scholarly journals Elastodynamic singular points and their applications

1981 ◽  
Vol 4 (4) ◽  
pp. 795-803 ◽  
Author(s):  
A. D. Alawneh ◽  
R. P. Kanwal
Keyword(s):  
Elastic Medium ◽  
Approximate Solutions ◽  
Higher Order ◽  
Singular Points ◽  
Isotropic Elastic Medium ◽  
Set Up

Suitable singularites such as a dynamical Kelvin quadropole are defined to study the dynamical displacements set up in an infinite homogeneous and isotropic elastic medium. Approximate solutions are presented up to terms which are of higher order than those known so far.

Vibration of Rectangular Plates by the Ritz Method

1950 ◽  
Vol 17 (4) ◽  
pp. 448-453 ◽  
Author(s):  
Dana Young
Keyword(s):  
Ritz Method ◽  
Normal Modes ◽  
Approximate Solutions ◽  
The Other ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Modes Of Vibration ◽  
Ritz’S Method ◽  
Square Plate ◽  
Set Up

Abstract Ritz’s method is one of several possible procedures for obtaining approximate solutions for the frequencies and modes of vibration of thin elastic plates. The accuracy of the results and the practicability of the computations depend to a great extent upon the set of functions that is chosen to represent the plate deflection. In this investigation, use is made of the functions which define the normal modes of vibration of a uniform beam. Tables of values of these functions have been computed as well as values of different integrals of the functions and their derivatives. With the aid of these data, the necessary equations can be set up and solved with reasonable effort. Solutions are obtained for three specific plate problems, namely, (a) square plate clamped at all four edges, (b) square plate clamped along two adjacent edges and free along the other two edges, and (c) square plate clamped along one edge and free along the other three edges.

scholarly journals Existence and Iterative Algorithms of Positive Solutions for a Higher Order Nonlinear Neutral Delay Differential Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-28 ◽  
Author(s):  
Zeqing Liu ◽  
Ling Guan ◽  
Sunhong Lee ◽  
Shin Min Kang
Keyword(s):  
Differential Equation ◽  
Positive Solutions ◽  
Delay Differential Equation ◽  
Iterative Algorithms ◽  
Approximate Solutions ◽  
Higher Order ◽  
Banach Fixed Point Theorem ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Delay Differential

This paper is concerned with the higher order nonlinear neutral delay differential equation[a(t)(x(t)+b(t)x(t-τ))(m)](n-m)+[h(t,x(h1(t)),…,x(hl(t)))](i)+f(t,x(f1(t)),…,x(fl(t)))=g(t),for allt≥t0. Using the Banach fixed point theorem, we establish the existence results of uncountably many positive solutions for the equation, construct Mann iterative sequences for approximating these positive solutions, and discuss error estimates between the approximate solutions and the positive solutions. Nine examples are included to dwell upon the importance and advantages of our results.

scholarly journals Numerical Solution of Higher Order Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Shahid S. Siddiqi ◽  
Muzammal Iftikhar
Keyword(s):  
Boundary Value Problems ◽  
Homotopy Analysis Method ◽  
Present Method ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Higher Order ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Linear And Nonlinear

The aim of this paper is to use the homotopy analysis method (HAM), an approximating technique for solving linear and nonlinear higher order boundary value problems. Using HAM, approximate solutions of seventh-, eighth-, and tenth-order boundary value problems are developed. This approach provides the solution in terms of a convergent series. Approximate results are given for several examples to illustrate the implementation and accuracy of the method. The results obtained from this method are compared with the exact solutions and other methods (Akram and Rehman (2013), Farajeyan and Maleki (2012), Geng and Li (2009), Golbabai and Javidi (2007), He (2007), Inc and Evans (2004), Lamnii et al. (2008), Siddiqi and Akram (2007), Siddiqi et al. (2012), Siddiqi et al. (2009), Siddiqi and Iftikhar (2013), Siddiqi and Twizell (1996), Siddiqi and Twizell (1998), Torvattanabun and Koonprasert (2010), and Kasi Viswanadham and Raju (2012)) revealing that the present method is more accurate.

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