scholarly journals INVESTIGATIONS OF VIBRO-OSCILLATORY PROVESSES OF THE SUPPORTS OF OFFSHORE STATIONARY PLATFORMS UNDER CONDITIONS OF ALTERNATING VORTEX FORMATION CAUSED BY THE INFLUENCE OF SEA CURRENTS

Akustika ◽  
2019 ◽  
Vol 32 ◽  
pp. 262-266
Author(s):  
Ivan Starokon ◽  
Y.M. Ovsannikov ◽  
A.O. Golovachev
Keyword(s):  
Frequency Spectrum ◽  
Characteristic Frequency ◽  
Natural Frequencies ◽  
Vortex Formation ◽  
Natural Oscillation ◽  
Hydrodynamic Forces ◽  
Offshore Platforms ◽  
Wide Range ◽  
Sea Currents ◽  
Oscillation Frequencies

Offshore platforms are exposed to hydrodynamic forces of a non-stationary nature and a wide range of frequencies. At present, hydrodynamic forces arising under conditions of alternating vortex formation have been poorly studied. These vortices are caused by the sea currents flowing around the supports of the platform, and due to their periodic occurrence and disruption, they lead to oscillations of the supports of the offshore platforms. Of particular danger are the cases of resonance of the characteristic frequency spectrum of hydrodynamic forces from the "occurrence-stalling" of vortices and natural frequencies of elements of the platform supports, which can cause fatigue damages in the platform supports. The article developed a method for determining the natural oscillation frequencies of marine supports and described the conditions under which the occurrence of alternating vortex formation is possible.

scholarly journals Analysis of the natural frequencies of oscillations of a planar truss with an arbitrary number of panels

Vestnik MGSU ◽  
2019 ◽  
pp. 284-292
Author(s):  
Mikhail N. Kirsanov ◽  
Dmitriy V. Tinkov
Keyword(s):  
Analytical Solutions ◽  
Natural Frequencies ◽  
Average Frequency ◽  
Natural Oscillation ◽  
Frequency Function ◽  
Compliance Matrix ◽  
Frequency Spectra ◽  
Alternative Approach ◽  
Inertia Properties ◽  
Oscillation Frequencies

Introduction. Analytical solutions for problems of structural mechanics are not only an alternative approach to solving problems of strength, reliability and dynamics of structures, but also the possibility for simple performance evaluations and optimization of structures. Frequency analysis of planar trusses, most often used in construction and engineering, is an important part of the study of structures. Objectives - development of a three-parameter induction algorithm for deriving the analytical dependence of the natural oscillation frequencies of the truss on the number of panels. Materials and methods. A flat, statically definable truss with one additional external link and double braces has been considered. The inertia properties of the truss are modeled by point masses located in the nodes of the lower straight truss belt. Each mass is assumed to have only one vertical degree of freedom. The stiffness of all truss rods is assumed to be the same. The task is to obtain analytical dependences of the oscillation frequencies of the proposed truss model on the number of panels. The derivation of the desired formulas is performed by the method of induction in three stages - according to the numbers of rows and columns of the compliance matrix, calculated using the Maxwell - Mohr formula and the number of panels. To find common members of the obtained sequences of coefficients, an apparatus was used to compile and solve the recurrent equations of the Maple computer mathematics system. The task of determining frequencies has been reduced to the eigenvalue problem of a bisymmetric matrix. Results. For the elements of the compliance matrix, general formulas have been found, according to which the frequency equations are compiled and solved. It is shown that in the frequency spectra of trusses with different numbers of panels there is always one common frequency (middle frequency) located in the middle of the spectrum. An expression is found for the maximum value of the average oscillation frequency as a function of the height of the truss. Conclusions. The proposed truss scheme, despite its external static indeterminacy and the lattice, which does not allow for the calculation of forces by such methods as the method of cutting nodes and the cross section method, allows analytical solutions for the natural frequencies of loads in the nodes. The obtained formulas have a rather simple form, and some general properties, such as frequency coincidences for different numbers of panels and the presence of an analytically calculated maximum of the average frequency function of the truss height, make this solution convenient for practical structural evaluations.

scholarly journals ON THE RESULTS OF STUDYING THE INFLUENCY OF VIBRATION-FLUCTUATIONS PROCESSES ON THE RESOURCE OF WELDED JOINTS OF MARINE STATIONARY PLATFORMS FOR OIL, GAS AND OTHER USEFUL MINERALS ON THE SHELF

Akustika ◽  
2019 ◽  
Vol 34 ◽  
pp. 148-151
Author(s):  
Ivan Starokon
Keyword(s):  
Fluid Flow ◽  
Frequency Spectrum ◽  
Welded Joints ◽  
Natural Frequencies ◽  
Practical Importance ◽  
Offshore Platforms ◽  
Hydrodynamic Load ◽  
Great Practical Importance ◽  
Oil Gas

The study of the occurrence of resonant oscillations when the frequency spectrum from the hydrodynamic load coincides with the natural frequencies of the elements of the offshore platforms, as a result of which the acting stresses multiply, has a great practical importance. In the process of research it was found that the most loaded elements of the platform under such an impact are the supports. In this research, the degree of influence on the supports of the force arising due to the formation and breakdown of vortices during the flow around the supports with a fluid flow is estimated. A conclusion about the influence of vibrational-fluctuations processes on the resource of offshore stationary platforms is based on this research.

On the problem of finding the parameters of elastic fastening of the edges of a rectangular plate

2006 ◽  
Vol 4 ◽  
pp. 11-22
Author(s):  
A.M. Akhtyamov ◽  
A.V. Muftakhov
Keyword(s):  
Rectangular Plate ◽  
Natural Frequencies ◽  
Natural Oscillation ◽  
The Other ◽  
Elastic Beams ◽  
Oscillation Frequencies

A rectangular plate is considered, in which two opposite edges are freely supported, while the other two are supported by elastic beams. In this paper, we prove the duality of the solution of the problem of finding the rigidities of elastic beams by all natural oscillation frequencies of a plate. It is also shown that if the rank of a certain matrix is equal to 9, then both solutions of the problem of finding the rigidities of elastic beams can be found from 9 natural frequencies.

On Developing the Theory of Resonant Processes in Power Transformer Windings. Part 2. Frequency Responses of a Circuit with Four PI Sections

2021 ◽  
pp. 28-34
Author(s):  
Vasily S. LARIN ◽  
Keyword(s):  
Equivalent Circuit ◽  
Natural Frequencies ◽  
Power Transformer ◽  
Natural Oscillation ◽  
Frequency Responses ◽  
Voltage Resonance ◽  
A Chain ◽  
Oscillation Frequencies ◽  
Analytical Expressions ◽  
Resonant Processes

In the first part of the article, the results from theoretical studies of frequency responses in a homogeneous chain circuit containing two PI sections were presented, and conclusions about the voltage resonance occurrence conditions were drawn. A circuit with two PI sections has a single independent node and one natural frequency, whereas transformer windings are more complex oscillatory circuits and have a much larger number of natural oscillation frequencies. The second part of the article presents the results from studies of frequency responses in a homogeneous chain circuit containing four PI sections, three independent nodes, and three natural oscillation frequencies. Analytical expressions for the admittances of the equivalent circuit individual parts and the voltages at the intermediate nodes, as well as expressions for the natural frequencies are obtained. Using an analysis of the frequency dependences of the admittances of the equivalent circuit parts, the conditions and frequency ranges under which voltage resonance may occur at the first, second, and third natural frequencies, are shown. It has been demonstrated that for the considered resonant circuits there is a critical frequency above which the conditions for voltage resonance are not satisfied. Formulas for impedances and voltages at intermediate nodes of a chain circuit with an arbitrary number of PI sections are given.

scholarly journals A STUDY OF THE IMPACT OF THE PNEUMATIC LOADING RATE ON DYNAMIC PARAMETERS FOR A LARGE-SIZED CYLINDRICAL SHELL

2020 ◽  
pp. 118-125
Author(s):  
Pestrenin V.M. ◽  
◽  
Pestrenina I.V. ◽  
Rusakov S.V. ◽  
Buzmakova G.V. ◽  
...  
Keyword(s):  
Cylindrical Shell ◽  
Solid Mechanics ◽  
Outer Space ◽  
Natural Oscillation ◽  
Elastic Cylindrical Shell ◽  
Time Interval ◽  
Rectangular Plates ◽  
Wide Range ◽  
Oscillation Frequencies ◽  
The Impact

The solid mechanics problem on the packaging and subsequent pneumatic deployment of large-sized shells is relevant due to the need to operate such structures in hard-to-reach places. In particular, such a place is outer space. The paper considers the elastic cylindrical shell deployment from a packed state by internal pressure in a finite time interval. The packaged shell consists of two rectangular plates joined by ideal (with no bending resistance) joint-hinges arranged at the edges. Both static and dynamic problems are considered. Solutions are obtained on the basis of a geometrically nonlinear model of an elastic body using the ANSYS engineering package. It is shown that the pneumatic loading of an elastic structure is accompanied by its oscillations with increasing frequency and the amplitude decreasing in time. The period of shell oscillations is found to be dependent on the operating loading pressure and independent of the pressure supply rate, and it almost equals the period of oscillations of the statically loaded shell under the same pressure. The wide range variation in the natural oscillation frequencies of the structure during pneumatic deployment, which is revealed in the study, is of great importance since it makes possible to predict resonant modes accompanying the process. The results of the study will be used in problems of mechanics related to the pneumatic deployment of shell structures (for example, telescope reflectors, antennas, etc.) in space.

Algorithm for diagnosing fastenings of pipe with liquid

2007 ◽  
Vol 5 ◽  
pp. 96-100
Author(s):  
A.M. Akhtyamov ◽  
F.F. Safina
Keyword(s):  
Frequency Spectrum ◽  
Natural Frequencies ◽  
Algebraic Equations ◽  
Bending Vibrations ◽  
Narrow Tube

An algorithm is considered for diagnosing fastening of a narrow tube filled with a fluid by a spectrum of natural frequencies of its bending vibrations. The constructed algorithm, based on the solution of systems of algebraic equations, allows one to determine any pipe fastenings by 9 values from the frequency spectrum of its vibrations when the liquid is flowing through the pipe.

scholarly journals Vibration of Rotating and Revolving Planet Rings with Discrete and Partially Distributed Stiffnesses

2020 ◽  
Vol 11 (1) ◽  
pp. 127
Author(s):  
Fuchun Yang ◽  
Dianrui Wang
Keyword(s):  
High Speed ◽  
Differential Operators ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Distribution Area ◽  
Vibration Modes ◽  
Governing Equations ◽  
Vibration Properties ◽  
Wide Range ◽  
Forced Responses

Vibration properties of high-speed rotating and revolving planet rings with discrete and partially distributed stiffnesses were studied. The governing equations were obtained by Hamilton’s principle based on a rotating frame on the ring. The governing equations were cast in matrix differential operators and discretized, using Galerkin’s method. The eigenvalue problem was dealt with state space matrix, and the natural frequencies and vibration modes were computed in a wide range of rotation speed. The properties of natural frequencies and vibration modes with rotation speed were studied for free planet rings and planet rings with discrete and partially distributed stiffnesses. The influences of several parameters on the vibration properties of planet rings were also investigated. Finally, the forced responses of planet rings resulted from the excitation of rotating and revolving movement were studied. The results show that the revolving movement not only affects the free vibration of planet rings but results in excitation to the rings. Partially distributed stiffness changes the vibration modes heavily compared to the free planet ring. Each vibration mode comprises several nodal diameter components instead of a single component for a free planet ring. The distribution area and the number of partially distributed stiffnesses mainly affect the high-order frequencies. The forced responses caused by revolving movement are nonlinear and vary with a quasi-period of rotating speed, and the responses in the regions supported by partially distributed stiffnesses are suppressed.

Vibration Suppression of an Elastically Supported Beam With Closely Spaced Natural Frequencies

2020 ◽  
Author(s):  
Haizhou Liu ◽  
Hao Gao
Keyword(s):  
Natural Frequencies ◽  
Vibration Suppression ◽  
Fixed Point Theory ◽  
Dynamic Performance ◽  
Point Theory ◽  
Primary System ◽  
Computationally Efficient ◽  
Wide Range ◽  
Univariate Optimization ◽  
Elastically Supported

Abstract Vibration suppression of distributed parameter systems is of great interest and has a wide range of applications. The dynamic performance of a primary system can be improved by adding dynamic vibration absorbers (DVA). Although the relevant topics have been studied for decades, the trade-off between capability of suppressing multiple resonant peaks and complexity of absorbers has not been well addressed. In this paper, the vibration suppression problem of a uniform Euler-Bernoulli beam with closely spaced natural frequencies is investigated. To achieve desired vibration reduction, a two-DOF DVA is connected to the beam through a pair of a spring and a dashpot. By introducing a virtual ground spring, the parameters of the absorber are determined via extended fixed point theory. The proposed method only requires univariate optimization and is computationally efficient. Numerical examples conducted verify the viability of the proposed method and the effectiveness of a two-DOF DVA in suppressing double resonances.

External Excitation of Planar Jets

1972 ◽  
Vol 39 (4) ◽  
pp. 883-890 ◽  
Author(s):  
D. O. Rockwell
Keyword(s):  
Reynolds Number ◽  
Vortex Formation ◽  
External Excitation ◽  
Formation Region ◽  
Initial Formation ◽  
Planar Jet ◽  
Periodic Disturbances ◽  
Wide Range

A planar jet was subjected to transverse periodic disturbances of appropriate dimension-less frequency such that the vortex growth of the jet could be controlled for a wide range of jet Reynolds number (1860 to 10,800). Changes in the apparent time mean characteristics of the jet in its initial formation region, due to the applied disturbances, are related to the behavior of vortices. The processes of vortex formation, growth, and coalescence in the initial formation region are portrayed. The alterations of these processes as a function of the dimensionless applied disturbance are classed into regimes identified with respect to the natural breakdown state of the jet.

scholarly journals An investigation into the free vibrations of carbon nanotubes using analytical and finite element methods

2021 ◽  
Author(s):  
Ishan Ali Khan
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Nonlinear Eigenvalue Problem ◽  
Dynamic Stiffness ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Wide Range ◽  
Walled Cnts

Since their discovery, immense attention has been given to carbon nanotubes (CNTs), due to their exceptional thermal, electronic and mechanical properties and, therefore, the wide range of applications in which they are, or can be potentially, employed. Hence, it is important that all the properties of carbon nanotubes are studied extensively. This thesis studies the vibrational frequencies of double-walled and triple-walled CNTs, with and without an elastic medium surrounding them, by using Finite Element Method (FEM) and Dynamic Stiffness Matrix (DSM) formulations, considering them as Euler-Bernoulli beams coupled with van der Waals interaction forces. For FEM modelling, the linear eigenvalue problem is obtained using Galerkin weighted residual approach. The natural frequencies and mode shapes are derived from eigenvalues and eigenvectors, respectively. For DSM formulation of double-walled CNTs, a nonlinear eigenvalue problem is obtained by enforcing displacement and load end conditions to the exact solution of single equation achieved by combining the coupled governing equations. The natural frequencies are obtained using Wittrick-Williams algorithm. FEM formulation is also applied to both double and triple-walled CNTs modelled as nonlocal Euler-Bernoulli beam. The natural frequencies obtained for all the cases, are in agreement with the values provided in literature.

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