The response of a hysteretic structure under horizontal and vertical random excitations is considered. The excitations are modeled by segments of stationary and nonstationary Gaussian white noise and filtered white noise processes. The linearization technique is used and the moments equations of the responses are evaluated. The transition probability density of the response is described and the associated second moment equations are derived. The transient and nonstationary response statistics for a range of values of parameters are obtained. A Monte-Carlo digital simulation study is performed. The results are compared with the theoretical findings and good agreements is observed. Particular attention is given to the amplification effects of the vertical acceleration. It is shown that the effect of the vertical excitation is usually insignificant, unless the load coefficient is quite large.

The dynamics of nonlinear structures under harmonic and random excitations is studied. The harmonic excitation is modeled by periodic loadings while the random excitations is modeled by segments of stationary Gaussian white noise processes. Transient responses of a single-degree-of-freedom model is studied to illustrate the characteristic of nonlinear responses. A free play type of nonlinearity is considered. The effects of nonlinearities on the overall dynamics of structure is investigated. The linearization technique is used to calculate the response statistics. To check the accuracy of the linearization technique, the results are compared with Monte-Carlo digital simulations and good agreement are observed.

Model predictive control (MPC) has become more attractive in control engineering for the last decades because of its efficiency and robustness. In this paper, an effective control strategy is proposed for vibration reduction of mechanical flexible systems in which establishment of a global dynamic model of the controlled system is not necessary. A modified model-free adaptive predictive controller is designed by combination of MPC and model-free control theory. The novel idea of this contribution is that by using the compact-form dynamic linearization technique, the upcoming system outputs within a specified prediction horizon can be predicted in sequence. The data-based prediction model of the system only requires input/output information, and therefore the future control input increments as well as the unknown system parameters called pseudo-jacobian matrix can be estimated. To improve parameter estimation accuracy, another online estimation method namely recursive least-squares algorithm is applied instead of using the conventional projection algorithm. The control performance is verified nummerically for vibration control of a flexible ship-mounted crane represented as a multi-input multi-output (MIMO) system. Simulation results indicate that significant reduction of the crane oscillations and better control performance are observed when using the proposed controller in comparison with other traditional methods.

Large-scale design problems are high dimensional and deeply-coupled in nature. The complexity of such large-scale systems prevents designers from solving them as a whole. Analytical target cascading (ATC) provides a systematic approach in solving decomposed large-scale systems that has solvable subsystems. By coordinating between subsystems, ATC can obtain the same optima as they were undecomposed. However, a convergent coordination requires series of ATC iterations that may hinder the efficiency of ATC. In this research, a sequential linearization technique is proposed to improve the efficiency of ATC. The proposed linearization technique is applied to each ATC iteration, therefore each iteration has all linear subsystems that can be solved with high efficiency. One further motivation of the proposed strategy is its perceived potential in handling multilevel problems with random design variables. As previously studied, the sequential linear programming (SLP) algorithm in [1] provides a good balances between efficiency, accuracy and convergence for single-level design optimization under random design variables. The proposed linearization technique can integrate with the SLP algorithm for multilevel systems. The global convergence of this approach is ensured by a filter to determine the acceptance of the optima at each iteration and the corresponding trust region. A geometric programming example and a structure design example demonstrate the efficiency of the proposed method over standard ATC solution process without loss of accuracy.