Reference no: EM132388801 , Length: word count : 4000

48601 Mechanical Vibration and Measurement

University of Technology Sydney, Australia

Project 2: Dynamic modelling of structures using finite elements

The objective of this project is to mathematically model a scale model of an eight-storey tower using the finite element method and verify the theoretical results against those obtained experimentally during the Lab 3 session. As such, this project is divided into three separate sections including modelling, experimental investigation and reporting on results. This project is to be conducted individually.

Project 2 Part 1: Mathematical modelling

Configuration of a model structural system

Model the structure in MATLAB using the required number of finite elements.

Figure 1 shows schematically of the structural system built in the laboratory. Note that the two structures in the lab are deliberately different (different rectangular hollow section geometry) – you need to be clear which system you are working on when you model the system. Eight equally spaced lumped masses are rigidly attached to a rectangular hollow section column 2 m in height. The column is rigidly fixed to the ground. The lateral vibration of the model structure is of interest.

Figure 1 – Schematic of the model structure and table of structural properties

Project 2 Part 2: Experimental analysis and report

In the laboratory session the first five natural frequencies at least were extracted from experimental data obtained during a roving modal impact hammer measurement campaign. The Frequency Response Functions (FRFs) were collected and saved for each of the eight storeys. The approximate mode shapes of each of the eight natural frequencies can be determined by extracting the peak values from the Imaginary
part of the FRF for each natural frequency and plotting these against the position of the storey from which the peak value was obtained. This is a technique known as “Quadrature Peak Picking”. At least the first five of these mode shapes, and their corresponding natural frequencies, should be reported.

Additionally, a precise mode shape for the second natural frequency was extracted using a shaker excited roving accelerometer measurement campaign. This mode shape can be compared and contrasted with the equivalent obtained through quadrature peak picking. All of the above experimentally determined results are to be compared with those theoretically determined in Part 1 for the first five natural
frequencies and the collected mode shape.

Project 2 Part 3: Comparison to theoretical results

Prepare a brief (10 pgs max – see below for detail) technical report on the experimental analysis of the eight-storey tower model. This section should include a formally prepared lab report (abstract, introduction inc. aims, method, results and conclusion) limited by the requirements set out below. The instructions and items required for the report will be handed out during the lab session.

Project 2 Part 4: Optional extension to modify system

– complete only if you wish to be considered for D/HD and declare this on the front page of the report

Task: Designing a vibration absorber

A machine or structure may experience large oscillations under harmonic excitation with frequencies near a natural frequency of the system. In such circumstances, the vibrations of the system can be reduced by using a dynamic vibration absorber.

Assume that a rotating machine (such as an air-conditioning system) has been placed on the top level of the tower (roof of the tower in a possible practical real-world scenario) and that it operates at constant speed where its frequency coincides with the second natural frequency of the tower.

Design a mechanical absorber to reduce excessive vibration of the system. Do a comprehensive analysis and determine the specification of the absorber including its mass, stiffness, and where to put it (what level). Note that you may come up with several designs. So, present all possible scenarios and make engineering judgment to select the best design.