Re: Modal Analysis

ok. checkout the last part regarding the practical side of the modal analysis and how such analysis can help u redesign a piping system that is behaving differently than predicted (peter lecture note). analysis per se without practical application wont be much help. ok let us say that the computer analysis (theoritical)has provided the ist mode, 2nd, 3rd and 4th mode of vibration of your piping model plus the natural frequency. how would u relate it to the resonant frequency and from the operating deflection shape of piping vibrating at the field. this is what modal analysis is all about.

theory has remain the same, but the role of modal analysis has now change. predicion is ok, but direct field measurement of velocity and frequency is req'd if u hope of fixing a pipe in motion. for measurement to take place, an excitiation force has to be present. cyril harris (shock and vibration handbook) chapter 21 is clear on this. advances in digital signal processing plus the software to reduce data and extract modal frequencies has made a new application for the modal analysis.

checkout also the coade lecture noteChapter 4 of the Coade Pipe Stress Seminar Notes. here's some excerpts.

4.3.1 Modal Analysis
The free vibration response of any system with N degress of freedom is the sum of N independent cyclic function. Each of these vibration functions are called modes of vibration of the system and each has its own natural frequency and has a single DOF, vibrating back and forth about the set of displacement. Since its mode responds to external loading in exactly the same way as does a ssingle DOF oscillator.

Therefore, the dynamic response of any system can be determined using modal analysis. Modal analysis breaks up a complex system into a number of modes of vibration, each of which can be considered to behave like a single DOF oscialltor – i.e., having a unique vibration response. The total response of a system is the superposition of all individual modal responses. The specific procedures consist of:
Using the formulas ( its complex so im not typing it here, if interested try vibetech.com/papers/paper10.pdf ) described, solve for the natural frequencies and normalized shapes of all N modes of vibration in the system.
Determine the constant C's by which each of the modal responses are to be multiplied. (now hear this) These constants are a function of the magnitude of the imposed load, the DLF (dynamic load factor – corresponding to the frequency of each mode on the DLF curve for the imposed load), and the mode and load participation factors for each mode.
Since each mode of vibration behaves as a single DOF oscillator, the modal response is alos based upon the DLF for that modes frequency under the imposed load. The final contributor to the modal response multiplier is of coursed the imposed load itself. The results of the individual modal loads are then calculated and summed to provide the total system response.

It goes on to say that free vibration is harmonic in nature.

maybe u conduct the analysis differently than we do, but where i work we got a 5 full time vibration specialist and a vibraion lab that could rival nasa. maybe its called harmonic as u say, but then again that'll make the vibration institure wrong too (we're certified).

regards
andoks .