musings of structural dynamics

MUSINGS OF STRUCTURAL DYNAMICS Prabhakar Gundlapalli Addl. Chief Engineer (Civil), Nuclear Power Corporation of India Limited, Anushakti Nagar, Mumbai – 400094. [email protected]

Any living or non-living being is familiar with structural dynamics, and responds to vibrations. At first instance, it seems to be unrelated, but the fact remains same. Take an example of a bamboo, standing in a remote forest, untouched by human inhabitation. The seasoned bamboo may have some holes on its body, made by wood peckers or termites and what not ! When the wind passes through this forest area, it gives fine sounds from the bamboo. The termites, perhaps have the great god- gifted sense of music, and thus make holes at the desired precise locations. The resulting sound is not of any kind of noise, but a pure and divine music. Then how come the music is linked to dynamics ! An unbroken link, existed before the humans exist. Look at any vibrating string, a membrane, a falling object, they all produce various kinds of sound, and when they are split and put into proper fashion (by the expert mathematicians, trying to fit in different kinds of mathematical series, obviously give musical sounds. Come back to ancient structures, made by nature due to wind erosion, and thus standing as free stone columns, and produce magical sounds in hilly areas. The dried tree trunks, falling leaves, flowing water in streams, all of them are so musical, one has to have an ear for listening. Let us come back to a vibrating string, as a simple example, which vibrates at its first or fundamental or natural mode of vibration, with most of the mass participating in its first mode itself, predominantly, when compared to higher modes of vibration. As the physical characteristics of the string, (meaning, the density, cross section area, diameter, etc.) are uniform; the sound produced by this string has to be so uniform and pleasing. Just try to add a small disturbance, in the form of an additional mass (a small cotton thread or a ball of wax) to the string, and see, the entire frequency characteristics gets a dramatic change, with fantastic perturbations. These effects of music are often used by great musicians for various effects during their performances to mesmerize the audiences. Buildings and structures (particularly temples of worship) built during 10th to 19th century have great distinction for their structural dynamic characteristics. They

The Master Builder, Vol. 12, No.11, Nov. 2010, pp 210-214

are all near perfect structures, designed to withstand most of the catastrophic dynamic loads, which they are being subjected to. Examples are many, such as, the towers (Gopuram) of majestic temples of southern part of India, The Tajmahal, Kutub Minar, Pyramids of Egypt, and Leaning Tower of Pisa; and there are many around the world. One such great example seems to be the ‘Music Pillars’, (carved out of stones), of Madurai Meenakshi Amman temple, located just outside (towards the west) the ‘Aayiram Kaal Mandapam’ or ‘Thousand Pillar Hall’, contains 985 (instead of 1000) pillars of. Each of the music pillars, when struck, produces a different musical note. There are many similar pillars in the temples of Southern part of India. In the Nellaiyappar temple (near Tirunelveli), gentle tap on the cluster of columns hewn out of a single piece of rock, can produce the keynotes of Indian classical music. One can hear the seven basic notes (saptha swaras), coming like a wave from any good musical instrument. Hardly anybody knows the intricacies of how these were constructed to resonate to a certain frequency. But, it is so obvious that, more aesthetically inclined person with some musical knowledge can bring out the rudiments of some rare ragas from these pillars. Another example is ‘Vijaya Vittala temple’, the most splendid of temple at Hampi, constructed by Krishnadeva Raya. This temple has 56 ornate monolithic pillars which have world class architecture, because of getting musical notes from the pillars. Each pillar is surrounded by stone columns. On striking these columns / pillars gently, one can hear different musical notes. This requires great accuracy in carving (constructing in our day to day usage) the pillars in-situ to get the desired dynamic characteristics. But, how and why the structures of 20th century get damaged or collapse more frequently, when compared to those ancient structures. Best analytical tools, design methods are available today, and they are being upgraded continuously by dedicated research. Still great structures are rarely built, and can be counted on fingers. Is this because of our lack of understanding of structures and dynamics ! Another stunning aspect of ancient structures is their acoustics and dynamic characteristics. When the wind passes through them, they produce soft low frequency


sounds, which help in calming the body and soul together. It is will well known fact that, during deep meditation and practice of yoga, the mind is in a calm ‘alpha’ state with low frequency of vibrations and relaxes ultimately. Though, research from current generation proved this by electronic instrumentation of the human body and brain mapping, this fact is known to the saints and yogis of India. This clearly indicates that, structural engineers are great musicians, understanding the music (or dynamics) of structures they design. They take care of the details of each element of the structure being designed, so that the finally completed structure does not have any unwanted vibrations (music) for the entire life of the structure. They try all other options to limit the disturbing dynamics for the structures, by various passive or active dampers, base isolators, tuned mass dampers, tuned liquid mass dampers, etc., whose design is highly technical and involves state of the art of present day’s research and development activities. The ultimate aim of all these efforts is to minimize the vibratory disturbances, from design basis and beyond design basis loads, such as, operating pumps, machines, compressors, and ground motion due to various expected and unexpected earthquakes, impact and shock, blast, etc. The ultimate goal of a musician is to give a pleasant state of mind for the listener, by virtue of producing divine music, through thorough understanding and manipulating the dynamics of various musical instruments, such as, strings, percussion, wind pipes, and intelligent combination of these musical sounds for a multiplying and soothing effect. Similarly, the role of structural engineer is to understand the dynamics of structure thoroughly, manipulate the layout and detailing of a structure in such a way, that none of the unwanted vibrations are capable of damaging the structure, and thus, providing a pleasant stay for the occupants, with a limit state of displacements and vibrations. May I request one and all, to understand the music, the dynamics, and the structures in-toto and put combined efforts, to create great music and great structures together ! Happy musical musings and dynamics together to one and all !
