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Abstract

The paper presents the solutions, calculation results and dynamic observations of three-layers, annular plate with thick core subjected to increasing in time load. The presented solutions use approximate methods: orthogonalization method and finite difference method in analytical and numerical solution of the problem, and finite element method. The observed phenomenon of the reduction of critical load values of the plates, in which the buckling mode is not global and there are different additional deflections of respective plate layers was comprehensively analysed in order to evaluate the critical state and supercritical plate behaviour. The critical deformation could have a form with strong deformation in the region of the loaded plate edge. The observation of the dynamic behaviour of plates, which buckling modes have circumferential waves is an important element of the analysis. Presented in this work the analytical and numerical solution to the problem of dynamic plate deflection was generalized on the case of plates with buckling waves in circumferential direction.

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Authors and Affiliations

Dorota Pawlus

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Abstract

The paper presents the results of tests on dynamic stability of Bernoulli-Euler beam with damages. Damages (cracks) were modeled using three rotational springs. An analysis of the influence of crack depth and their position relative to the beam ends on dynamic stability of the beam was carried out. 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 analyzed. Stable and unstable solutions were analyzed using the Strutt card.
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Authors and Affiliations

W. Sochacki
1
ORCID: ORCID
S. Garus
1
ORCID: ORCID
J. Garus
1
ORCID: ORCID

  1. Czestochowa University of Technology, Department of Mechanics and Fundamentals of Machinery Design, Faculty of Mechanical Engineering and Computer Science, 73 Dąbrowskiego Str., 42-201 Częstochowa, Poland
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Abstract

The study analyzed the influence of materials and different types of damping on the dynamic stability of the Bernoulli-Euler beam. Using the mode summation method and applying an orthogonal condition of eigenfunctions and describing the analyzed system with the Mathieu equation, the problem of dynamic stability was solved. By examining the influence of internal and external damping and damping in the beam supports, their influence on the regions of stability and instability of the solution to the Mathieu equation was determined.
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Authors and Affiliations

Sebastian Garus
1
ORCID: ORCID
Justyna Garus
1
ORCID: ORCID
Wojciech Sochacki
1
ORCID: ORCID
Marcin Nabiałek
2
ORCID: ORCID
Jana Petru
3
ORCID: ORCID
Wojciech Borek
4
ORCID: ORCID
Michal Šofer
5
ORCID: ORCID
Paweł Kwiatoń
1
ORCID: ORCID

  1. Faculty of Mechanical Engineering and Computer Science, Czestochowa University of Technology, Poland
  2. Faculty of Production Engineering and Materials Technology, Department of Physics, Czestochowa University of Technology, Armii Krajowej 19, 42-201 Czestochowa, Poland
  3. Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 70833 Ostrava, Czech Republic
  4. Department of Engineering Materials and Biomaterials, Silesian University of Technology, Konarskiego 18A, 44-100 Gliwice, Poland
  5. Department of Applied Mechanics, Faculty of Mechanical Engineering, VSB—Technical University of Ostrava, 17. listopadu 2172/15, 70800 Ostrava, Czech Republic
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Abstract

The paper presents the dynamic behaviour of three-layer annular plates with damaged facings. The plate is composed of thin laminated, fibre-reinforced composite facings and thicker, foam core. Failure of the plate facings is modelled as fibre or matrix cracks. The plate loaded in the plane of facings with quickly increasing radially compressed forces loses its dynamic stability. Evaluation of the critical state of the plate with failures was carried out using both analytical and numerical solutions. The comparison of results between plates with material properties treated as isotropic, quasi-isotropic and composite has been conducted. Presented tables and figures create the image of dynamic responses of examined composite plates with structure failures.

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Authors and Affiliations

Dorota Pawlus
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Abstract

Three-layered, annular plate with viscoelastic core is subjected to loads acting in the plane of the plate facings. One formulates the dynamic, stability problem concerning the action of time-dependent compressive stress on a plate with imperfection. This problem has been solved. One created the basic system of differential equations in which the approximation finite difference method was used for calculations. The essential analysis of the problem was concentrated on evaluation of the influence of the plate imperfection rate and the rate of plate loading growth on the results of calculation of critical parameters at the moment of loss of plate stability. It determines the analysed problem of sensitivity of the plate to imperfection and loading. In the evaluation of the dynamics of this problem, the dynamic factor defined as the quotient of the critical, dynamic load to the static one was used. The idea of dynamic factor and the type of the accepted criterion of the loss of plate stability were taken from the Volmir's work. The observations were confirmed by comparable results of calculations of plate models built in finite element method using the ABAQUS system. The analysis of the stress state in an exemplary plate model calculated in FEM demonstrated the importance of the strength condition in total evaluation of the plate work. One achieved satisfactory correctness of results in both methods.

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Authors and Affiliations

Dorota Pawlus

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