Existence and uniqueness of solutions for singular fourth-order boundary value problems

AbstractBy mixed monotone method, the existence and uniqueness are established for singular fourth-order boundary value problems. The theorems obtained are very general and complement previous known results

Simultaneous Optimization of Road Tolls and Tradable Credits in Public-private Mixed Networks

This paper investigates a hybrid management policy of road tolls and tradable credits in mixed road networks with both public and private roads. In the public sub-network, a tradable credit scheme is applied to mitigate traffic congestion. In the private sub-network, tolls are collected by the private company, but the toll levels and toll locations are determined by the government. The purpose of toll charge is two-fold: on the one hand, the government uses it as a tool for mitigating congestion; on the other hand, a threshold of revenue should be guaranteed for the profitability of the private company. A bi-level programming model is formulated to minimize the total travel time in the network by taking into account the user equilibrium travel behaviour and the revenue requirement of private firms. To obtain a  global optimum solution, the bi-level model is transformed into an equivalent single-level mixed integer linear program that can be easily solved with commercial software. Numerical examples are provided to demonstrate the effectiveness of the developed model and the efficiency of the proposed algorithm. It is shown that the mixed management schemes can achieve favourable targets, namely, joint implementation of road tolls and tradable credits can effectively mitigate traffic congestion and meanwhile maintain reasonable revenue for the private company.</p

Advanced high performance vertical hybrid synthetic jet actuator

The present invention comprises a high performance, vertical, zero-net mass-flux, synthetic jet actuator for active control of viscous, separated flow on subsonic and supersonic vehicles. The present invention is a vertical piezoelectric hybrid zero-net mass-flux actuator, in which all the walls of the chamber are electrically controlled synergistically to reduce or enlarge the volume of the synthetic jet actuator chamber in three dimensions simultaneously and to reduce or enlarge the diameter of orifice of the synthetic jet actuator simultaneously with the reduction or enlargement of the volume of the chamber. The jet velocity and mass flow rate for the present invention will be several times higher than conventional piezoelectric synthetic jet actuators

Advanced high performance horizontal piezoelectric hybrid synthetic jet actuator

The present invention comprises a high performance, horizontal, zero-net mass-flux, synthetic jet actuator for active control of viscous, separated flow on subsonic and supersonic vehicles. The present invention is a horizontal piezoelectric hybrid zero-net mass-flux actuator, in which all the walls of the chamber are electrically controlled synergistically to reduce or enlarge the volume of the synthetic jet actuator chamber in three dimensions simultaneously and to reduce or enlarge the diameter of orifice of the synthetic jet actuator simultaneously with the reduction or enlargement of the volume of the chamber. The present invention is capable of installation in the wing surface as well as embedding in the wetted surfaces of a supersonic inlet. The jet velocity and mass flow rate for the SJA-H will be several times higher than conventional piezoelectric actuators

Cryogenic Piezoelectric Actuator

In this paper, PMN-PT single crystal piezoelectric stack actuators and flextensional actuators were designed, prototyped and characterized for space optics applications. Single crystal stack actuators with footprint of 10 mm x10 mm and the height of 50 mm were assembled using 10 mm x10mm x0.15mm PMN-PT plates. These actuators showed stroke > 65 - 85 microns at 150 V at room temperature, and > 30 microns stroke at 77 K. Flextensional actuators with dimension of 10mm x 5 mm x 7.6 mm showed stroke of >50 microns at room temperature at driving voltage of 150 V. A flextensional stack actuator with dimension of 10 mm x 5 mm x 47 mm showed stroke of approx. 285 microns at 150 V at room temperature and > 100 microns at 77K under driving of 150 V should be expected. The large cryogenic stroke and high precision of these actuators are promising for cryogenic optics applications

Advanced Modified High Performance Synthetic Jet Actuator with Curved Chamber

The advanced modified high performance synthetic jet actuator with optimized curvature shape chamber (ASJA-M) is a synthetic jet actuator (SJA) with a lower volume reservoir or chamber. A curved chamber is used, instead of the conventional cylinder chamber, to reduce the dead volume of the jet chamber and increase the efficiency of the synthetic jet actuator. The shape of the curvature corresponds to the maximum displacement (deformation) profile of the electroactive diaphragm. The jet velocity and mass flow rate for the ASJA-M will be several times higher than conventional piezoelectric actuators

Full Piezoelectric Multilayer-Stacked Hybrid Actuation/Transduction Systems

The Stacked HYBATS (Hybrid Actuation/Transduction system) demonstrates significantly enhanced electromechanical performance by using the cooperative contributions of the electromechanical responses of multilayer, stacked negative strain components and positive strain components. Both experimental and theoretical studies indicate that, for Stacked HYBATS, the displacement is over three times that of a same-sized conventional flextensional actuator/transducer. The coupled resonance mode between positive strain and negative strain components of Stacked HYBATS is much stronger than the resonance of a single element actuation only when the effective lengths of the two kinds of elements match each other. Compared with the previously invented hybrid actuation system (HYBAS), the multilayer Stacked HYBATS can be designed to provide high mechanical load capability, low voltage driving, and a highly effective piezoelectric constant. The negative strain component will contract, and the positive strain component will expand in the length directions when an electric field is applied on the device. The interaction between the two elements makes an enhanced motion along the Z direction for Stacked-HYBATS. In order to dominate the dynamic length of Stacked-HYBATS by the negative strain component, the area of the cross-section for the negative strain component will be much larger than the total cross-section areas of the two positive strain components. The transverse strain is negative and longitudinal strain positive in inorganic materials, such as ceramics/single crystals. Different piezoelectric multilayer stack configurations can make a piezoelectric ceramic/single-crystal multilayer stack exhibit negative strain or positive strain at a certain direction without increasing the applied voltage. The difference of this innovation from the HYBAS is that all the elements can be made from one-of-a-kind materials. Stacked HYBATS can provide an extremely effective piezoelectric constant at both resonance and off resonance frequencies. The effective piezoelectric constant can be alternated by varying the size of each component, the degree of the pre-curvature of the positive strain components, the thickness of each layer in the multilayer stacks, and the piezoelectric constant of the material used. Because all of the elements are piezoelectric components, Stacked HYBATS can serve as projector and receiver for underwater detection. The performance of this innovation can be enhanced by improving the piezoelectric properties

Vibration Analysis of a Unimorph Nanobeam with a Dielectric Layer of Both Flexoelectricity and Piezoelectricity

In this study, for the first time, free and forced vibrational responses of a unimorph nanobeam consisting of a functionally graded base, along with a dielectric layer of both piezoelectricity and flexoelectricity, is investigated based on paradox-free local/nonlocal elasticity. The formulation and boundary conditions are attained by utilizing the energy method Hamilton’s principle. In order to set a comparison, the formulation of a model in the framework of differential nonlocal is first presented. An effective implementation of the generalized differential quadrature method (GDQM) is then utilized to solve higher-order partial differential equations. This method can be utilized to solve the complex equations whose analytic results are quite difficult to obtain. Lastly, the impact of various parameters is studied to characterize the vibrational behavior of the system. Additionally, the major impact of flexoelectricity compared to piezoelectricity on a small scale is exhibited. The results show that small-scale flexoelectricity, rather than piezoelectricity, is dominant in electromechanical coupling. One of the results that can be mentioned is that the beams with higher nonlocality have the higher voltage and displacement under the same excitation amplitude. The findings can be helpful for further theoretical as well as experimental studies in which dielectric material is used in smart structures

Hybrid Electrostatic/Flextensional Mirror for Lightweight, Large-Aperture, and Cryogenic Space Telescopes

A lightweight, cryogenically capable, scalable, deformable mirror has been developed for space telescopes. This innovation makes use of polymer-based membrane mirror technology to enable large-aperture mirrors that can be easily launched and deployed. The key component of this innovation is a lightweight, large-stroke, cryogenic actuator array that combines the high degree of mirror figure control needed with a large actuator influence function. The latter aspect of the innovation allows membrane mirror figure correction with a relatively low actuator density, preserving the lightweight attributes of the system. The principal components of this technology are lightweight, low-profile, high-stroke, cryogenic-capable piezoelectric actuators based on PMN-PT (piezoelectric lead magnesium niobate-lead titanate) single-crystal configured in a flextensional actuator format; high-quality, low-thermal-expansion polymer membrane mirror materials developed by NeXolve; and electrostatic coupling between the membrane mirror and the piezoelectric actuator assembly to minimize problems such as actuator print-through