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Additionally, hydraulic valves are also exposed to vibration. Vibrations of the substrate on which the hydraulic valve is installed force the control element of the hydraulic valve to vibrate. The control element's vibration produced in this way causes changes in the pressure pulsation spectrum of the hydraulic system. A friction model modified using mixed friction theory can be used for the oscillating motion of the hydraulic directional control spool. Passive vibration isolation methods are proposed to reduce valve vibration. The biomimetic approach can be implemented in hydraulic systems (for pipelines) to reduce mechanical vibration and fluid pulsation. Numerical methods are employed to analyze the effectof changes in the pressure pulsation spectrum on the hydraulic efficiency of the pipelines. Examples are provided for the implementation of numerical methods in the calculation of hydraulic components and systems. 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The asymmetric property of the dynamic link travel time function is clearly verified, which leads to a variational inequality formulation. 2. The flow propagation constraint is implicitly defined in our model through the incidence relationship between the link inflow and route flow. 3. The inflow, exit flow, and number of vehicles on a link are identified as the three different states over time for the same vehicles under the flow propagation process. Therefore, only one link variable needs to be used in our dynamic travel choice models. This treatment can largely simplify the models' complexity, and possibly reduce the computation time. 4. The developed time-space network is consistent with scaling units both in temporal and spatial dimensions. 5. The proposed nested diagonalization method takes care of two types of link interactions, i.e., actual link travel times, and inflows other than that on the subject time-space link. 6. 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