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Application of Adomian method on the solution of the elastic wave propagation in elastic bars of finite length with randomly and linearly varying Young’s modulus. (English) Zbl 1133.74312
Summary: The aim of the present problem is to investigate the efficiency of the Adomian method for the solution of nonlinear and complex equations in random medium. Here the problem is in connection with the investigation of mean and variance of the displacement distribution in a system of elastic bars of finite length with Young’s modulus varying slightly linearly and randomly from bar to bar due to time dependent displacement input at one of the ends, the other ends being kept fixed. Laplace transform on time for small random variation in Young’s modulus is utilized and a truncated series solution of the wave problem in the line of Adomian technique is achieved. The effects of randomness on the elastic wave motion for three particular cases of different continuous probability distribution of the random variable have been discussed.
MSC:
74H10Analytic approximation of solutions for dynamical problems in solid mechanics
74J05Linear waves (solid mechanics)