偏心構造物のパルス応答解析 : 区間線形近似モード分離応答解析法(I)

抄録

In order to make clear the ultimate states of structures under earth-quake excitations, approximate analysis methods, which are named as FINITE RESONANCE RESPONSE ANALYSIS (FRRA) and PULSE RE SPONSE ANALYSIS (Velocity Pulse Response Analysis : VPRA, and Acceleration Pulse Response Analysis : APRA), have been proposed by the authors. The former is used for estimating the cyclic responses (the cyclic displacement amplitude and the absorbed energy) of the structures subjected to a cyclic excitation, and the latter is used for evaluating the monotonic responses (the maximum monotonic displacements and deformation energy) of the structures subjected to an impulsive excitation. In this paper, the fundamental procedure of the PULSE RESPONSE ANALYSIS method is used, and an approximate analysis approach for the coupled asymmetrical structures is proposed. The main contents of the approach are described as follows : 1) By integrating the equation of motion of asymmetrical structures in the X, Y and θ directions respectively, a relationship of the amplitudes (velocity and acceleration in the X, Y and θ directions) and the duration of the impulsive excitations is obtained. And the relationship may be shown as a curve in a 4-dimensional coordinates in which the coordinate-axes represent the amplitudes of 3 directions and the duration of the excitation, and the curve is defined as the Pulse Spectrum-Curve for the torsionally coupled systems. 2) The Excitations of the analysis for the asymmetric structures subjected to the impulsive excitations in multi-directions are idealized as a Spectrum-Surface in the same 4-dimensional coordinates as the one which the Pulse Spectrum-Curve is shown in. 3) Then, the analysis process may be concluded as how to find the point of contact of the Pulse Spectrum-Curve and the Excitation Spectrum-Surface. The responses at the point are considered as the result of the Pulse Response Analysis. 4) For developing the process, the resistant force-deformation relation of the structure is approximately divided and linearized in some small sections, and the elastic response analysis is applied in each section. As the result of combination of the elastic analysis processes in all the sections divided, the vibration mode-separating responses are obtained. To verify the analysis approach proposed in this paper, an example of earthquake response analysis for a mono-eccentrical structure subjected to an unidirectional impulsive excitation is performed. The results are compared with those obtained by a numerical integration analysis, and confirmed good coincidence between them.