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

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.

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.

CFD Solution of a Two-Canopy Parachute in a Top-to-Top Formation With a Vent of Air From One of Its Canopy

2008 ◽  
Author(s):  
Mohammad J. Izadi
Keyword(s):  
Cross Sectional Area ◽  
The Body ◽  
The Other ◽  
Bluff Bodies ◽  
Variable Cross ◽  
Sectional Area ◽  
Cross Sectional ◽  
Drag Forces ◽  
Varied Form ◽  
Two Bodies

A CFD study of a 3 Dimensional flow field around two bodies (Two Canopies of a Parachutes) as two bluff bodies in an incompressible fluid (Air) is modeled here. Formations of these two bodies are top-to-top (One on the top of the other) with respect to the center of each other. One canopy with a constant cross sectional area with a vent of air at its apex, and the other with a variable cross sectional area with no vent is studied here. Vertical distances of these two bodies are varied form zero to half, equal, double and triple radius of the body with a vent on it. The flow condition is considered to be 3-D, unsteady, turbulent, and incompressible. The vertical distances between the bluff bodies, cross sectional area, and also vent ratio of bluff bodies are varied here. The drag forces with static pressures around the two bodies are calculated. From the numerical results, it can be seen that, the drag coefficient is constant on the range of zero to twenty percent of the vent ratio and it decreases for higher vent ratios for when the upper parachute is smaller than the lower one, and it increases for when the upper parachute is larger than the lower one. Both Steady and Unsteady cases gave similar results especially when the distance between the canopies is increased.

Development of an Analog Controller for Tuning an Adaptive-Passive Control Device

2005 ◽  
Author(s):  
Marty Johnson ◽  
Edward C. Diggs
Keyword(s):  
Passive Control ◽  
Low Frequency ◽  
Helmholtz Resonator ◽  
Dc Motor ◽  
Control Device ◽  
Inner Product ◽  
Variable Cross ◽  
Error Signal ◽  
Cross Sectional ◽  
Drive Frequency

Adaptive-passive devices such as adaptive Helmholtz Resonators (HR) and tunable vibration absorbers have been shown to be suitable for controlling both narrowband disturbances and lightly damped structural/acoustic modes driven by broadband disturbances. In order to track changes in the disturbance or changes in the modes, the natural frequency of the absorber, ωn, is tuned to match the observed signals. This is achieved by altering some physical parameter of the control device such as the stiffness of a vibration absorber or the neck cross-sectional area of a Helmholtz resonator. In order to automatically adjust these devices, control systems and tuning algorithms have been developed, most of which involve a digital controller. However, this paper looks specifically at the development of a simple analog controller used to drive a DC motor in order to tune a mechanical device. A two sensor dot product method is employed where one sensor is placed inside of the control device, such as a Helmholtz Resonator, and the other on/in the system under control, such as in a room. The outputs from the two sensors are multiplied together and subsequently low passed in order to extract a low frequency “DC” voltage which acts as an error signal. The error signal is related to the relative phase of the two sensor signals and determines the direction in which the device should be tuned. When the two signals are 90° apart, the system is tuned (i.e. the inner product produces zero DC level). If the drive frequency ω is different than the tuned frequency, then the system is mis-tuned. The relationship between the mis-tuning, ωn-ω, and the error is not linear, but for small perturbations a linear approximation can be used to investigate the stability and performance of the system. The gradient of the function is shown to be largest when the mis-tuning error is zero and is inversely proportional to the damping level in the control device. Once stability of the system has been ensured the ability of the system to track changes in drive frequency is investigated experimentally. The control system is demonstrated using an adaptive Helmholtz resonator which has a variable cross-sectional neck via an iris diaphragm. The iris is controlled using a small DC motor; two microphones (one mounted internally and one externally) are used to supply the driving signal to the circuit.

scholarly journals Buckling Optimization of Wood Composite Columns with Variable Cross-Sectional Area: A Comparison between two Tree Species

2010 ◽  
Vol 19 (6) ◽  
pp. 096369351001900
Author(s):  
Yeliz Pekbey ◽  
Aydogan Ozdamar ◽  
Onur Sayman
Keyword(s):  
Numerical Analysis ◽  
Optimization Problem ◽  
Buckling Load ◽  
Sufficient Optimality Conditions ◽  
Variable Cross ◽  
Wood Composite ◽  
Minimum Thickness ◽  
Cross Sectional ◽  
Important Conclusion ◽  
Optimum Solution

The minimization of structural weight and the maximization of critical buckling load are problems that have been addressed many times. The problem of maximizing the buckling load of a wood composite column of given volume, length and material is studied. Tadjbakhsh and Keller were the first to obtain an optimum solution analytically for the case of clamped-clamped case. Unimodal solutions obtained by Tadjbaksh-Keller are not optimal because they buckle by the modes with discontinuities of the slope corresponding to the lower critical load. This leads to taking into account bimodal formulation of the optimization problem. Olhoff-Rasmussen (1977) first discovered that the unimodal solution given for the clamped by Tadjbaksh-Keller (1962) is incorrect. The optimal columns must be considered from the point of view of practical design. In this paper, it will be shown that bimodal solution is not practical and optimal since in points of minimum thickness crush occurred but not buckling. This leads to the necessity of both stability and crush formulation of the optimization problem. The present contribution of this paper is that crush is taken into account in the formulation of column optimization problem allowing for bimodal optimum solution. To test the accuracy of our new optimization column with clamped ends, experimental data were compared to numerical analysis using ANSYS. Both necessary and sufficient optimality conditions are derived. One important conclusion of this paper is that our new optimal solution is in agreement with results obtained by numerical analysis and by experiments.

On Difference Methods for Shock Wave Propagation in Variable Area Ducts Including Wall Friction

1973 ◽  
Vol 95 (2) ◽  
pp. 327-332
Author(s):  
R. H. Fashbaugh ◽  
A. Widawsky
Keyword(s):  
Shock Wave ◽  
Wave Attenuation ◽  
Fluid Dynamic ◽  
Finite Difference Methods ◽  
Wall Friction ◽  
Variable Cross ◽  
Viscous Effects ◽  
Cross Sectional ◽  
Basic Fluid ◽  
Difference Methods

Results are presented of an analytical study concerned with the prediction of the propagation of shock waves through air ducting systems. The solution is one-dimensional but is appropriate for ducts which have a variable cross-sectional area and includes attenuation due to viscous effects at the wall of the duct. Finite-difference methods are utilized to obtain an approximate solution to the basic fluid dynamic equations. Comparisons are given between analytical results and shock tube experimental data which validate the capabilities of the methods used to predict shock wave attenuation and the effect of duct area variation on shock strength.

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