Research of Total Mechanical Energy of Steel Roof Truss during Structurally Nonlinear Oscillations

Ufimtsev, E. K.; Voronina, M D

doi:10.1016/j.proeng.2016.07.188

Cited by 6 publications

(2 citation statements)

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“…There are not found the publications on the calculation of floating bridges of continuous system with limiting rigid supports under the action of the moving loading, which are the structural and non-linear systems. Papers [14][15][16] are devoted to the study of structural and nonlinear oscillations of constructions. The solution of some problems of building structures static calculation can be obtained in analytic form that allows to study the impact of various construction parameters in an explicit form [17].…”

Section: Introductionmentioning

confidence: 99%

Modeling of Constructions’ Structurally Nonlinear Oscillations Using Chebyshev's Polynomials

Gridnev

Skalko

Shimanovsky

2020

mech

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A numerical algorithm for solving initial-boundary value problems with nonlinear boundary conditions was developed and implemented. The algorithm is constructed with reference to modeling of oscillations of an elastically supported deformable rod with limit stops at the ends under the action of a moving variable force. Such a rod is the design scheme of a number of building structures, including the span structure of a floating bridge of continuous system with limiting rigid supports at the ends. Chebyshev's polynomials were used to improve the computational schemes for realizing the practical problems of modeling constructive-nonlinear oscillations of building structures. The solution does not lose stability for large values of the elasticity coefficients of elastic couplings. Using the developed approach, it is possible to perform virtual computing experiments to skip a variety of movable loads on the floating bridge to analyze its deformed state and to make well-grounded design decisions.

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Section: Introductionmentioning

confidence: 99%

Modeling of Constructions’ Structurally Nonlinear Oscillations Using Chebyshev's Polynomials

Gridnev

Skalko

Shimanovsky

2020

mech

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“…The periodicity of the truss structure [11][12][13][14] allows applying the induction method in order to obtain the dependence of the solution on the panels number. Nonlinear oscillations of trusses were studied in [15]. In [16][17][18], oscillations of flat elastic trusses with an orthogonal structure were studied with allowance for internal friction under the Voigt model by the method of "gluing" solutions.…”

Section: Introductionmentioning

confidence: 99%

Lower estimate of the fundamental frequency of natural oscillations of a truss with an arbitrary number of panels

Kirsanov

2019

Vestnik MGSU

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Introduction: the paper deals with oscillations of a statically definable plane, truss with a double lattice of racks and descending braces with massive loads in the nodes of the lower chord. The weight of the truss rods is not taken into account. It is assumed that the freights are moved only vertically. The fundamental frequency of natural oscillations is estimated from the Dunkerley formula by the values of partial frequencies. Materials and methods: an analytical estimate is obtained by generalizing formulas obtained from a series of estimates for trusses with a consistently increasing number of panels. The stiffness of the truss was determined using the Mohr’s integral. The double lattice of the truss does not allow using the cross-section method; therefore, the forces in the rods were calculated (or estimated) in an analytical form using the method of cutting nodes with the compilation of a system of equilibrium equations simultaneously for all rods and three support reactions. The matrix of equilibrium equations was compiled in a software program written in the language of the Maple computer mathematics system based on the coordinates of the nodes and the values of the direction cosines of the forces. For a sequence of coefficients of the desired formula, linear homogeneous recurrent equations were found and solved by means of special operators of the Maple system. Results: the resulting formula estimating the relationship between the fundamental frequency and the panels number has the form of a sixth degree polynomial with coefficients depending on the parity of the number of panels. The analytical result is compared with the smallest frequency obtained numerically from the solution of the problem of oscillation of the cargo system. It is shown that the main frequency, depending on the truss height, has an extremum. Conclusions: the method of generalizing particular solutions using the Maple system operators allowed authors to obtain and analyze a formula for a lower estimate of the fundamental frequency of oscillation of a truss model with an arbitrary number of panels. The resulting estimate can be used as a test for numerically obtained solutions. The formula is especially efficient for systems with a large number of panels; as numerical methods for their calculation are time-consuming require considerable time and have a tendency for accumulating rounding errors.

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Application of a fundamental solution to a problem operator for modeling vibrations of elastically supported load-bearing structures

Skalko

Gridnev

Minaeva

2020

J. Phys.: Conf. Ser.

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The work is devoted to the construction of effective computational algorithms for modeling vibrations of elastically supported load-bearing systems. An approach is developed based on the representation of a mathematical model in the form of partial differential equations for generalized functions. With this approach, the presence of elements with a very high stiffness in the design made it necessary to carry out the calculation with a very small time step. To build a computational algorithm, a fundamental solution to the problem operator is used, which allows one to obtain a solution at the next time step for each point of the spatial grid independently. The need to carry out the calculation with a very small time step arises only in nodes that coincide with the location of structural elements with very high stiffness. The proposed approach allows simulating impact forces and instantaneous change of boundary conditions. The possibility of using the model with an absolutely rigid restraining support as a limit transition from a model of elastic bond of high rigidity was researched on.

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Research of Total Mechanical Energy of Steel Roof Truss during Structurally Nonlinear Oscillations

Cited by 6 publications

References 0 publications

Modeling of Constructions’ Structurally Nonlinear Oscillations Using Chebyshev's Polynomials

Modeling of Constructions’ Structurally Nonlinear Oscillations Using Chebyshev's Polynomials

Lower estimate of the fundamental frequency of natural oscillations of a truss with an arbitrary number of panels

Application of a fundamental solution to a problem operator for modeling vibrations of elastically supported load-bearing structures

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