Open AccessDOI
Bilateral Analytical Estimation of the First Frequency of a Plane Truss
Oleg Vladimirovich Vorobev
- Vol. 92, Iss: 7, pp 9204-9204
TLDR
In this paper, the vertical displacement of nodes is derived from the Maxwell-Mohr method with the premise of linear elasticity, and Dunkerley's and Rayleigh's estimations of primary truss frequency on the number of panels are deduced from the inductive analysis of the set of particular trusses with an increasing number of columns.Abstract:
The object of research is the statically determinate cantilever truss. The trass consists of rectangular panels with downward diagonal beams. The truss has two supports, one of which is fixed hinged, and another one is roller support. Masses are located in the nodes of top and bottom chords. Forces in the bars and reactions at supports are determined using the method of joint isolation. The vertical displacement of nodes is derived from the Maxwell-Mohr method with the premise of linear elasticity. Dependence of vertical displacement, Dunkerley’s and Rayleigh’s estimations of primary truss frequency on the number of panels is deduced from the inductive analysis of the set of particular trusses with an increasing number of panels. Recurrence equations that meet particular coefficients are derived using special functions of the computer algebra system Maple. Obtained solutions are polynomial, with the number of panels as variables. Rayleigh’s quotient is calculated with the assumption that the first mode of vibration is equal to truss deflection under the uniformly distributed load. Graphs of the dependencies of obtained estimations on nodes masses, the number of panels, stiffness, and size of the truss are plotted.read more
Citations
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The formula for the lower estimate of the fundamental frequency of natural vibrations of a truss with an arbitrary number of panels
Abstract: The object of the research is a planar, statically determinate girder of the beam type with a triple diagonal lattice.The truss mass is modeled by equal masses distributed over the nodes of the lower chord. By the Dunkerley method, under the assumption of vertical vibrations of loads, a lower analytical estimate of the first natural vibration frequency is obtained. Method. The forces in the members are calculated by cutting out nodes from the solution of a system of linear algebraic equations. Generalization of individual solutions to the case of an arbitrary number of panels is carried out by the induction method with the involvement of operators of the Maple computer mathematics system. Results. Comparison with the numerical solution found from the solution on the spectrum of natural vibrations of a multi-mass system shows that the estimation accuracy depends on the number of panels and varies from 16% for trusses with two panels to 4% for trusses with more than 11 panels. With a decrease in the ratio of the panel height to its length, the accuracy slightly increases. Based on the analysis of the derived formula, it is shown that the dependence of the first frequency on the height of the truss has a maximum. An algorithm for generalizing the solution to the case of members of different stiffness is proposed.
Proceedings ArticleDOI
Mathematical model of deformations of the antenna frame for space communications
TL;DR: In this paper , a triangular pyramid-shaped truss with a concave dome was used as a space communication antenna, and the forces in the rods were calculated using the Maple symbolic mathematics system, and coefficients are obtained as general terms of sequences of coefficients in specific solutions.
Journal ArticleDOI
Analytical calculation of deformations and kinematic analysisof a flat truss with an arbitrary number of panels
Mikhail Kirsanov,O. V. Vorob'ev +1 more
TL;DR: In this article , analytical dependences of the deflection and displacement of the support of a flat lattice truss on the number of panels are obtained for two types of loading, according to the Maxwell-Mohr formula, and an algorithm for identifying the corresponding distribution of possible velocities of the joints is presented.
Journal ArticleDOI
Formulas for Calculating Deformations of Power Line Supports
TL;DR: In this paper , the static deformations of the spatial model of a statically determined truss of a power line support were investigated, and a series of solutions for trusses with different numbers of panels were summarized by the induction method in the Maple computer mathematics system.
References
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Journal ArticleDOI
Truss optimization with natural frequency bounds using improved symbiotic organisms search
TL;DR: This work proposes an improved version of a recently proposed Symbiotic Organisms Search (SOS) called an Improved SOS (ISOS) to tackle the above-mentioned challenges and shows that ISOS is more reliable and efficient as compared to the basis SOS algorithm and other state-of-the-art algorithms.
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3D acoustic metamaterial-based mechanical metalattice structures for low-frequency and broadband vibration attenuation
TL;DR: In this paper, a new type of 3D truss-lattice structures for low-frequency and broadband elastic wave absorption is proposed, where the cross-struts in each unit-cell have a radius jump discontinuity.
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Multi-class teaching–learning-based optimization for truss design with frequency constraints
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Journal ArticleDOI
Non-probabilistic method to consider uncertainties in frequency response function for vibration-based damage detection using Artificial Neural Network
TL;DR: A combination of a non-probabilistic method with PCA is proposed to consider the problem of the existing uncertainties and the inefficiency of using FRF data in ANN-based damage detection and demonstrates that the proposed method is efficient in dealing with uncertainties usingFRF for damage detection.
Journal ArticleDOI
Doing Least Squares: Perspectives from Gauss and Yule
TL;DR: In this article, the matrix and vector space formalisms used in modern regression analysis were compared with Gauss' least square estimates and their precisions. But they were not adapted to correlation analysis.
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