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1
Content available remote Influence of crack location on divergence and flutter instability of a column subjected to generalized load
100%
Sokół K.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2011
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tom Vol. 10, nr 1
223-230
EN
In this paper, the results of numerical studies on the divergence and flutter instability and vibration of a geometrically nonlinear column subjected to generalized load are presented. The system is loaded by axially applied external force P. The direction of action of the force is dependent on follower factor η. The Hamilton principle was used to formulate the boundary problem. Due to the geometric nonlinearity, the solution to the problem was performed by means of the perturbation method. The main purpose of this paper is to investigate the influence of the location of the crack on divergence and flutter loading as well as natural vibration frequency. The presented results of numerical calculations also concern the influence of rotational spring stiffness and follower factor η on the investigated parameters.
2
Content available remote Shape control of the column with imperfections of loading heads by means of the stiffening rod
100%
Sokół K.
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tom Vol. 9, nr 1
195-202
EN
This paper concerns an influence of the imprecise manufacturing or improper assembling processes of supporting and loading heads on transversal displacements, bending moments and axial force distribution of a column consisted of two rods, where one of rods is a stiffening element. The problem has been formulated by means of the principle of stationary total potential energy, the von Karman theory and linear constitutive equations for column material. The results of numerical calculation have shown how important it is to provide the axial load of the beams and columns.
3
Content available remote The local and global instability and vibration of a nonlinear column subjected to Euler's load
100%
Sokół K.
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tom Vol. 9, nr 1
187-194
EN
In this paper, the results of numerical studies on the local and global instability and vibration of a geometrically nonlinear column subjected to Euler's load are presented. The Hamilton principle was used to formulate the boundary problem. Due to the geometrical nonlinearity, the solution of the problem was performed by means of the perturbation method. The magnitude of the bifurcation load of the nonlinear column, the local and global instability regions and characteristic curves have also been presented.
4
Content available On bifurcation load of a three-member slender system with an internal crack subjected to Euler’s load
63%
Uzny S. , Sokół K.
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2018
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tom Vol. 56 nr 1
269--281
EN
The results of numerical simulations presented in this paper are concerned with instability of a three member slender system subjected to Euler load. The investigated column is built up as a flat frame composed of three rods. In the internal one, the defect is present in form of a crack. The boundary problem has been formulated on the basis of a static criterion of instability. The boundary conditions associated with different types of supports are obtained by proper selection of parameters of the generalized load. On the basis of these results, the magnitude of bifurcation load can be determined.
5
Content available Free vibrations of column subjected to Euler's load with consideration of Timoshenko's theory
63%
Uzny S. , Sokół K.
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tom Vol. 26
319--326
EN
In this paper the single-rod cantilever column subjected to compressive Euler's load is investigated. The boundary problem has been formulated on the basis of Hamilton's principle and Timoshenko's theory. Numerical simulations of characteristic curves have been plotted on the plane external load-vibration frequency for different magnitudes of slenderness factor of the system. The results of numerical calculations of Timoshenko's beam are compared to the ones obtained from mathematical Bernoulli-Euler's model. The comparison of the results of characteristic curves calculated by means of Timoshenko's theory and Bernoulli-Euler's model are done for first three vibration frequencies.
6
Content available remote Influence of the piezoelectric force on vibrations of a two-rod column
63%
Przybylski J. , Sokół K.
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2008
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tom Vol. 23
321--326
EN
This study details the investigation of the non-linear vibrations of a column consisted of two rods, one of which is made of piezoceramic material. The actuator, possessing its flexural stiffness is discretely attached to the main carrying rod. The role of the piezoelectric force generated by the actuator is to moderate the flexural displacement of the column which arises due to an unintensional eccentricity of the external load. The piezoelectric force influences also the natural frequency of the system, which tends to zero for the growing values of the external load.
7
Analiza statyczna kolumny z dodatkowym prętem piezoceramicznym
63%
Przybylski J. , Sokół K.
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tom T. 5, nr 36
257-264
PL
Celem pracy jest opisanie zachowania przedwyboczeniowego kolumny geometrycznie nieliniowej złożonej z pręta nośnego swobodnie podpartego, do którego zamocowano dyskretnie pręt piezoceramiczny. Z uwagi na mimorodowo obciążenia zewnętrznego względem osi pręta nośnego układ znajduje się w stanie równowagi krzywoliniowej. Na rozkład się w prętach układu wpływaj, oprócz obciążenia zewnętrznego i siły piezoelektrycznej, wartości mimośrodów obciążenia, relacje między sztywnościami na zginanie i ściskanie oraz warto dystansu między osiami prętow zasadniczego i pomocniczego.
EN
The purpose of this work is to determine the relation between axial forces in the column and the rod resulting from both the applied external load and the piezoelectric force. On the base of a variational principle (on the potential energy functional), by using the constitutive equations for the piezoelectric material, one derives an equation describing the dependence between the force generating by actuators and the axial forces in both elements of the system. The piezoforce is then implemented into buckling equations, which are analytically solved. The obtained solution is used for preparing the code for numerical simulation of the static behaviour of the system. It is assumed that the external load can be applied axially or eccentrically. The piezoelectric force, which dependently on the direction of the electric field can compress or stretched the column, may be used for controlling the flexural displacement or the bending moment in the column.
8
Content available Numerical studies on stability of slender supporting structures
63%
Sokół K. , Uzny S.
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2016
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tom Vol. 15, nr 2
157--165
EN
In this paper the results of studies on stability of the geometrically non-linear column (slender system) composed of two rods have been presented. The supporting structure has a defect in the form of cracks which are present in each of rods. The cracks are simulated by means of rotational springs. On the basis of the total potential energy principle, the boundary problem is being formulated. The results show an influence of the crack size on the stability of the column in particular on bifurcation load magnitude.
9
Content available Analiza parametrów trakcyjnych pociągów dużych prędkości
51%
Anuszczyk J. , Sokół K. , Wawrzyniak A.
Maszyny Elektryczne : zeszyty problemowe
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2011
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tom Nr 2(90)
87-93
EN
The current "Governmental Program of Construction and Operation of High Speed Railway in Poland" develops. Is analyzed for routing high-speed rail and widely understood aspects of power and infrastructure. Next steps include selection of stock for a new line (the line Y). Worldwide industry today has a wide range of high-speed trainsets. The article presents an analysis of traction characteristics of existing stock.
10
Stateczność kolumny przegubowej z aktuatorami piezoelektrycznymi
51%
Przybylski J. , Gąsiorski G. , Sokół K.
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tom T. 5, nr 36
249-256
PL
W pracy zbadano wpływ siły piezoelektrycznej generowanej przez dwa aktywatory na obciążenie krytyczne kolumny z przegubem wzmocnionym sprężyną rotacyjną. Rozpatruje się różne warunki podparcia kolumny ograniczające przemieszczenia osiowe jej końców. Na podstawie zasady wariacyjnej w odniesieniu do funkcjonału energii potencjalnej przy uwzględnieniu równań konstytutywnych materiału piezoelektrycznego wyprowadza się równanie opisujące związek między siłą generowaną przez aktywatory a siłą osiową rozcigając kolumn. Badania numeryczne dotyczą wpływu położenia piezosegmentu i przegubu oraz relacji sztywności na ściskanie piezoaktuatorów do sztywności kolumny na jej obciążenie krytyczne, a następnie także wpływu naprężenia residualnego na stateczność układu.
EN
The problem of buckling of continuous slender columns is one of the main subjects of the structural mechanics. In many engineering applications a column can be treated as a system of articulated segments with joints strengthen by rotational springs. The purpose of this work is to examine the influence of the piezoelectric force induced by two colocally bonded actuators on the buckling load of an internally hinged column with a rotational spring. Different ways of supporting of the column with axially restrained ends are considered. The stress stiffening equation leading to establishing the relation between the piezoelectric force and the axial force stretching the column was derived by using the variational principle. Numerical investigations concern the influence of the location of piezoceramics and the hinge as well as the relation between the axial stiffness of the piezo to that of the column on the critical buckling load. it is shown also that the stress stiffening can be used to counteract the effect of a compressive force leading to the instability of the column.
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