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# Structural Dynamics

Lecturer (assistant) Sommersemester 2023 See TUMonline See TUMonline

### Objectives

The procedure for the calculation of the structural response under dynamic loads is dependent on the characteristics of the load. In the lecture the students will, in a first step, learn how the dynamic response of simple systems can be calculated for different load characteristics. General periodic loads (e.g. due to rotating machines), aperiodic (transient) loads (e.g. an impact) or random, stochastic loads (e.g. wind or vibrations) are presented together with the respective methodologies for their calculation. The mentioned approaches are adapted for the calculation of complex building structures using efficient methodologies (modal superposition). The aim of the lecture consists in a profound knowledge of the procedures that can be used for the computation of free and forced vibrations of the building systems (beam, plate, frame) by equivalent multi-mass systems (as it is used in engineering approaches or in the Finite Element Method). The students learn how to use impedance approaches in order to calculate the system's response to a dynamic load. The Statistical Energy Analysis is understood after the lecture Structural Dynamics.

### Description

Thematic outline: - Overview over tasks and methodologies - Determination of characteristic variables of dynamic systems - Description of harmonic oscillations by complex numbers - Fourier Transformation with complex numbers - Evaluation of the differential equation for Single-Degree-Of-Freedom-Systems (SDOF-Systems) - Evaluation of the differential equation for Multi-Degree-Of-Freedom-Systems (MDOF-Systems) - Natural vibrations - Classification of influences - Impedances and Wavenumber-Impedances - Differential equations for continuous systems - Modeling and Calculations - Stochastic Vibrations - Dynamic Calculation of multistorey frame systems - Approximation approaches for the calculation of eigenfrequencies and eigenvectors