Open AccessA simple method of finding the approximate period of stable systems
Author(s) -
A. Mallock
Publication year - 1913
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1913.0033
Subject(s) - vibration , period (music) , simple (philosophy) , stiffness , oscillation (cell signaling) , pendulum , mode (computer interface) , mathematics , spring (device) , mathematical analysis , control theory (sociology) , computer science , calculus (dental) , structural engineering , physics , engineering , mechanical engineering , acoustics , artificial intelligence , control (management) , medicine , philosophy , epistemology , dentistry , biology , genetics , operating system
In practical engineering work it is often a great convenience to be able to find the period of a structure, the calculation of which, by ordinary mathematical processes, would be difficult or even impossible. To find the period of a structure for any particular mode of vibration involves a knowledge of its stiffness (regarded as a spring) and of the distribution of the mass, but if the latter is known, even approximately, a knowledge of the period gives the stiffness, and the deflections for a given load can be found by simple arithmetic. In nearly every case likely to occur in practice a stable structure can be represented, as far as its elastic displacements are concerned, by an equivalent pendulum, a pendulum, that is, which has the same period as the particular mode of vibration under consideration, and an effective mass equal to that part of the mass of the structure which is subject to vibration, but concentrated at what, for the present purpose, may be called the centre of oscillation.