Modelling of dynamics systems with multi degrees of freedom

Cílem této práce je pro zadanou dynamickou soustavu s více stupni volnosti sestavit a vyřešit pohybové rovnice. V úvodu práce jsou shrnuty základní poznatky o dynamických kmitavých soustavách, jejich rozdělení, způsob matematického popisu apod. V další části jsou pro zadanou soustavu hmotných bodů sestaveny rovnice metodou Lagrangeových rovnic druhého druhu. Řešení rovnice ve frekvenční oblasti je provedeno v matematickém systému MAPLE. K určení polohy těles v čase byl využit systém MATLAB. Výsledky řešení jsou grafy amplitudové a frekvenční charakteristiky a graf polohy hmotných bodů v čase. Je provedena diskuse vlivu parametrů soustavy na kmitání. V závěru práce je srovnání analytického řešení s řešením metodou konečných prvků v systému ANSYS.The aim of this work is for a dynamic system with multiple degrees of freedom to assemble and solve the equations of motion. In the beginning of work are summarized the basic knowledge about the dynamic oscillating systems, their distribution, method of mathematical description etc. In the following part of work are for the given set of particles assembled equations using Lagrange equations of the second kind. The solution of equation is made in mathematical system MAPLE for frequency domain. To determine the position of particles in time was used MATLAB. Research results are graphs of amplitude and frequency characteristics and graph of positions of particles in time. There is discussion on the influence of systems parameters on oscillation. The conclusion is a comparison of analytical solution with the solution of finale elements conclusion in ANSYS.

Creation of Modal Parameter Estimation Application for Experimental Modal Analysis

Cílem této práce je tvorba aplikace pro získání modálních parametrů z naměřených dat. Modální parametry (vlastní frekvence, tlumení a vlastní tvary) jsou používané v mnoha další analýzách a jejich přesné určení velmi důležité, proto proces získání modálních parametrů je jedním z nejdůležitějších při experimentální modální analýze. Pro určování těchto parametrů bylo vyvinuto spoustu metod a technik, které stojí na různých předpokladech a jsou různě přesné. Na začátku této práce je zpracována teorie související s modální analýzou a teorie, která je nutná pro pochopení presentovaných metod. Potom jsou popsány čtyři rozdílné metody pro získání modálních parametrů - Peak Picking, Circle Fit method, Least Square methods a Eigensystem Realization Algorithm. Výstupem této práce je aplikace, které kromě popsaných metod umožnuje provádět celou experimentální modální analýzu včetně zpravování naměřených dat do vhodného formátu, animaci výsledných vlastních tvarů, různé druhy porovnání modálních parametrů atd. V závěru práce jsou presentovány tři příklady na kterých byla aplicace a metody otestovány.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.

Non-linear system identification in structural dynamics: advances in characterisation of non-linearities and non-linear modal analysis

Many new methods for theoretical modelling, numerical analysis and experimental testing have been developed in non-linear dynamics in recent years. Although the computational power has greatly improved our ability to predict non-linear behaviour, non-linear system identification, a central topic of this thesis, still plays a key role in obtaining and quantifying structural models from experimental data. The first part of the thesis is motivated by the industrial needs for fast and reliable detection and characterisation of structural non-linearities. For this purpose a method based on the Hilbert transform in the frequency domain is proposed. The method detects and characterises structural non-linearities from a single frequency response function and does not require a priori knowledge of the system. The second part of the thesis is driven by current research trends and advances in non-linear modal analysis and adaptive time series processing using the Hilbert-Huang transform. Firstly, the alternatives of the Hilbert transform, which is commonly used in structural dynamics for the estimation of the instantaneous frequency and amplitude despite suffering from a number of numerical issues, are compared to assess their potential for non-linear system identification. Then, a possible relation between the Hilbert-Huang transform and complex non-linear modes of mechanical systems is investigated. Based on this relation, an approach to experimental non-linear modal analysis is proposed. Since this approach integrates the Hilbert-Huang transform and non-linear modes, it allows not only to detect and characterise structural non-linearities in a non-parametric manner, but also to quantify the parameters of a selected model using extracted non-linear modes. Lastly, a new method for the identification of systems with asymmetric non-linear restoring forces is proposed. The application of all proposed methods is demonstrated on simulated and experimental data.Open Acces

Creation of Modal Parameter Estimation Application for Experimental Modal Analysis

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