Analysis of dynamic response of isotropic, orthotropic and composite plates by applying tools used in dynamics
Analiza odpowiedzi dynamicznej płyt izotropowych, ortotropowych oraz kompozytowych z wykorzystaniem narzędzi stosowanych w dynamice
Project type: Research and development
Keywords: Odpowiedź dynamiczna stateczność dynamiczna portrety fazowe mapy Poincaré wykładniki Lapunowa analiza FFT.
Keywords (english): Dynamic response dynamic stability phase portraits Poincaré maps Lyapunov exponents FFT analysis
Consortium members: Project was not implemented as part of a consortium
Project implementation period: 30/01/2020 - 29/10/2023
Funding institution: Narodowe Centrum Nauki
Program name: Opus
Project manager:
Funding value: 600 700,00 PLN
Total project value: 600 700,00 PLN
projekt posiada tylko wersję anglojęzyczna streszczenia
Research project objective / research hypothesis: The aim of the project is to develop a method allowing to analyze the stability and load capacity of thin-walled plate subjected to in-plane time depended loads. The analysis will cover plates made of isotropic, ortotropic and composite (laminates). In the proposed method, the evaluations implemented and adapted to the deformation analysis of deformable bodies will be tools used mainly in the theory of dynamic systems vibrations (e.g. in the theory of bifurcation and chaos). The damping effect and its influence on the dynamic response of the study structure will be analyzed. The proposed method a two-parameter function of deflection will take into account. Numerical investigations for the loads of moderately large amplitude and durations from the time of equal periods of fundamental vibrations of the plate to the times many times greater than the period of fundamental vibrations of the structures will be made. Adopted research hypothesis assumes that using dynamic methods will be able to determine not only the stability (dynamic buckling) of the study construction, but also – for the analysis time many times larger than the period of fundamental vibration – presentation the nature of the solution. It is expected to receive fixed, periodic, quasi-periodic (e.g. 2D torus), as well as chaotic solutions. Preliminary analyzes allow to formulate another research hypothesis, which indicates a significant change in the stability of the solution after taking into account the damping effect and after applying a more detailed description, i.e. a two-parameter function of deflection. Concept and research plan: The work plan provides an analysis of analyze isotropic, ortotropic and composite plates (laminates) in terms of its dynamic response, by applying unpopular dynamic method. The damping effect and its influence on the dynamic response of the study structure will be analyzed. In addition, plates including the two-parameter function of deflection will be examined. Numerical study will be performed for the loads of moderately large amplitude and durations from the time of equal periods of fundamental vibrations of the plate to the times many times greater than the period of fundamental vibrations of the structures will be made. The work plan provides for the implementation of the project the following specific objectives: 1. Dynamic analysis for isotropic, ortotropic and composite plates (laminates) without damping effect and two-parameter function of deflection. 2. Determination the impact of damping effect on the nature of dynamic response for isotropic, ortotropic and composite plates. 3. Determination the impact of two-parameter function of deflection on the nature of dynamic response and improving the accuracy of the solution in a postbuckling range for isotropic, ortotropic and composite plates. Methodology: The research methodology assumes the use of dynamic tools to evaluate the dynamic stability of the analyzed structures, but also - for the times of analyzes many times greater than the period of fundamental vibrations - presentation of the character of the solution. It is expected to receive fixed, periodic, quasi-periodic (e.g. 2D torus), as well as chaotic solutions. Numerical analysis will carried out by using the tools of visualization and identification of solutions such as: phase portraits, Poincaré maps, FFT analysis, the largest Lyapunov exponents. Expected impact of the research project on the development of science, civilization and society: The successful implementation of the project objective will provide a valuable contribution to the study of dynamic stability (dynamic response) of plate structures by using unpopular dynamic method. The results significantly expand the knowledge in the field of dynamic stability of the test structures by applying tools such as: phase portraits, Poincaré maps, Lyapunov exponents, FFT analysis. Using above tools allow not only estimate the stability (or lack thereof) of analyzed structures but also present the nature of solution. In addition, it should be noted that the applicants undertake scientific issue of interdisciplinary nature. The results of this work will have a universal character, because the dynamics of nonlinear systems and transition from stationary to quasi-periodic or chaotic solutions relate to various fields of science.
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