This work investigates the modal properties of general cyclically symmetric systems and the multi-stage systems with cyclically symmetric stages. The work generalizes the modal properties of engineering applications, such as planetary gears, centrifugal pendulum vibration absorber (CPVA) systems, multi-stage planetary gears, etc., and provides methods to improve the computational efficiency to numerically solve the system modes when cyclically symmetric structures exist. Modal properties of cyclically symmetric systems with vibrating central components as three-dimensional rigid bodies are studied without any assumptions on the system matrix symmetries: asymmetric inertia matrix, damping, gyroscopic, and circulatory terms can be present. In the equation of motion of such a cyclically symmetric system, the matrix operators are proved to have properties related to the cyclic symmetry. These symmetry-related properties are used to prove the modal properties of general cyclically symmetric systems. Only three types of modes can exist: substructure modes, translational-tilting modes, and rotational-axial modes. Each mode type is characterized by specific central component modal deflections and substructure phase relations. Instead of solving the full eigenvalue problem,all vibration modes and natural frequencies can be obtained by solving smaller eigenvalue problems associated with each mode type. This computational advantage is dramatic for systems with many substructures or many degrees of freedom per substructure. Group theory is applied to further generalize the modal properties of cyclically symmetric systems when both rigid-body and compliant central components exist, such as planetary gears with an elastic continuum ring gear. The group theory for symmetry groups is introduced, and the group-theory-based modal analysis does not rely on any knowledge of the properties of system matrices in system equations of motion. The three types of modes (substructure modes, translational-tilting modes, and rotational-axial modes) are characterized by specific rigid-body central component modal defections, substructure phase relations, and nodal diameter components of compliant central components. The general formulation of reduced eigenvalue problems for each mode type is obtained through group-theory-based method, and it applies to discrete, continuous, or hybrid discrete-continuous cyclically symmetric systems. The group-theory-based modal analysis also applies to systems with other symmetry types. The group-theory-based modal analysis is generalized to analyze the multi-stage systems that are composed of symmetric stages coupled through the motions of rigid-body central components. The proposed group-theory-based modal analysis applies to multi-stage systems with cyclically symmetric stages, such as multi-stage planetary gears and CPVA systems with multiple groups of absorbers. The method also applies to multi-stage systems with component stages that have different types of symmetry. For a multi-stage system with symmetric stages, a unitary transformation matrix can be built through an algorithmic and computationally inexpensive procedure. The obtained unitary transformation matrix provides the foundation to analyze the modal properties based on the principles of group-theory-based modal analysis. For general multi-stage systems with symmetric component stages, the vibration modes are classified into two general types, single-stage substructure modes and overall modes, according to the non-zero modal deflections in each component stage. Reduced eigenvalue problems for each mode type are formulated to reduce the computational cost for eigensolutions. Finite element models of multi-stage bladed disk assemblies consist of multiple cyclically symmetric bladed disks that are coupled through the boundary nodes at the inter-stage interface. To improve the computational efficiency of calculating the full system modes, a numerical method is proposed by combination of the multi-stage cyclic symmetry reduction method and the subspace iteration method. Compared to the multi-stage cyclic symmetry reduction method, the proposed method improves the accuracy of obtained eigensolutions through an iterative process that is derived from the subspace iteration method. Based on the cyclic symmetry in each component stage of bladed disk, the proposed iterative method that can be performed using single stage sector models only, instead of using matrix operators for the full multi-stage bladed disks. Parallel computations can be performed in the proposed iterative method, and the computational speed for eigensolutions can be increased significantly. / Doctor of Philosophy / Cyclically symmetric structures exist in many engineering applications such as bladed disks, circular plates, planetary gears, centrifugal pendulum vibration absorbers (CPVA), etc. During steady operation, these cyclically symmetric systems are subjected to traveling wave dynamic loading. Component vibrations result in undesirable effects, including high cycle fatigue (HCF) failure, noise, performance reduction, etc. Knowledge of the modal properties of cyclically symmetric systems is helpful to analyze the system forced response and understand experimental modal testing. In this work, single stage cyclically symmetric systems are proved to have highly structured modes. The single stage systems considered in this work can have both rigid bodies and elastic continua as components. Group theory is used to study the modal properties, including the system mode types and the characteristics of different mode types. All the vibration modes of single stage cyclically symmetric systems can be solved from reduced eigenvalue problems. The methodology also applies to systems with other types of symmetry. For multi-stage systems with cyclically symmetric substructures, such as multi-stage planetary gears, a group-theory-based method is developed to analyze the modal properties. For industrial applications, such as multi-stage bladed disk assemblies, this work develops an iterative method to facilitate the calculations of system modes. The modal properties and methods for solving system modes apply to mechanical systems, including CPVA systems, the single/multi-stage planetary gears in power transmission systems, bladed disk assemblies in turbines, circular plates, elastic rings, etc.

<p>The paper deals with the problem of the moral status of human embryos <em>in vitro</em> obtained via somatic cell nuclear transfer, <em>in vitro</em> fertilization and similar biotechnologies. The purpose of research is to investigate whether it is possible to ascribe the position of full moral status to the embryo <em>in vitro</em> relying on its intrinsic properties. In particular, the property of totipotency of a human zygote was taken as presupposition in carrying out further moral assessments. To achieve these goals I have examined the applicability of the potentiality argument for evaluating moral status of the embryo within the frameworks of modal logic. The potential of the human embryo to become a person with full-fledged number of moral rights was interpreted using real, dispositional and counterfactual predicates. It was found that the role of potentiality argument is reduced to a precautionary principle and it failed to provide full moral status to the embryo <em>in vitro</em>. The potential of the embryo proper has a strong relational component that assigns it certain instrumental value. The latter implies that biomedical experimentation with the embryos <em>in vitro</em> cannot be considered as morally unacceptable.</p>

The paper deals with the problem of the moral status of human embryos in vitro obtained via somatic cell nuclear transfer, in vitro fertilization and similar biotechnologies. The purpose of research is to investigate whether it is possible to ascribe the position of full moral status to the embryo in vitro relying on its intrinsic properties. In particular, the property of totipotency of a human zygote was taken as presupposition in carrying out further moral assessments. To achieve these goals I have examined the applicability of the potentiality argument for evaluating moral status of the embryo within the frameworks of modal logic. The potential of the human embryo to become a person with full-fledged number of moral rights was interpreted using real, dispositional and counterfactual predicates. It was found that the role of potentiality argument is reduced to a precautionary principle and it failed to provide full moral status to the embryo in vitro. The potential of the embryo proper has a strong relational component that assigns it certain instrumental value. The latter implies that biomedical experimentation with the embryos in vitro cannot be considered as morally unacceptable.

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The presented master's thesis deals with the safety assessment of several variants of the impeller with different blades length. The motivation for creating this thesis is to find the solution of the problem situation which is characterized by the breakdown of the steam turbine impeller with blades length of 30mm. As confirmed in this thesis, the impeller with blades length of 30mm is operated in the resonance. Likewise, according to the technical standard ČSN EN ISO 10437 its operation is not safe. As the correction action for the problem situation solving is proposed the prolongation of the impeller's blades. The safety is detected for six variants of impeller with dierent blades length. For each variant, there is executed a modal analysis and its results are drawn up into the Campbell diagram. On the basis of this diagram, the safety of individual components is evaluated. The last part of the masters thesis concerns with the examination of the influence of blades length on the modal properties of the impeller.

The aim of this diploma thesis is to determine and compare modal properties of four swirl turbine wheels, each with a different geometry. Natural frequencies and mode shapes were obtained based on computer modelling using Ansys software and they were compared with experimental modal analysis' results. The computer modelling and the experimental modal analysis were carried out for different boundary conditions and in different environments. The beginning of the thesis is dedicated to a brief overview of literature with similar issues. Then a brief introduction of a dynamics theory is mentioned in which equations of motion for a damped and an undamped single degree of freedom system are derived. The creation of a geometry model which is obtained by a reverse engineering is shown in the second part of the thesis. The geometry model was subsequently used for the computer based modelling of the modal parameters. In the third part an experimental equipment, setting, measurement and processing of data are described. The conclusion of the thesis is dedicated to the comparison of the results obtained by the experimental modal analysis and the computing modelling is presented. Moreover, influence of boundary conditions and influence of the environment on the natural frequencies are evaluated.

The aim of this diploma thesis is a creation of modal parameter estimation application. Modal properties (natural frequencies, damping factors and mode shapes) are used in many dynamics analysis and their accurate determination is very important therefore the modal parameter estimation is one of the most significant part of the experimental modal analysis. Many methods have been developed for modal parameter estimation, each of them with different assumptions and with different accuracy. In the beginning of this thesis, a theory connected with modal analysis and a theory which is necessary for understanding to presented modal parameter methods are given. Then four different modal parameter estimation methods are presented - Peak Picking, Circle Fit, Least Square method and Eigensystem Realization Algorithm. The application for the modal parameter estimation is the output of this diploma thesis. In addition, the application allows performing all experimental modal analysis such as estimation of frequency response functions, animation of the found mode shapes, different kinds of comparison etc. In the conclusion, three structures are shown on which the application and modal parameter estimation methods were tested.

This diploma thesis deals with the issue of operational modal analysis, which is one of the newer areas of structural dynamics that makes it possible to estimate modal properties of structures directly during their operation. The aim of this work is to create theoretical basis of operational modal analysis, more specifically of Frequeny Domain Decomposition method. Furthermore, apply this method to a selected structure and verify the achieved results using computational modelling and experimental modal analysis. The technique of dividing the experiment to separate measurements using reference sensor was used. Evaluation of the operational modal analysis was performed using self-created function for the MATLAB software and using the commercial PULSE Operational Modal Analysis software. Obtained results were verified by computational modelling and experimental modal analysis.

In one of the first hours of study at the Institute of Mechanics of Bodies, Mechatronics and Biomechanics, the author of this work received three basic recommendations regarding measurement: 1) Do not measure! 2) If you measure, do not repeat the measurement!! 3) If you repeat the measurement, do not compare the measurements!!! However, this thesis boldly violates all three recommendations. In the introductory theoretical part, it briefly introduces the vibration of multi-degree of freedom damped systems and describes experimental ways of determining the modal damping. It also summarizes the Operational Modal Analysis (OMA) approach, explains the principle of the FDD method, and introduces EFDD (Enhanced Frequency Domain Decomposition) method which allows to determine not only natural frequencies and shapes as FDD does, but also modal damping of the shapes. A script in Matlab environment for processing vibrations using EFDD method is one of the thesis outputs. The script is first tested by computational model, where a model system with known damping is tested and damping is determined by the script. Subsequently, the work moves to the actual measurement of the real system - a bonded bar which is analysed by Experimental Modal Analysis and OMA, while the second variant uses commercial EFDD method (Brüel a Kjr company) and programmed script. In the conclusion of the thesis the damping results are compared to each other. The diploma thesis continues in Ing. M. Pop’s thesis – Modal Analysis Experimental Method Verification. From this work a part of measured data is taken. Specific cases of data use are always listed in the appropriate section of the text.

Tato diplomová práce uvádí dynamiku klikového mechanismu šestiválcového řadového motoru za účelem návrhu klikového hřídele v CAD programu Pro/Engineer. Následuje popis vibrací klikového mechanismu a analytický výpočet jeho torzních vibrací. Hlavní část diplomové práce se pak zabývá konverzí hřídele do konečno-prvkového modelu v programu ANSYS a jeho importem do prostředí Adams/Engine. V tom je provedena modální analýza klikového ústrojí pro získání vlastních frekvencí a tvarů. Na konec práce je porovnán výstup z analytického řešení a výsledky z multi-body systému.