How To Write A Viscous Damping Lab Report

Chapter I
Introduction
I.1. Overview
Mechanical, aeronautical or civil structures need to be lighter, stronger and more flexible because of the demands of safety and reliability. Furthermore predicting the response of a structure to an excitation is so critical. Because of these facts, vibration analysis of structures become a popular subject for engineers. Making experiments on a structure, constructing a mathematical model, controlling the structure or designing strong and stabilized structures are the main studies of vibration analysis. As an example, the vibration properties of Transamerica Building in Figure 1.1 were determined by forced vibration tests. The fundamental natural vibration periods of this 60-story steel building are 2:90

Damper elements shows a damping effect in an oscillatory system. Generally damper element absorbs energy and the absorbed energy is dissipated as heat. Viscous damping is a common form of damping which is inherently found in many engineering systems. As a result, the characteristic of damping is generally modelled as viscous damping for civil structures. In physics, viscous damping is mathematically defined as a force synchronous with the velocity of the object but opposite direction to it. The force equation of a viscous damper can be written

Since these roots are the poles of the transfer function, and * 1 symbols can be used instead of s1 and s1* (1.54) The IRF of the system can be found by taking inverse Laplace transform of Equation 1.54, (1.55) (1.56) where is the decay rate and is the damped natural frequency. The main objective of this study is to estimate the values of and from the measurements. Besides that Civil engineers are also interested in the values of m, c, and k.
I.2.2. Analysis of Multi Degree of Freedom Systems
For Multi Degree of Freedom (MDOF) systems, system parameters are M, C and K matrices. There are N natural frequencies and N damping ratios for a N-degree of freedom system. For example in Figure 1.12, there are 2 mass blocks and they can move Fig1.12. 2 DOF System independently. If any of the masses is excited by an external force, the other one can move by the effect of this force. This system is a two degree of freedom system (2-DOF). While constructing the mathematical model of the system, the degree of freedom number must be known. Equations of motion can be written according to degree of freedoms as shown in Equations 1.57 and 1.58.