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On approach for obtaining approximate solution to highly nonlinear oscillatory system with singularity

Acta Mechanica Sinica 2020年第4期36卷 910-917页

作者： Zvonko Rakaric boris Stojic Department of Mechanics Faculty of Technical SciencesUniversity of Novi Sad21000 Novi SadSerbia Department of Mechanization and Design Engineering Faculty of Technical SciencesUniversity of Novi Sad21000 Novi SadSerbia

This paper deals with further investigations of recently introduced so-called low-frequency pendulum mechanism,which represents an extended form of classical *** equation of motion,which is in Eksergian’s form,is a singular and highly nonlinear second order differential *** is transformed by suitable choice of a new “coordinates”into classical form of nonlinear conservative oscillator containing only inertial and restoring force ***,due to the singularity of coefficient of governing equation that shows hyperbolic growth,Laurent series expansion was *** these,we derived a nonsingular nonlinear differential equation,for which there exists an exact solution in the form of a Jacobi elliptic *** using this exact solution,and after returning to the original coordinate,both explicit expression for approximate natural period and solution of motion of mechanism were *** between approximate solution and solution is obtained by numerical integration of exact equation shows noticeable *** of impact of mechanism parameters on period is given.

关键词： Pendulum mechanism Low frequency Singularity Laurent series Jacobi elliptic function

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Bending the Foundation Beam on Elastic Base by Two Reaction Coefficient of Winkler’s Subgrade

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Open Journal of Civil Engineering 2019年第2期9卷 123-134页

作者： Mirko Balabusic boris Folic Slobodan Coric Independent Designer of Structure Herceg NoviMontenegro Innovation Center Faculty of Mechanical EngineeringUniversity of BelgradeBelgradeSerbia Faculty of Mining and Geology University of BelgradeBelgradeSerbia

A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the foundation beam with the ground. The solution is found by using the numerical analysis of the Winkler’s model, with variation of different moduli of the subgrade reaction k2 outside the force zone r, while under the force P exists the modulus of the subgrade reaction k, up to the definition of minimum bending moments. The exponential function k2(r), as the geometric position of the minimum moments is approximately assumed. From the potential energy conditions of the reciprocity of displacement and reaction, the width of the zone r and the modulus of the subgrade reaction k2 are explicitly determined, introducing in the calculation initial and calculation soil displacement wsi successively. At the end of the paper, it presented numerical example in which the influence of k and k2 values on bending moments of the counter beam is analyzed. The essential idea of this paper is to decrease the quantity of the reinforcement in the foundations, beams, i.e. to obtain a cost-efficient foundation construction.

关键词： Foundation Beam Winkler’s Model Coefficient of Subgrade Reaction Modulus k and k2 Zone r under the Force P Soil Displacement wsi

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