On Power Flow Suppression in Straight Elastic Pipes by Use of Equally Spaced Eccentric Inertial Attachments

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Sergey Sorokin ◽  
Ole Holst-Jensen
Keyword(s):  
Experimental Data ◽  
Exact Solution ◽  
Cross Section ◽  
Power Flow ◽  
Floquet Theory ◽  
Boundary Integral Equations ◽  
Flow Analysis ◽  
Elastic Beam ◽  
Boundary Integral ◽  
Parametric Studies

The paper addresses the power flow suppression in an elastic beam of the tubular cross section (a pipe) at relatively low excitation frequencies by deploying a small number of equally spaced inertial attachments. The methodology of boundary integral equations is used to obtain an exact solution of the problem in vibrations of this structure. The power flow analysis in a pipe with and without equally spaced eccentric inertial attachments is performed and the effect of suppression of the energy transmission is demonstrated theoretically. These results are put in the context of predictions from the classical Floquet theory for an infinitely long periodic structure. Parametric studies are performed to explore sensitivities of this effect to variations in the number of attachments. The theoretically predicted eigenfrequencies and insertion loss are compared with the dedicated experimental data.

Exact Solution for Bending of Shape Memory Alloy Superelastic Beams

2011 ◽  
Author(s):  
Ahmadreza Eshghinejad ◽  
Mohammad Elahinia
Keyword(s):  
Experimental Data ◽  
Exact Solution ◽  
Finite Element ◽  
Numerical Methods ◽  
Shape Memory ◽  
Cross Section ◽  
Analytical Approach ◽  
Thermomechanical Behavior ◽  
Linear Distribution ◽  
Mode Of Application

Bending is a common mode of application and operation of shape memory alloys (SMA). So far the coupled thermomechanical behavior of these alloys have been modeled with numerical methods such as finite element. The issue in developing exact solutions for a SMA beam in bending is because of the distributed and hysteric stress-strain profile. In this paper an analytical approach is developed to find the exact solution for the displacement due to the applied force on the SMA superelastic beam. The approach is based on the assumption of linear distribution of strain along the height of a cross section in the beam. The solution is validated by experimental data and the results of the solution for a superelastic beams for different cases are illustrated.

scholarly journals MODELING OF FINITE INHOMOGENEITIES BY DISCRET SINGULARITIES

2021 ◽  
pp. 138-144
Author(s):  
G. M. Zrazhevsky ◽  
V. F. Zrazhevska
Keyword(s):  
Boundary Value Problems ◽  
Boundary Integral Equations ◽  
Boundary Value ◽  
Differential Forms ◽  
Elastic Beam ◽  
Convergent Series ◽  
Boundary Integral ◽  
Model Description ◽  
Nonsmooth Coefficients ◽  
The Impact

This work focuses on development of a mathematical apparatus that allows to perform an approximate description of inhomogeneities of finite sizes in a continuous bodies by arranging the sources given on sets of smaller dimensions. The structure and properties of source densities determine the adequacy of the model. The theory of differential forms and generalized functions underlies this study. The boundary value problems with nonsmooth coefficients are formulated. The solutions of such problems is sought in the form of weakly convergent series and as an alternative - an equivalent recurrent set of boundary value problems with jumps. A feature of this approach is the ability to consistently improve the adequacy of the description of inhomogeneity. This is important because it allows to qualitatively assess the impact of real characteristic properties on the accuracy of the model description. Reducing the dimensions of inhomogeneities allows the use of efficient methods such as the Green's function and boundary integral equations to obtain a semi-analytic solution for direct and inverse problems. The work is based on a number of partial problems that demonstrate the proposed approach in modeling of inhomogeneities. The problems of modeling of the set of finite defects in an oscillating elastic beam, the set of inhomogeneities of an arbitrary shape in an oscillating plate, fragile cracks in a two-dimensional elastic body under static loading are considered.

Analysis of Elastic Torsion in a Bar With Circular Holes by a Special Boundary Integral Method

1983 ◽  
Vol 50 (1) ◽  
pp. 101-108 ◽  
Author(s):  
D. A. Caulk
Keyword(s):  
Integral Equations ◽  
Cross Section ◽  
Boundary Integral Equations ◽  
Torsional Rigidity ◽  
Circular Cross Section ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Warping Function ◽  
Special Boundary ◽  
Circular Holes

Special boundary integral equations developed in an earlier paper are generalized here for torsion of an elastic bar with circular holes. In this approach, the solution on the boundary of each hole is represented by a series of circular harmonics, and the coefficients in these series are determined by a special system of boundary integral equations. For a cross section with only one hole, the entire system of equations is reduced without approximation to a single integral equation involving only the warping function on the outer boundary. For multiple holes, approximate equations are derived that retain only the first harmonic in the solution representation on each hole. The latter equations are solved analytically for a circular cross section weakened by a concentric ring of circular holes. Simple expressions are derived for torsional rigidity, warping, and maximum stress. The results for torsional rigidity are an improvement over previous ones obtained by another approximate method.

Fusion and Breakup Reactions of 17S + 208Pb and 15C + 232ThHalo Nuclei Systems

2015 ◽  
Vol 11 (2) ◽  
pp. 2972-2978
Author(s):  
Fouad A. Majeed ◽  
Yousif A. Abdul-Hussien
Keyword(s):  
Experimental Data ◽  
Cross Section ◽  
Fusion Reaction ◽  
Fusion Cross Section ◽  
Reaction Cross ◽  
Recent Experimental Data ◽  
Barrier Distribution ◽  
Coupled Channel ◽  
Total Fusion ◽  
Full Quantum

In this study the calculations of the total fusion reaction cross section have been performed for fusion reaction systems 17F + 208Pb and 15C + 232Th which involving halo nuclei by using a semiclassical approach.The semiclassical treatment is comprising the WKB approximation to describe the relative motion between target and projectile nuclei, and Continuum Discretized Coupled Channel (CDCC) method to describe the intrinsic motion for both target and projectile nuclei. For the same of comparsion a full quantum mechanical clacualtions have been preforemd using the (CCFULL) code. Our theorticalrestuls are compared with the full quantum mechaincialcalcuations and with the recent experimental data for the total fusion reaction  checking the stability of the distancesThe coupled channel calculations of the total fusion cross section σfus, and the fusion barrier distribution Dfus. The comparsion with experiment proves that the semiclassiacl approach adopted in the present work reproduce the experimental data better that the full quantal mechanical calcautions. 

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