塔状振子の力学的性質について
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概要
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In a compound pendulum, which consists of ligid unit pendulums A_1, A_2, …, A_n, …, A_N, and three-demensional pins, B_0, B_1, …, B_n, …, B_<N-1>, unit pendulum A_n with center of gravity D_n and mass m_n supports A_<n+1> on pin B_n, and is supported by A_<n-1> on B_<n-1> and A_1 is supported by the foundation on B_0. Point E_n is defined on the straight line B_n-D_n, by m_n : Σ^^N___<i=n>m_<i>=(length B_n-E_n) : (length B_n-D_n). Plane π_n is perpendicular to the straight line B_n-B_<n-1> and intersect B_<n-1>. If D_n and E_n exist at the opposite side of π_n to B_n in every A_n, every B_n takes higher position than B_<n-1> in stable equilibrum. In this paper, such a compound pendulum is named Tower Pendulum. If B_n, B_<n-1> and D_n exist on a straight line in every A_n, every B_n and B_<n-1> take position on a vertical perpendicular line in stable equilibrum. In the stable equilibrum, B_n and B_<n-1> could be changed to pins which have axes intersecting the center points of the former three-dementional pins. In the free vibration of this system, if the natural vibration are defined as 1st, 2nd, …, j-th, …, N-th degree, degree, from vibration of the longest natural period to that of the shortest, the number of changes of signs in the j-th natural mode {_ju} is N-j. In the forced vibration of the system caused by ground acceleration, denoting β_j as modal participation factor, about particitation vectors, [numerical formula] Displacements, velocities, and shearing coefficients of every parts of the Tower Pendulum, caused by earthquake ground motion and wind force which vary with the lapse of time, can be calculated using those of one mass point system.
- 社団法人日本建築学会の論文
- 1976-01-30
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