Hybrid method for the computation of dynamic soil-structure ...

Asymptotic expansion for ω → ∞Hybrid domain methodIntroductionHybrid methodTime Domain BEMFE-BEConclusions■ Force-displacement relationship for ω → ∞:ũ x (k x , ω) = iωρC s˜t x (k x , ω) (7)ũ y (k x , ω) = iωρC s˜t y (k x , ω) (8)ũ z (k x , ω) = iωρC p˜t z (k x , ω) (9)■ The stiffnesses are independent of the wavenumber:û x (x, ω) = iωρC sˆt x (x, ω) (10)û y (x, ω) = iωρC sˆt y (x, ω) (11)û z (x, ω) = iωρC pˆt z (x, ω) (12)■ The result is extended to the 3D-case, using a Fourier series in the circumferentialdirection. The results remain valid.LMSSMat Hybrid method for the computation of dynamic soil-structure interaction in the time domain - p. 13/44