The closed-form solutions of plane and shear stresses were deduced by using the shear lag model.
For the adhesive, the displacement field is expressed in terms of those of laminates by using the shear-lag model.
The residual stiffness was then predicted by using the partial-crack shear-lag model, and the post-fatigued tensile strength was predicted by using the load carrying capacity of fibers proposed previously for brittle matrix composites.
The modal frequencies, phase hysteresis loops and phase lag values due to non-collocated placement of the acceleration sensor and the piezoelectric patch actuator are experimentally obtained, and the phase lag is compensated by using the phase shifting technology.
The optimum lag was determined by using the first minimum of the mutual information [ 11].
In order to obtain c(n,m), the signal with complex-lag argument is calculated by using the concept of analytic extension as follows: (18).
The active control is generated with non-negligible time lag by using a pneumatic actuator, and the road profile is estimated by using the minimum order observer based on a linear system transformed from the exact non-linear system.
The optimal parameters of the lead/lag controller are obtained by using the tabu search algorithm (TSA), so that both performance and robustness are satisfied.
By using again the lag operator B, we write the operator Open image in new window Contrarily to (phi (B)), for example, which is a polynomial because only the positive powers of B appear, the operator (nu ^{P}) ((B,B^{-1})) includes lags B but also leads (B^{-1}).
Second, we estimate the system by GMM and use the lags of the regressors as instruments, as the transformation keeps the orthogonality between lagged regressors and transformed variables unchanged [56].
