Optimal Plastic Design of Beams with Freely Variable Cross-Sectional Dimensions

1989 ◽  
pp. 81-114
Author(s):  
George I. N. Rozvany
Keyword(s):  
Variable Cross ◽  
Cross Sectional ◽  
Plastic Design ◽  
Optimal Plastic Design

DETERMINATION OF THE FUNCTION OF THE ROD’S CROSS-SECTIONAL AREA USING VIBRATION EIGENFREQUENCIES

2020 ◽  
Vol 0 (4) ◽  
pp. 19-24
Author(s):  
I.M. UTYASHEV ◽  
◽  
A.A. AITBAEVA ◽  
A.A. YULMUKHAMETOV ◽  
◽  
...  
Keyword(s):  
Cross Sectional Area ◽  
Variable Cross ◽  
Sectional Area ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Method Error ◽  
Various Boundary Conditions ◽  
Elastic Fixation ◽  
Crosssectional Area

The paper presents solutions to the direct and inverse problems on longitudinal vibrations of a rod with a variable cross-sectional area. The law of variation of the cross-sectional area is modeled as an exponential function of a polynomial of degree n . The method for reconstructing this function is based on representing the fundamental system of solutions of the direct problem in the form of a Maclaurin series in the variables x and λ. Examples of solutions for various section functions and various boundary conditions are given. It is shown that to recover n unknown coefficients of a polynomial, n eigenvalues are required, and the solution is dual. An unambiguous solution was obtained only for the case of elastic fixation at one of the rod’s ends. The numerical estimation of the method error was made using input data noise. It is shown that the error in finding the variable crosssectional area is less than 1% with the error in the eigenvalues of longitudinal vibrations not exceeding 0.0001.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

Decomposition in optimal plastic design of structures

1981 ◽  
Vol 17 (1) ◽  
pp. 39-56 ◽  
Author(s):  
T.H. Woo ◽  
L.A. Schmit
Keyword(s):  
Plastic Design ◽  
Optimal Plastic Design

Distribution of Flow Across the Radius of an Axisymmetric Shock Tube With Variable Cross-Sectional Area

1991 ◽  
Author(s):  
Stephen J. Schraml ◽  
Richard J. Pearson
Keyword(s):  
Shock Tube ◽  
Dynamic Pressure ◽  
Computer Code ◽  
Turbulence Modelling ◽  
Variable Cross ◽  
Cross Sectional ◽  
Flow Simulations ◽  
First Order ◽  
Series Of Experiments ◽  
Dynamic Pressure Measurements

Abstract Experiments were conducted to study the characteristics of unsteady flow in a small, axisymmetric shock tube. These experiments have been supplemented by calculational results obtained from the SHARC hydrodynamic computer code. Early calculational results indicated that a substantial gradient in flow velocity and dynamic pressure may exist along the cross-section of the shock tube. To further investigate this phenomenon, a series of experiments was performed in which dynamic pressure measurements were made at various radii in the expansion section of the shock tube. Additional calculations with the SHARC code were also performed in which turbulence modelling, artificial viscosity and second order advection were employed. The second set of calculations agree very well with the experimental results. These results indicate that the dynamic pressure is nearly constant across the radius of the shock tube. This contradicts the early computational results which were performed with first order advection and without turbulence modelling. As a result of these findings, it was concluded that turbulence modelling was necessary to obtain accurate shock tube flow simulations.

Nonlinear Dynamics Investigation of Variable Cross-Sectional Solar-Sail Masts

2021 ◽  
pp. 1-11
Author(s):  
Xiangjie Yu ◽  
Bindi You ◽  
Xiaomeng Liu ◽  
Qian Cao
Keyword(s):  
Nonlinear Dynamics ◽  
Solar Sail ◽  
Variable Cross ◽  
Cross Sectional
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