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1
Content available Vibration analysis of composite circular and annular membranes
Siedlecka U., Zamorska I., Kukla S.
Journal of Applied Mathematics and Computational Mechanics
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2016
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Vol. 15, nr 1
149--159
EN
In this paper a solution to the free vibration problem of composite circular and annular membranes is presented. The vibrations of membranes whose material densities and/or thicknesses varied step-wise with the radial co-ordinate are considered. This approach is applied to approximate the solution to the vibration problem of a membrane with continuously varying density and/or thickness with the radial co-ordinate. The obtained analytical solutions are used in numerical investigations into the effect of parameters characterizing the composite membranes on their eigenfrequencies.
2
Content available Damage identification of a beam with a variable cross-sectional area
Cekus D., Miara M., Zamorska I.
Journal of Applied Mathematics and Computational Mechanics
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2016
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Vol. 15, nr 4
23--32
EN
In the paper, the process of identification of crack parameters occurring in the cantilever beam with the variable cross-sectional area has been presented. For identification, the non-destructive vibration method has been applied. The analytical solution of the free vibration problem of the beam described according to the Bernoulli-Euler theory has been obtained with the help of Green’s functions.
3
Content available Effect of crack parameters on free vibrations of the Bernoulli-Euler beam
Zamorska I., Cekus D., Miara M.
Journal of Applied Mathematics and Computational Mechanics
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2015
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Vol. 14, nr 4
167--174
EN
The paper presents the problem of free vibration of the cantilever Bernoulli-Euler beam with a crack. The beam along the length has a variable cross-sectional area, and the crack parameters (thickness, depth and location) undergo changes. The work includes an analytical solution of the vibration problem and the results obtained with the use of FEM and CATIA program.
4
Content available Solution of differential equation for the Euler-Bernoulli beam
Zamorska I.
Journal of Applied Mathematics and Computational Mechanics
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2014
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Vol. 13, nr 4
157--162
EN
The paper presents the solution of a fourth order differential equation with various coefficients occurring in the vibration problem of the Euler-Bernoulli beam. The concerning equation is written as a first order matrix differential equation. To solve the equation, the power series method is proposed.
5
Content available Power series solution of first order matrix differential equations
Kukla S., Zamorska I.
Journal of Applied Mathematics and Computational Mechanics
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2014
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Vol. 13, nr 3
123--128
EN
In the paper, the solution of second order differential equations with various coefficients is presented. The concerning equations are written as first order matrix differential equations and solved with the use of the power series method. Examples of application of the proposed method to the equations occurring in the technical problems are presented.
6
Content available remote Green's functions for interior and exterior Helmholtz problems
Kukla S., Siedlecka U., Zamorska I.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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Vol. 11, nr 1
53-62
EN
In the paper, the derivation of Green's functions for Helmholtz equation in circular, annular and exterior circular domains is presented. The Green's functions are assumed of the form a cosine series. An example of application of the Green's functions in frequency analysis of a composite membrane is presented.
7
Content available remote Frequency analysis of composite annular membranes
Zamorska I., Kukla S., Siedlecka U.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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Vol. 11, nr 1
129-135
EN
In this paper, the free vibration of an annular membrane consisting of three concentric segments is considered. The frequency equation and mode shapes are obtained by the use of the Green's function method. A numerical example to vibration problem of nonhomogeneous annular membrane is presented.
8
Content available remote Free vibration of composite circular membranes
Siedlecka U., Kukla S., Zamorska I.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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Vol. 11, nr 1
99-105
EN
In this paper, the object of consideration is a membrane consisting of one circular and two annular segments. The Green's functions method for the free vibration of this membrane is applied. A numerical example illustrating this method is given.
9
Content available remote Application of Green's matrix method in vibration problems of Timoshenko beams
Zamorska I.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2011
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Vol. 10, nr 2
243-248
EN
In the present paper, a Green's matrix used to solve vibration problems of Timoshenko beams is determined. The problem formulation includes beam vibrations which are described by differential equations with variable parameters. To determine the Green's matrix, the power series method was used.
10
Content available remote Free transverse vibrations of non-uniform beams
Zamorska I.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2010
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Vol. 9, nr 2
243-249
EN
In this paper the Green's function method for the free vibration problem of nonuniform Bernoulli-Euler beams is presented. To find the Green's function of the fourth order differential operator, occurring at the beam's equation of motion, the power series method is proposed.
11
Content available remote Free vibration of stepped Timoshenko beams with attachements
Zamorska I.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2008
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Vol. 7, nr 1
199-205
EN
In this paper is presented a solution of the free vibration problem of multistepped Timoshenko beam with attachments. The Green's functions method is used to obtain the solution in an form. The presented approach can be used for the vibration analysis of beams consisting of an arbitrary number of segments and an arbitrary number of attached discrete elements.
12
Content available remote Longitudinal vibrations of a non-uniform rods coupled by double spring-mass systems
Zamorska I.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2007
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Vol. 6, nr 1
277-284
EN
The purpose of this paper is free longitudinal vibration problem of a non-uniform rods coupled by spring-mass systems. The solution of the boundary problem is obtained by the use of the Green's function method. In the paper examples of the Green's functions corresponding to the second order differential operator are presented.
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