scholarly journals ANALYSIS OF COMBINED DISKS WITH PIECEWISE THICKNESS

2021 ◽  
Vol 17 (2) ◽  
pp. 12-21
Author(s):  
Elena Koreneva
Keyword(s):  
Closed Form ◽  
Analytical Approach ◽  
Laguerre Polynomials ◽  
Legendre Functions ◽  
Circular Disks

The combined constructions subjected to an action of expanding loads and consisting of separate sections are examined. Each of the mentioned sections has its own rigidity. These parts may be made from the same or from the various materials. The materials can be anisotropic or isotropic, homogeneous or inhomogeneous. The constructions under study have the round scheme and they are considered as circular disks with piecewise thickness. In the places of the separate parts conjugation the disks’ thickness can be discontinuous or continuous. The analytical approach is used. The solutions are obtained in closed form and expressed in terms of Legendre functions, Legendre, Gegenbauer and Laguerre polynomials.

Closed-form analytical approach for calculating noise contours of directive aircraft noise sources

2021 ◽  
Author(s):  
Daniel C. Amargianitakis ◽  
Rodney H. Self ◽  
Antonio J. Torija ◽  
Anderson Proenca ◽  
Athanasios P. Synodinos
Keyword(s):  
Closed Form ◽  
Analytical Approach ◽  
Aircraft Noise ◽  
Noise Sources

Generalized Heine’s identity for complex Fourier series of binomials

2010 ◽  
Vol 467 (2126) ◽  
pp. 333-345 ◽  
Author(s):  
Howard S. Cohl ◽  
Diego E. Dominici
Keyword(s):  
Fourier Series ◽  
Closed Form ◽  
Legendre Functions ◽  
Associated Legendre Functions ◽  
Complex Fourier Series

In his treatise, Heine ( Heine 1881 In Theorie und Anwendungen ) gave an identity for the Fourier series of the function , with , and z >1, in terms of associated Legendre functions of the second kind . In this paper, we generalize Heine’s identity for the function , with , and , in terms of . We also compute closed-form expressions for some  .

A NOVEL ANALYTICAL APPROACH FOR PRICING DISCRETELY SAMPLED GAMMA SWAPS IN THE HESTON MODEL

2016 ◽  
Vol 57 (3) ◽  
pp. 244-268
Author(s):  
SANAE RUJIVAN
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Analytical Approach ◽  
Solution Procedure ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Variance Swaps ◽  
Closed Form Solutions ◽  
Volatility Model ◽  
Closed Form Formula

The main purpose of this paper is to present a novel analytical approach for pricing discretely sampled gamma swaps, defined in terms of weighted variance swaps of the underlying asset, based on Heston’s two-factor stochastic volatility model. The closed-form formula obtained in this paper is in a much simpler form than those proposed in the literature, which substantially reduces the computational burden and can be implemented efficiently. The solution procedure presented in this paper can be adopted to derive closed-form solutions for pricing various types of weighted variance swaps, such as self-quantoed variance and entropy swaps. Most interestingly, we discuss the validity of the current solutions in the parameter space, and provide market practitioners with some remarks for trading these types of weighted variance swaps.

Corner-Filleted Flexure Hinges

2000 ◽  
Vol 123 (3) ◽  
pp. 346-352 ◽  
Author(s):  
Nicolae Lobontiu ◽  
Jeffrey S. N. Paine ◽  
Ephrahim Garcia ◽  
Michael Goldfarb
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Finite Element Simulation ◽  
Analytical Approach ◽  
Flexure Hinge ◽  
Closed Form Solutions ◽  
Flexure Hinges ◽  
Element Simulation ◽  
Model Predictions ◽  
The Right

The paper presents an analytical approach to corner-filleted flexure hinges. Closed- form solutions are derived for the in-plane compliance factors. It is demonstrated that the corner-filleted flexure hinge spans a domain delimited by the simple beam and the right circular flexure hinge. A comparison that is made with the right circular flexure hinges indicates that the corner-filleted flexures are more bending-compliant and induce lower stresses but are less precise in rotation. The finite element simulation and experimental results confirmed the model predictions.

ON THE TIME-DEPENDENT OCCUPANCY DISTRIBUTION OF THE G/G/1 QUEUING SYSTEM

2009 ◽  
Vol 23 (2) ◽  
pp. 261-280 ◽  
Author(s):  
Jorge Limón–Robles ◽  
Martin A. Wortman
Keyword(s):  
Closed Form ◽  
Analytical Approach ◽  
Marked Point ◽  
Fixed Time ◽  
Queuing System ◽  
Time Dependent ◽  
Marked Point Process ◽  
Batch Arrivals ◽  
Occupancy Distribution

This article offers an approach for studying the time-dependent occupancy distribution for a modest generalization of the GI/G/1 queuing system in which interarrival times and service times, although mutually independent, are not necessarily identically distributed. We develop and explore an analytical model leading to a computational approach that gives tight bounds on the occupancy distribution. Although there is no general closed-form characterization of probability law dynamics for occupancy in the GI/G/1 queue, our results offer what might be termed “near-closed-form” in that accurate plots of the transient occupancy distribution can be constructed with an insignificant computational burden. We believe that our results are unique; we are unaware of any alternative analytical approach leading to a numerical characterization of the time-dependent occupancy distribution for the G/G/1 queuing systems considered here.Our analyses employ a marked point process that converges to the occupancy process at any fixed time t; it is shown that this process forms a Markov chain from which the transient occupancy law is available. We verify our analytical approach via comparison with the well-known closed-form expressions for time-dependent occupancy distribution of the M/M/1 queue. Additionally, we suggest the viability of our approach, as a computational means of obtaining the time-dependent occupancy distribution, through straightforward application to a Gamma[x]/Weibull/1 queuing system having batch arrivals and batch job services.

scholarly journals Probing the shear modulus of two-dimensional multiplanar nanostructures and heterostructures

Nanoscale ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 5280-5294 ◽  
Author(s):  
T. Mukhopadhyay ◽  
A. Mahata ◽  
S. Adhikari ◽  
M. Asle Zaeem
Keyword(s):  
Shear Modulus ◽  
Closed Form ◽  
Analytical Approach ◽  
High Fidelity ◽  
Two Dimensional

Generalized high-fidelity closed-form formulae have been developed to predict the shear modulus of hexagonal graphene-like monolayer nanostructures and nano-heterostructures based on a physically insightful analytical approach.

scholarly journals Spherical-multipole analysis of an arbitrarily directed complex-source beam diffracted by an acoustically soft or hard circular cone

2015 ◽  
Vol 13 ◽  
pp. 57-61 ◽  
Author(s):  
A. Reinhardt ◽  
H. Bruens ◽  
L. Klinkenbusch ◽  
M. Katsav ◽  
E. Heyman
Keyword(s):  
Numerical Analysis ◽  
Boundary Value Problem ◽  
Analytical Approach ◽  
Circular Cone ◽  
Legendre Functions ◽  
Soft Or ◽  
Associated Legendre Functions ◽  
Multipole Analysis ◽  
Complex Source ◽  
Complex Valued

Abstract. An analytical approach to analyze the diffraction of an arbitrarily directed complex-source beam (CSB) by an acoustically soft or hard semi-infinite circular cone is presented. The beam is generated by assigning a complex-valued location to a point source; its waist and direction are defined by the real and imaginary parts of the source coordinate, respectively. The corresponding scalar boundary-value problem is solved by a spherical-multipole analysis. The solution requires the calculation of associated Legendre functions of the first kind for complex-valued arguments which turns out to be a non-trivial task. Beside a numerical analysis of the corresponding algorithms we present numerical results for the total near- and scattered far-fields.

Elastic Fields Resulting From Concentrated Loading on a Three-Dimensional Incompressible Wedge

1995 ◽  
Vol 62 (3) ◽  
pp. 557-565 ◽  
Author(s):  
M. T. Hanson
Keyword(s):  
Closed Form ◽  
Three Dimensional ◽  
Elastic Field ◽  
Point Force ◽  
Legendre Functions ◽  
Two Dimensional ◽  
Elementary Functions ◽  
Normal Loading ◽  
Direction Parallel ◽  
Elastic Fields

This paper considers point force or point moment loading applied to the surface of a three-dimensional wedge. The wedge is two-dimensional in geometry but the loading may vary in a direction parallel to the wedge apex, thus creating a three-dimensional problem within the realm of linear elasticity. The wedge is homogeneous, isotropic, and the assumption of incompressibility is taken in order for solutions to be obtained. The loading cases considered presently are as follows: point normal loading on the wedge face, point moment loading on the wedge face, and an arbitrarily directed force or moment applied at a point on the apex of the wedge. The solutions given here are closed-form expressions. For point force or point moment loading on the wedge face, the elastic field is given in terms of a single integral containing associated Legendre functions. When the point force or moment is at the wedge tip, closed-form (nonintegral) expressions are obtained in terms of elementary functions. An interesting result of the present research indicates that the wedge paradox in two-dimensional elasticity also exists in the three-dimensional case for a concentrated moment at the wedge apex applied in one direction, but that it does not exist for a moment applied in the other two directions.

Dynamic Stiffness and Damping of Piles

1974 ◽  
Vol 11 (4) ◽  
pp. 574-598 ◽  
Author(s):  
Milos Novak
Keyword(s):  
Dynamic Response ◽  
Closed Form ◽  
Linear Elasticity ◽  
Analytical Approach ◽  
Dynamic Stiffness ◽  
Vertical Plane ◽  
Shallow Foundations ◽  
Pile Head ◽  
Pile Interaction ◽  
Stiffness And Damping

Dynamic response of footings and structures supported by piles can be predicted if dynamic stiffness and damping generated by soil–pile interaction can be defined. An approximate analytical approach based on linear elasticity is presented, which makes it possible to establish the dimensionless parameters of the problem and to obtain closed-form formulas for pile stiffness and damping. All components of the motion in a vertical plane are considered; that is, horizontal as well as vertical translations and rotation of the pile head. The stiffness and damping of piles are defined in such a way that the design analysis of footings and structures resting on piles can be conducted in the same way as is applied in the case of shallow foundations.

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