Wyniki wyszukiwania - BazTech

1

The dynamic stability of a simply supported stepped beam with additional discrete elements

Sochacki W.

Vibrations in Physical Systems

|

2012

|

Vol. 25

367--372

EN

The dynamic stability of a simply supported stepped beam with additional discrete elements was investigated in the paper. These elements are a rotational spring and a rotary inertia, both of which are connected to the beam. The discrete elements can be mounted at any chosen position along the beam length. The influence of step changes in the cross-section of the beam on its dynamic stability was also investigated in the paper. The problem of dynamic stability was solved by applying the mode summation method. Applying an orthogonal condition of eigenfunctions, the dynamic of the system was described with the use of the Mathieu equation. The obtained equation allowed the dynamic stability of the tested system to be analysed. The considered beam was treated as Euler-Bernoulli beam.

2

The dynamic stability of beams with step changes in cross-section

Sochacki W.

Vibrations in Physical Systems

|

2008

|

Vol. 23

327--333

EN

The influence of step changes in cross-section of beams with different boundary conditions on their dynamic stability was investigated in the paper. The change in the crosssections took place in an optional location along the beam length. The investigated beams were axially loaded by a force in the form P(t)= P0+Scosνt. The problem of dynamic stability was solved by applying the mode summation method. The obtained Mathieu equation allowed the dynamic stability of tested systems to be analysed. The analysis relied on testing the influence of step changes in beam cross-sections and their locations on the value of coefficient b in the Mathieu equation. The considered beams were treated as Euler- Bernoulli beams.

3

Green's function for an infinite piezoelectric strip with a general line defect

Nowacki J. P., Alshits V. L., Radowicz A.

Journal of Technical Physics

|

2002

|

Vol. 43, no 2

133-153

EN

The 2D electro-elastic fields are found in the piezoelectric strip with the straight general line defect parallel to the surfaces and consisting of the four coinciding sources: the line of forces, the charged line, the dislocation line and its electrostatic analogue. Electrically, the strip is supposed to be placed between two isotropic dielectric media. Mechanically, three boundary conditions are considered: (i) both the surfaces are free; (ii) both the surfaces are clamped; and (iii) one surface is free and the other is clamped. The solutions obtained for a general case of unrestricted anisotropy are presented in the form of convergent Fourier integrals, in terms of the eigenvectors and eigenvalues of the generalized Stroh problem. Determination of these eigenvalues and eigenvectors requires additional computing. Specific features of the derived solutions at infinity are analyzed.

4

Effective measurements of birefringence properties of nondichroic media using Poincare sphere.

Kurzynowski P., Ratajczyk F.

Optica Applicata

|

2001

|

Vol. 31, nr 1

203-207

EN

A method for measuring the birefringence properties of nondichroic media using the Poincare sphere is presented. Simple relations between coordinates of points on the Poincare sphere representing input and output polarization states of light and the point representing first eigenvector of the medium have been found. From these relations the desired polarization parameters of the medium were calculated.

5

Exact method of solution of free vibrations problem for one-dimensional rheological structures

Cabański J.

Journal of Technical Physics

|

2001

|

Vol. 42, no 1

85-102

EN

Free vibrations of one-dimensional rheological structure have been described by the system of the conjugated partial differential equations. A vector form of this system of equations allows to identify the self adjoint linear operators of inertia, damping and stiffness. These operators are not homothetic, hence the method of a separation of variables for the considered system of equations is applicable only in the introduced complex Hilbert space. Such a separation of variables leads to the system of ordinary differential equations in time and to the system of three ordinary differential equations with respect to spatial variables. Solution of the obtained boundary-value problems proceeds in a classical way, however, the results are of a complex conjugated type. Applying the fundamental principle of the general orthogonality of complex eigenvectors, the problem of free vibrations of the system with arbitrary initial conditions was solved in exact form.