(16)縮退される動力学系の固有値問題の解構造と各部減衰性に応じたカギー行列

概要

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Features observed in redundantly higher modes of infinite frequency are mathematically clarified with relation to the deflation of dynamic systems according to partial absence of inertia. Choosing a single factor representing uniform vanishing of the set of absent inertia and retaining its first-order terms, the entire family of eigenvalues and eigenmodes is shown to be well separated into lower and higher groups. The expression permits to identify relative order of magnitude for singular solutions tending to zero or infinity, and leads to determination of the characteristic measures of dynamics pertinent to residual components arising from the higher group. Then the discussion continues with regard to construction of an associated Caughey-type damping matrix under the assumption of segmentally different damping capacities. The Biggs rule for approximating equivalent modal damping is reviewed in a generalized form to allow frequency-dependence in the imaginary parts of complex-valued inertia and stiffness, with its verification basis provided from the standpoint of overall equivalence of energy dissipation. It is concluded that the redundantly higher components can be totally irrelevant to the current damping formulation.
一般社団法人日本建築学会の論文
1999-03-10