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 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.

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.

Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

Evaluation of a Wide Range of AmplitudeFrequency Responses for the Hearing Impaired

1995 ◽  
Vol 38 (1) ◽  
pp. 211-221 ◽  
Author(s):  
Ronald A. van Buuren ◽  
Joost M. Festen ◽  
Reinier Plomp
Keyword(s):  
Frequency Spectrum ◽  
Speech Intelligibility ◽  
Dynamic Range ◽  
Finite Impulse Response ◽  
Sound Quality ◽  
Average Frequency ◽  
Frequency Spectra ◽  
Low Frequencies ◽  
Speech Reception ◽  
Wide Range

The long-term average frequency spectrum of speech was modified to 25 target frequency spectra in order to determine the effect of each of these spectra on speech intelligibility in noise and on sound quality. Speech intelligibility was evaluated using the test as developed by Plomp and Mimpen (1979), whereas sound quality was examined through judgments of loudness, sharpness, clearness, and pleasantness of speech fragments. Subjects had different degrees of sensorineural hearing loss and sloping audiograms, but not all of them were hearing aid users. The 25 frequency spectra were defined such that the entire dynamic range of each listener, from dB above threshold to 5 dB below UCL, was covered. Frequency shaping of the speech was carried out on-line by means of Finite Impulse Response (FIR) filters. The tests on speech reception in noise indicated that the Speech-Reception Thresholds (SRTs) did not differ significantly for the majority of spectra. Spectra with high levels, especially at low frequencies (probably causing significant upward spread of masking), and also those with steep negative slopes resulted in significantly higher SRTs. Sound quality judgments led to conclusions virtually identical to those from the SRT data: frequency spectra with an unacceptably low sound quality were in most of the cases significantly worse on the SRT test as well. Because the SRT did not vary significantly among the majority of frequency spectra, it was concluded that a wide range of spectra between the threshold and UCL levels of listeners with hearing losses is suitable for the presentation of speech energy. This is very useful in everyday listening, where the frequency spectrum of speech may vary considerably.

An Approach on Tuning the Frequency of a Rotating Blade

2008 ◽  
Author(s):  
L. Duong ◽  
K. Kazerounian ◽  
K. D. Murphy
Keyword(s):  
Structural Integrity ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
The Finite Element Method ◽  
Turbine Engine ◽  
Rotating Blade ◽  
Alternative Approach ◽  
Excited Vibration ◽  
Speed Range ◽  
Analytical Expressions

In a gas turbine engine, the forced vibration of a turbine blade under resonant conditions is undesirable and may lead to premature high cycle fatigue failure. From the aspect of structural integrity, this demonstrates that it is extremely important to tune the excited vibration mode out of the operating speed range. This leads to the question: Is it possible to perform structural perturbations, namely to the mass and stiffness, in such a way that only the eigenvalue of choice significantly changes — while causing little or no change in the other natural frequencies? This is focus of the present paper. Due to the complexity of the blade structure, it is difficult to obtain an analytical solution from the eigenvalue perturbation theory. Nevertheless, the derived analytical expressions provide guidance from which the finite element method may successfully be applied as an alternative approach. This tuning approach is validated experimentally.

Dynamic Characteristics of Tsing Ma Suspension Bridge

1996 ◽  
Vol 1541 (1) ◽  
pp. 43-50 ◽  
Author(s):  
Siu Kui Au ◽  
Neil Mickleborough ◽  
Paul N. Roschke
Keyword(s):  
Analytical Solutions ◽  
Bridge Deck ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Suspension Bridge ◽  
Mode Shapes ◽  
Out Of Plane ◽  
Quantitative Results ◽  
Suspension Cable ◽  
Bending Modes

Numerical simulation was carried out to determine the dynamic properties of the Tsing Ma Suspension Bridge. Both the structure as a whole and individual subcomponents were modeled. Classical analytical solutions for simplified models from the available literature were compared with the results obtained from a finite-element code. Quantitative results for static deflection, natural frequencies, and mode shapes were compared with analytical solutions from linear theory. Out-of-plane modes were shown to be dominant. For in-plane antisymmetric and symmetric bending modes, in which the suspension cable and bridge deck vibrate in the same direction, the natural frequency of the main span of the bridge is determined to be approximately equal to the square root of the sum of the squares of the frequencies of the cable and bridge deck.

scholarly journals Dynamic characteristics of frame buildings, taking into account the European standards of the Republic of Kazakhstan in construction

2020 ◽  
Vol 77 (4) ◽  
pp. 119-123
Keyword(s):  
Dynamic Characteristics ◽  
Analytical Solutions ◽  
Natural Frequencies ◽  
Frame Building ◽  
Transverse Vibrations ◽  
Frame Buildings ◽  
The Republic ◽  
European Standards ◽  
Nodal Displacements

The dynamic characteristics of the frame building are considered. As a result of numerical and analytical solutions, the values of the natural frequencies of the transverse vibrations of a singlestorey building, nodal displacements and forces under horizontal seismic actions, taking into account the stiffness diaphragms for various connections with the base, were obtained.

Free Vibration of the Triple-Walled Carbon Nanotubes

2009 ◽  
Author(s):  
Demetris Pentaras ◽  
Isaac Elishakoff
Keyword(s):  
Carbon Nanotubes ◽  
Natural Frequencies ◽  
Polynomial Equation ◽  
Galerkin Methods ◽  
Frequency Spectra ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Cubic Polynomial ◽  
Walled Carbon Nanotubes ◽  
Frequency Squares

Natural frequencies of the triple-walled carbon nanotubes (TWCNTs) are determined both exactly and approximately. For the case of TWCNT which is simply supported at it ends closed-form solutions are obtained. It is shown that there are three series of natural frequencies corresponding to the cubic polynomial equation for natural frequency squares. For the TWCNT that has other boundary conditions approximate Bubnov-Galerkin and Petrov-Galerkin methods are applied. Simple polynomial coordinate functions are utilized. Each of these methods yields three natural frequencies corresponding to the lower and of each frequency spectra.

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