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1
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The Influence of Local Increase of Stress on Eigenvalues for a Simply Supported Beam

100%
Kasprzyk S., Marczuk R.
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vol. 125
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issue 4A
A-169-A-173
EN
Local increase of bending stress in a beam may be caused by a decrease of the cross-section (fracture) or a local increase of bending torque. The increase of stress issues from the well known interdependence between the stress, the bending torque and the sectional modulus. The work presents a derivation of differential equations for eigenfunctions in both cases. Knowing the eigenfunctions and boundary conditions we determine a system of algebraic equations for the eigenvalues that are different from the eigenvalues of the beam without local stress disturbances. Two computational models of local increase of stress were constructed: with fracture and with local increase of bending torque.
2
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Construction of Equivalent Models of Continuous and Discrete-Continuous Systems

100%
Kasprzyk S., Marczuk R.
Acta Physica Polonica A
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2012
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vol. 121
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issue 1A
A-191-A-196
EN
New models have been constructed for three physical systems. These models are characterized by a uniform and transparent mathematical description. The mathematical description belongs to the class of generalized functions, which means that all equations as well as their solutions are understood in the sense of weak topology. The elements of the set of generalized functions need not be differentiable (in the classical sense) at each point domain of the function. Analyzing of actual systems in the class of generalized functions does not require a division into subsystems, which simplifies significantly execution of all mathematical operations. As compared with the classical methods, those presented in the study allow for a much faster achievement of the goal.
3
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Applicability of the Fourier Expansion Method of Separation of Variables in the Linear Discrete-Continuous Systems with Distributional Coefficients

100%
Kasprzyk S.
Acta Physica Polonica A
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2011
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vol. 119
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issue 6A
981-985
EN
The analytical examination of mechanical systems in the aspect of their vibro-isolation can be limited to the construction of a computational system. The analytical description of the adopted appropriate computational model may be executed with the help of a set of differential equations of the second order, differential equations with partial derivatives or of both types at the same time. The latest description is associated with the so-called discrete-continuous systems. It is the most convenient to analyze the vibrations of the linear discrete-continuous systems in the class of functions generalized with the Fourier method of separation of variables. Until now it was possible to execute only for a small set of parameters of the system's structure. In the work the author presents a computational model that covers all the structural parameters of the system.
4
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New Concepts of the Study of an Infinite Beam on Elastic Foundation Based on the Distribution Theory

100%
Felis J., Kasprzyk S.
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vol. 125
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issue 4A
A-190-A-196
EN
The new approach to investigation the bending of the infinite length beam on the elastic foundation, applying the theory of distributions, is presented.
5
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An Analytical Study of Nonlinear Vibrations οf Buckled Euler-Bernoulli Beams

80%
Pakar I., Bayat M.
Acta Physica Polonica A
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2013
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vol. 123
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issue 1
48-52
EN
The current research deals with a way of using a new kind of periodic solutions called He's max-min approach for the nonlinear vibration of axially loaded Euler-Bernoulli beams. By applying this technique, the beam's natural frequencies and mode shapes can be easily obtained and a rapidly convergent sequence is obtained during the solution. The effect of vibration amplitude on the non-linear frequency and buckling load is discussed. To verify the results some comparisons are presented between max-min approach results and the exact ones to show the accuracy of this new approach. It has been discovered that the max-min approach does not necessitate small perturbation and is also suitably precise to both linear and nonlinear problems in physics and engineering.
6
Content available remote

Investigation on Vibrations of a Cantilever Beam with Magnetorheological Fluid by Using the Acoustic Signal

80%
Snamina J., Sapiński B., Wszołek W., Romaszko M.
Acta Physica Polonica A
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2012
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vol. 121
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issue 1A
A-188-A-190
EN
The paper presents results of laboratory investigations of a vibrating three-layer cantilever beam with magnetorheological fluid. The goal of the study was to determine changes of the acoustic field around the vibrating beam caused by modifications of the magnetorheological fluid properties. The experimental studies have been carried out on a dedicated measuring stand. The construction of the measuring stand allows fixing one end of the beam in a holder attached to the moving part of the electrodynamic shaker. The magnetic field is produced by an external electromagnet. During the measurements the beam displacements and the acoustic pressure have been simultaneously registered. Frequency analysis of the registered signals has been carried out in 1/12 octave bands near the second natural frequency of the beam. The results reveal that the acoustic signal emitted by the vibrating beam decreases when the magnetic field is applied.
7
Content available remote

The Idea of the Selection of PZT-Beam Interaction Forces in Active Vibration Protection Problem

80%
Brański A., Borkowski M., Szela S.
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issue 1
17-22
EN
The paper concerns an active vibration protection (p-reduction) of the structure. This problem corresponds to the active vibration reduction (a-reduction). The quantity and effectivness of the a-/p- reduction, measured with reduction and effectiveness coefficient respectively, depends on, inter alia, the PZT distribution on the structure subdomains with the largest curvatures (quasi optimal distribution) are considered. The aim of this paper is to determine such interacting forces PZT-structure, assuming QO distribution of PZTs, which maximize the effectiveness of p-reduction. The beam clamped at one end, vibrating separately with first three modes, is chosen as the research object. The interacting forces are searched requiring that the shear force and bending moment at the clamped side are equal to zero. The total p-reduction is achieved for separate modes. Assuming the QO distribution of the PZTs, the best p-effectiveness is achieved. The validation of theoretical considerations is confirmed numerically.
8
Content available remote

Modes Orthogonality of the Mechanical System Simple Supported Beam-Actuators-Concentrated Masses

80%
Brański A.
Acta Physica Polonica A
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2012
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vol. 121
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issue 1A
A-126-A-131
EN
This paper deals with simple supported beam-actuators-concentrated masses mechanical system; it appears in active vibration reduction problem. To solve the problem with the Fourier method, the system is discretized into uniform elements. In the paper the orthogonality condition of the modes of the discretized system is derived. Furthermore, the solution of the forced vibration problem of the above system, appearing inherently in the active vibration reduction problem, is outlined.
9
Content available remote

Modelling and Simulation of 3 Blade Helicopter's Rotor Model

61%
Latalski J., Bocheński M., Warmiński J., Jarzyna W., Augustyniak M.
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vol. 125
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issue 6
1380-1384
EN
Results of model tests of a rotating composite beam with integrated piezoelectric active element are presented in the paper. A proposed electromechanical system is a simplified model of the structure of a modern helicopter rotor blade. Numerical analysis of the considered system is developed by means of the finite element method. In addition, the laboratory setup has been built in order to perform real experimental studies. Selected static and dynamic characteristics of the object are determined by a series of numerical simulations. The results are compared with the outcomes of tests performed on the experimental setup. A very good agreement between numerical simulation and experiment results is observed.
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