Oleg Vladimirovich Vorobev

Bio: Oleg Vladimirovich Vorobev is an academic researcher. The author has contributed to research in topics: Truss & Plane (geometry). The author has an hindex of 1, co-authored 1 publications receiving 6 citations.

Bilateral Analytical Estimation of the First Frequency of a Plane Truss

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.

Analytical Dependence of Deflection of the Lattice Truss on the Number of Panels

Abstract: The case of load in the middle of the span is considered. An algorithm is given for deriving the analytical dependence of the deflection of a truss on the number of panels. It is shown that for a certain combination of panel numbers over the height of the truss and along the length of the span, the determinant of the system of equations of node equilibrium turns to zero that corresponds to the kinematic variability of the structure. It is noted that numerical calculation can obscure this feature due to inaccuracy of calculations. To obtain an exact formula, the computer mathematics system Maple is used. The coefficients of the final formula are obtained from the solution of linear homogeneous recurrent equations found from the analysis of the sequence of solutions for trusses with different number of panels. An example of a scheme of possible velocities of nodes of a variable truss is given. The formula for the deflection of the truss for the number of panels for which the truss is unchanged is derived by induction.

Minimum Weight Optimal Design of Truss Structure with Frequency Response Function Constraint

Abstract: The dynamic sizing optimization problem of a truss structure is studied for its weight minimization with a constraint of the frequency response function (FRF) over a certain frequency bandw...

Calculating model of a frame type planar truss having an arbitrary number of panels

Abstract: ABSTR ACT Introduction. The subject of the study is the kinematic variability and deformations of a planar statically-determinate elastic truss with a horizontal bolt, lateral supporting trusses and a cross-shaped grid under the action of various types of static loads. The structure has three movable supports and one fixed support. Objectives — derivation of formulas giving the dependence of the deflection of the structure in the middle of the span and the displacement of one of the three movable supports from the dimensions, load and number of panels; analysis of the kinematic variability and derivation of the analytical dependence of the forces in the rods of the middle of the span from the number of panels. Materials and methods. Forces in the rods of the truss are calculated in symbolic form by cutting out nodes using the Maple symbolic and numeric computational environment. In order to calculate the deflection, the Maxwell – Mohr formula was used. Calculation formulas for the deflection and displacement of the support were derived using the induction method based on the results of analytical calculations of a number of trusses with a different number of panels in the crossbar and lateral support trusses. The special operators of the genfunc package for managing the rational generating functions of the Maple system were used to identify and solve the recurrence equations satisfied by the sequences of coefficients of the formulas for deflection and forces. It is assumed that all the rods of the truss have the same rigidity. Results. Several variants of loads on the truss are considered. A combination of panel numbers is found in which the truss becomes kinematically variable. The phenomenon is confirmed by the corresponding scheme of possible velocities. All required dependences have a polynomial form by the number of panels. The curves of the dependence of the deflection on the number of panels and on the height of the truss are constructed in order to illustrate the analytical solutions. Conclusions. The proposed scheme of a statically determinate truss is regular, allowing a fairly simple analytic solution of the deflection problem. The curves of the identified dependencies have significant areas of abrupt changes, which can be used in problems of optimising the design by weight and rigidity.

One feature of the constructive solutions of the lattice girder

Abstract: The problem of the deflection of a planar symmetric statically determinable truss with a double lattice depending on the number of panels was solved in an analytical form. The angle of inclination of the ascending and descending rods of the truss is different. A load is applied to the truss, evenly distributed over the nodes of the lower chord. Special operators of the Maple computer math system and the induction method were used to generalize individual particular solutions to an arbitrary case. Formulas are obtained for the forces the most compressed and stretched truss rods. Cases of kinematic variability of the structure are revealed. A picture of the possible speeds of truss nodes in these cases is constructed. The asymptotic behavior of the deflection is found with a large number of panels and a fixed span length. The deflection was determined by the formula of Maxwell – Mohr.

The lower limit of the first frequency of natural vibrations externally statically indeterminate truss: analytical solution

Abstract: A scheme of a statically determinate planar truss with two additional supports duplicating the main ones is proposed. The formula for the dependence of the lower estimate of the first natural frequency on the number of panels is obtained. The solution is compared with the numerical one. Determination of the forces in the rods by the method of cutting out the nodes and with all the transformations performed in the Maple computer mathematics system. The high accuracy of the result is shown with a large number of panels.