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This paper considers the effect of time delays on the saturation control of first-mode vibration of a stainless-steel beam. Time delay is commonly caused by measurements of the system states, transport delay, on-line computation, filtering and processing of data, calculating and executing of control forces as required in control processing. The method of multiple scales is employed to obtain the analytical solutions of limit cycles and their stability and to investigate the bifurcations of the system under consideration. All the predictions from analytical solutions are in agreement with the numerical simulation. The analytical results show that a delay can change the range of the saturation control, either widening or shrinking the effective frequency bandwidth. Thus, vibration control of a beam can be achieved using an appropriate choice of the delay in a self-feedback signal. From the examples illustrated, this paper provides a positive example that time delay can also be utilized to suppress vibration in systems when time delay cannot be neglected.

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A pH-responsive supramolecular nanoparticles was constructed through the electrostatic interaction from anionic sulfobutyl ether-β-cyclodextrin (SBE 7β-CD) and two positively charged chitosan (CS-75% and CS-95%). The prepared nanoparticles were characterized by UV-vis absorption spectra, x-ray diffraction, dynamic light scattering, transmission electron microscopy, and zeta potential. It was found that the CS/SBE 7-β-CD nanoparticles can be disassembly by increasing pH value and reassembled by reducing to the original pH value. To explore the potential of the obtained nanoparticles as a drug delivery vehicle, a negatively charged anticardio cerebrovascular drug sodium ferulate (SF) was loaded. The result indicated that the SF could be efficiently encapsulated in its nanoparticle nucleus under simulated gastric conditions with lower pH (pH 2.0), while effective release is triggered in a simulated intestinal environment with higher pH (pH 8.5). The assembly/disassembly behavior and drug loading/release property make CS/SBE 7-β-CD nanoparticles promising candidates for pH stimulation responsive drug delivery system, which has a broad application prospect in the treatment of cardiovascular and cerebrovascular diseases, diabetes and other chronic diseases.