The Analysis of a Wave Equation Possessing a Randomly Distributed Parameter : 1st Report, The Step Response and Its Stochastic Characteristics

抄録

The authors studied the technique to estimate the step response of a complex system whose parameters are not known exactly but statistically. For the theoretical model they used a system expressed by one dimensional wave equation. At first they obtained the step response of stress and acceleration when the shape of a rod is described with a function of small variation deterministically. To prove the solution they compared it with their experimental results and got fairly good agreement between them. At the second step, they treated the sectional shape function as a stochastic variable, then they could describe the stochastic characteristics of the stress response as follows ; the mean value of the stress agrees with that of a uniform rod, and its variance becomes zero at T=1, 3, 5…, and between such moments it goes up and comes down with a quadratic shape. The maxima in each duration increase squarely.