Theory of the Modes

(I don't usually bother apologizing for my bad writing and for my horrible use of grammar and punctuations. Generally it is because of my simple acknowledgement of the fact that I am horrible at grammar and punctuations. But, I am going to apologize for this particular piece as it is going to get posted without a second glance, due to a lack of time. The reason for my lack of time to review this write up will go down as my attempts to learn and understand better Modal theory and its applications in engineering. To all the unassuming souls who chance upon this piece, my sincerest apologies if this turns out to be a murder of the english language and writing.)

      Modal Analysis theory is the study of the dynamic responses of systems and one of its approaches is to break down the responses into summations of contributions of various modes. Essentially what it says is that "what happens to you or how your life pans out can be broken down into a sum of the contributions of the people/events that you cross paths with and how strongly it can impact the various inherent modes in you". The contribution no matter how large or small, how negative or positive has a part in the sum total. So if you are happy right now as you read this, then it is not wrong to assume that a large/tiny bit of that is because of me and my effort in writing this piece of nonsense.

     To try and make you understand better I am going to try and talk to you about the essentials of a dynamic response and try and compliment it with a day to day life experience. To begin with, it is essential to understand that to get a response from a system some force has to act on it. As mentioned before, the reaction to this force can be broken down as an combination of the different response modes of the system that this force manages to excite. Forces can be positive or negative and if the forces are instantaneous, then one of the characteristics it exhibits is that the responses to these tend to die with time. The amplitude of the response decreases as time passes by. 

     Imagine you are running late to a seminar. The mismanagement of time on your part is to be blamed on the guy in your lab, a bad listener, who kept you engaged even after you told him you had to rush. The negative impact brings a frown on your face as your plans get offset in time. As you inch closer to the seminar hall the intensity of the frown decreases. (Amplitude tends to die with time!). 

   Note also that the initial amplitude the excitation (being late) has produced will depend on how effectively it has excited the modes. If in this case, you were not looking forward to the seminar with as much enthusiasm as you would have to a Manchester United  Vs Real Madrid match up, then the irritated frown mode might not get excited well enough to be noticed. (The modes need not be well excited by a force)

    As the effects of being late started to die out, a smile appears on your face. You seem to have perfectly timed your entry into a lift to coincide with that of a girl you have been wanting to speak to but not managed to so far. The positive excitation increases in amplitude. The girl and you being the only people in the lift, she asks you for the time and you get to reply to her. Amplitude hits peak. Big wide smile as you exit the lift and you forget about why you are late. (The happy smile mode is excited very well by the external excitation.)

     A few seconds down the line you realize, that was a chance to introduce yourself and get her name too might be?.. The 'hmmm.. I am so dumb' mode gets well excited and you trudge with heavy steps into the seminar hall and take a seat to listen to the talk. If you are lucky enough, the talk might be one of the most brilliant technical seminars you have attended and might excite your 'Woah.. that's interesting..!' mode. Whether this new response mode can help mask the earlier response that highlights  your not so great social skills and ability to strike a conversation, will depend totally on the system and the level to which each mode has been activated.

    To summarize, most of the dynamic responses can be broken down as a sum of responses to a combination of harmonic excitations with contribution of the modes excited varying depending on the systems construction. It might be of interest to note that a system that undergoes persistent forces (positive or negative) tends to show different characteristics with time. This can attributed to changing modal or system characteristics upon submission to repeated and persistent forces. Keeping aside such situations, usually the modal analysis theory can be used to address any system issues or to understand better the system characteristics.