## Machine Dynamics I

The concept of the signal. Frequency analysis, Fourier series, spectra. Fourier transform, convolution, cross- and autocorrelation. Modulated signals, demodulation. Discrete signals. Sampling Theorem. Discrete and fast Fourier transform. Restrictions of the Discrete Fourier Transform, aliasing, leakage, resolution. Vibrations and fault diagnosis. Vibration measurements, and international standards. Fault diagnosis: basic principles, unbalance, misalignment, looseness, impacts, fault detection in bearings and gears. Experimental modal analysis – Introduction. Theoretical concepts. Determination of natural frequencies and mode shapes in the frequency and time domains.

### Objectives

The approach a complex problem by a simpler, but for which they can devise dynamic equations to analyze its behavior. The preparation of mathematical models describing the dynamics of a model. In this step the final course is usually linear SBS to be resolved and further analyzed. Analytical calculation of the response of q (t) B.E. system (or equivalent of MK) from the dynamic equations (SDE system) describing the system, the initial conditions and external stimulation. Calculation of the characteristic modes (eigenvectors) to which oscillates (in the respective eigenfrequencies) a linear dynamic system of many degrees of freedom. Analysis of the response of a system with harmonic excitations.

### Prerequisites

A comfort to the content of the following courses (Department of Mechanical Engineering, NTUA) is essential to a proper understanding of the course: - Yves Mathematics: Linear algebra, Vector Math compartments- IIa: Functions of several variables, basic vector analysis; Mathematics IIb : Ordinary Differential Equations, M / x Laplace, M / x Fourier- Mechanics II: Energy, momentum, equations Lagrange, analysis deformable solid - Engineering III: Bending, twisting bodies shall Introduction to Electric Circuits and Systems: modeling systems, state variables , Bode diagrams. (!) Someone / a student / limits have the right to write in the course "Dynamic Machine I" regardless of whether it has passed these courses.

### Syllabus

Meaning of the signal. Frequency Analysis, Fourier Series. Signal Spectrum. Fourier transform. Convolution signals. Autocorrelation and cross correlation signals. Modulated signals, Demodulation. Discrete signals, sampling theorem. Discrete Fourier transform signal. Discrete Fourier Transform (DFT). Fast Fourier Transform (FFT). Limitations of Transformation Discrete Fourier, Show aliasing, leakage, Sharpness. Vibration and fault diagnosis, Introduction. Vibration Sensors. Measurement and analysis of vibration standards. Fault diagnosis: basic principles, unbalance, eccentricity, kakiefthygrammisi, looseness, abrasion, impacts, ball bearings errors and teeth. Experimental morphic analysis Introduction. Theoretical bases. Methods of extracting resonance frequencies and mode shapes in the frequency and time domains.

COURSE DETAILS