the plate deflection. This type of basis cubic B-spline functions can satisfy simply supported, clamped, free, and guided edge conditions with easy numerical manipulation. The frequency characteristic equation is formulated based on classical thin plate theory by performing Hamilton's principle. The present solutions are verified with the analytical ones. Fast convergence, high accuracy and computational efficiency have been demonstrated from the comparisons. Frequency parameters for 13 cases of rectangular plates with at least one guided edge, which are possible by approximate or numerical methods only, are presented. These results are new in literature.

On the Literature of B-Spline Interpolation Functions

2009 ◽  
pp. 214-222
Author(s):  
Carlo Ciulla
Keyword(s):  
Scientific Community ◽  
Polynomial Interpolation ◽  
Spline Interpolation ◽  
Spline Functions ◽  
Great Effort ◽  
Formal Definition ◽  
B Spline ◽  
B Splines ◽  
Scientific Disciplines ◽  
Definition Of

This chapter reviews the extensive and comprehensive literature on B-Splines. In the forthcoming text emphasis is given to hierarchy and formal definition of polynomial interpolation with specific focus to the subclass of functions that are called B-Splines. Also, the literature is reviewed with emphasis on methodologies and applications of B-Splines within a wide array of scientific disciplines. The review is conducted with the intent to inform the reader and also to acknowledge the merit of the scientific community for the great effort devoted to B-Splines. The chapter concludes emphasizing on the proposition that the unifying theory presented throughout this book has for what concerns two specific cases of B-Spline functions: univariate quadratic and cubic models.

BICUBIC SPLINE INTERPOLATION AS A METHOD FOR TREATMENT OF POTENTIAL FIELD DATA

Geophysics ◽  
1969 ◽  
Vol 34 (3) ◽  
pp. 402-423 ◽  
Author(s):  
B. K. Bhattacharyya
Keyword(s):  
Field Data ◽  
Spline Interpolation ◽  
Amplitude Spectrum ◽  
Accurate Method ◽  
Fourier Series Expansion ◽  
Small Scale ◽  
Spline Functions ◽  
Two Dimensional ◽  
Potential Field Data ◽  
Bicubic Spline

A method for the generation of bicubic spline functions is presented in this paper. From this method it becomes apparent that these functions derive their potential strength in accurate and reliable representation of two‐dimensional data by maintaining continuity of the variable and its slope and curvature throughout the area of observation. The results obtained by computing horizontal and vertical derivatives with model and field data illustrate the exceptional accuracy achieved with spline functions. The piecewise cubic polynomial functions expressing observed data analytically in space are used to estimate amplitude and phase spectra of magnetic anomalies. At relatively long wavelengths the amplitude spectrum thus calculated displays remarkable similarity with the true spectrum and is found to be superior to that obtained with two‐dimensional Fourier series expansion. A cubic spline method is also presented for computing values of an observed variable at equispaced points along two orthogonal directions with the help of irregularly distributed data. The interpolation technique applied to field data shows high resolution by maintaining the separation of neighboring anomalies and the small‐scale features. The shapes, peaks, and troughs of both large and small amplitude anomalies are faithfully reproduced. The gradients of the magnetic field do not undergo any appreciable distortion. It can thus be concluded that cubic splines are a reliable and accurate method of interpolation.

Inverse Design of Airfoils Using Target Pressure Optimization

2013 ◽  
Vol 694-697 ◽  
pp. 3183-3188
Author(s):  
Ya Feng Liu ◽  
Dong Li Ma
Keyword(s):  
Genetic Algorithm ◽  
Laminar Flow ◽  
Design Method ◽  
Spline Interpolation ◽  
Inverse Design ◽  
Spline Functions ◽  
Control Points ◽  
B Spline ◽  
Pressure Distributions ◽  
Target Pressure

The Direct Iterative Surface Curvature (DISC) airfoil design method developed by NASA Langley, which is one of the inverse design methods, is robust and effective. In order to determine the target pressure distributions of airfoils, this paper used the uniformed B-spline interpolation for the parameterization of the target pressure, and a Genetic Algorithm (GA) was used to optimize the coordinates of the control points of the B-spline functions. Two cases were given to prove the effect of the DISC design method. A laminar flow airfoil was then designed using DISC after a target pressure had been determined by a GA. Results show that the DISC method based on target pressure optimization using GAs is pretty effective.

Vibration analysis of flat shells by using B spline functions

1987 ◽  
Vol 25 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Peng-Chen Shen ◽  
Jun-Guo Wan
Keyword(s):  
Vibration Analysis ◽  
Spline Functions ◽  
B Spline

scholarly journals Use of Higher Order Plate Theory in dynamic analysis of SSFS and CSFS thick rectangular plates in orthogonal polynomials

2021 ◽  
Vol 40 (2) ◽  
pp. 199-209
Author(s):  
I.C. Onyechere ◽  
U.C. Anya ◽  
O.M. Ibearugbulem ◽  
A.U. Igbojiaku ◽  
E.O. Ihemegbulem ◽  
...  
Keyword(s):  
Potential Energy ◽  
Governing Equation ◽  
Plate Theory ◽  
Total Potential Energy ◽  
The Other ◽  
Frequency Function ◽  
Rectangular Plates ◽  
Total Potential ◽  
Edge Conditions ◽  
Simple Supports

This study applied polynomial expressions as displacement and shear deformation functions in the free-vibration study of thick and moderately thick isotropic rectangular plates. Rectangular plates with two different edge conditions investigated in this work are: one with simple supports at three of its edges and with no support at the other edge denoted with the acronym (SSFS) and a rectangular plate with simple supports at opposite edges while the other opposite edges has a fixed support at one edge and no support at the other edge, this is denoted with the acronym (CSFS). The total potential energy of the plate was derived using the general theory of elasticity. The general governing equation of the plate was derived by minimizing the total potential energy equation of the plate. Edge conditions of the SSFS and CSFS plates were met and substituted into the general governing equation to obtain a linear expression which was solved to generate fundamental natural frequency function for the plates with various span-depth proportion (m/t) and planar dimensions proportion (n/m). The results obtained from this research were found to agree favourably with the results of similar problems in the literature upon comparison.

Free-Vibration Analysis of Rectangular Plates With Clamped-Simply Supported Edge Conditions by the Method of Superposition

1977 ◽  
Vol 44 (4) ◽  
pp. 743-749 ◽  
Author(s):  
D. J. Gorman
Keyword(s):  
Differential Equation ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Formidable Challenge ◽  
Edge Conditions ◽  
Governing Differential Equation

In this paper attention is focused on the free-vibration analysis of rectangular plates with combinations of clamped and simply supported edge conditions. Plates with at least two opposite edges simply supported are not considered as they have been analyzed in a separate paper. It is well known that the family of problems considered here have presented researchers with a formidable challenge over the years. This is because they are not directly amenable to Le´vy-type solutions. It has been pointed out in the literature that most of the existing solutions are approximate in that they either do not satisfy exactly the governing differential equation or the boundary conditions, or both. In a new approach taken by the author the method of superposition is exploited for handling these dynamic problems. It is found that solutions of any degree of exactitude are easily obtained. The governing differential equation is completely satisfied and the boundary conditions are satisfied to any degree of exactitude by merely increasing the number of terms in the series. Convergence is shown to be remarkably rapid and tabulated results are provided for a large range of parameters. The immediate applicability of the method to problems involving elastic restraint or inertia forces along the plate edges has been discussed in an earlier publication.

Exact Solutions for Free-Vibration Analysis of Rectangular Plates Using Bessel Functions

2005 ◽  
Vol 74 (6) ◽  
pp. 1247-1251 ◽  
Author(s):  
Jiu Hui Wu ◽  
A. Q. Liu ◽  
H. L. Chen
Keyword(s):  
Differential Equation ◽  
Free Vibration ◽  
Exact Solutions ◽  
Thin Plate ◽  
Vibration Analysis ◽  
Bessel Functions ◽  
Free Vibration Analysis ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Edge Conditions

A novel Bessel function method is proposed to obtain the exact solutions for the free-vibration analysis of rectangular thin plates with three edge conditions: (i) fully simply supported; (ii) fully clamped, and (iii) two opposite edges simply supported and the other two edges clamped. Because Bessel functions satisfy the biharmonic differential equation of solid thin plate, the basic idea of the method is to superpose different Bessel functions to satisfy the edge conditions such that the governing differential equation and the boundary conditions of the thin plate are exactly satisfied. It is shown that the proposed method provides simple, direct, and highly accurate solutions for this family of problems. Examples are demonstrated by calculating the natural frequencies and the vibration modes for a square plate with all edges simply supported and clamped.

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