Abstract
It is very important to know how does the local modification of the system affect the natural frequency of the original system. In general, two different approaches are adopted to investigate about this kind of problem. One is the sensitivity analysis of the eigenvalue which is based on Rayleigh's quotient or Jacobi's variation. The another one is the combined dynamical system analysis which is based on the Weinstein's determinant or Kron's method, and by these approaches, a large amount of formulas has been proposed, but when we want to design the system to have a given natural period, these formulas are not enough to use. We need more simple theories and more convenient forms. In this paper, following new formulas are proposed which decide the exact value of added mass Δm or of added spring Δk in order to get the arbitrary natural period. Δm=g_m(T^*, T_i, Ψ_i, C) Δk=g_k(T^*, T_i, Ψ_i, C) where T^* is the given natural period, T_it and Ψ_i are natural periods and mode vectors of the original system, respectively, and C is a connection vector that is decided from which the mass or the spring is added. Simple examples are shown by using these formulas. Some considerations for the limitation of these formulas and some comparisons with other's works are done. Especially, Brameller's formula, Simpson's formula and Hirai's formula are chosen to compare.
