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Implicit and Explicit Method in nonlinear Dynamics
Vaněčková, Adéla ; Hradil, Petr (referee) ; Němec, Ivan (advisor)
The final thesis „Explicit and Implicit methods in nonlinear dynamics“ deals with the issue of geometrical and physical nonlinear analysis of structures exposed to seismic loading by the methods of direct integration of equations of motion. Solution by the explicit and the implicit method is compared for three material models. While the differences between the results of the explicit method and the implicit Newmark method are small as expected, the differences are substantial between the results of different material models. However, these differences are explained and they are in full concordance with the theoretical assumptions for the pertinent material models. The conclusion of the final thesis is check of correctness of the results of the new module of the program system RFEM for both tested numerical methods and all three analyzed material models. (linear elastic, plastic Drucker-Prager and the Mazars damage model). With sufficient precision of results, both explicit and implicit numerical methods showed to be suitable for seismic analysis. The implicit method can provide several times faster calculation than the explicit one, but the determination of the optimal time step is problematic and time consuming, so the suitability of use of both methods for seismic analysis is comparable.
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Implicit and Explicit Method in nonlinear Dynamics
Vaněčková, Adéla ; Hradil, Petr (referee) ; Němec, Ivan (advisor)
The final thesis „Explicit and Implicit methods in nonlinear dynamics“ deals with the issue of geometrical and physical nonlinear analysis of structures exposed to seismic loading by the methods of direct integration of equations of motion. Solution by the explicit and the implicit method is compared for three material models. While the differences between the results of the explicit method and the implicit Newmark method are small as expected, the differences are substantial between the results of different material models. However, these differences are explained and they are in full concordance with the theoretical assumptions for the pertinent material models. The conclusion of the final thesis is check of correctness of the results of the new module of the program system RFEM for both tested numerical methods and all three analyzed material models. (linear elastic, plastic Drucker-Prager and the Mazars damage model). With sufficient precision of results, both explicit and implicit numerical methods showed to be suitable for seismic analysis. The implicit method can provide several times faster calculation than the explicit one, but the determination of the optimal time step is problematic and time consuming, so the suitability of use of both methods for seismic analysis is comparable.
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Combined linear and non-linear time heteronymous damping in internal dynamics of non-linear parametric systems
Hortel, Milan ; Škuderová, Alena
In the process of the design of high speed planetary gear systems with minimum dimensions and masses are not sufficiently in advance known many of the functional dependencies of parameters such as constant or time heteronomous damping in gear mesh of kinematic pairs, etc. Therefore, it is necessary due to the safety and reliability of these systems that the basic research in this field dealt with this problem deeper both qualitatively and quantitatively, analytically and numerically. The values and functional dependencies, for example of damping parameters of solved systems, are often only estimated. Effects of variations in the size of the estimated parameters from their true values is solved in a wider variation expected ranges, including the impact on the internal dynamics of these systems. In this study are analyzed bifurcation resonance characteristics of relative motion in the gear mesh of system with combined linear and non-linear - quadratic time heteronymous damping on the model of one branch of power flow of pseudoplanetary weakly and strongly non-linear system with six degrees of freedom.
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Quantitative influence of heteronymous damping in gear mesh on internal dynamics of non-linear parametric systems
Hortel, Milan ; Škuderová, Alena
The theoretical works constitute only one side of the basic research of high-parametric complicated transmission planetary differential or pseudoplanetary systems in the process of their analysis. The complete basic reseach of mentioned category of mechanisms requires more deep experimental research by reason of verification of quantitative sizes of structural values of parameters. This is connected with high expenses because the change of parameter in theory can mean in experiment replacement of part or the substitution of whole subsystem. Therefore, the quantitative values, e.g. of the damping parameters, of the solved systems are often only estimated and the influences of these divergences of the estimated parameter sizes from their real values are solving in broad supposed ranges. The quantitative variations of possible influence of time heteronymous damping in gear mesh on the internal dynamics of non-linear parametric system with six degrees of freedom are showed in contribution.
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Non-linear time heteronymous dymping in non-linear parametric planetary systems
Hortel, Milan ; Škuderová, Alena
The analysis of dynamics of time heteronymous weakly and strongly non-linear planetary transmission systems with kinematic coupling - gears constitutes a study of complicated function of many parameters including the gearing material damping properties and damping viscous properties of lubricating oil film in gear mesh. The structures with lightening holes in cogwheel discs are characterized by time variable damping in gear meshes. The following contribution deals with this time heteronymous non-linear damping.
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Bifurcation characteristics in parametric systems with combined linear and non-linear damping
Hortel, Milan ; Škuderová, Alena
The damping or the damping forces represent certain speciality in the investigation of the internal dynamics of the transmission systems. The special significance has this damping parameter especially in the areas of impact effects in the high-speed light aircraft and mobile transmission constructions. On the example of gear mesh in one branch of forces-flow in the pseudoplanetary reducer deals the paper with some partial results of the analysis of the influence of combination damping, i.e. linear and non-linear damping, on the gear mesh dynamics.
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