Under a zero-mean, broad-band, stationary-random load, the symmetric elastic perfectly plastic oscillator and many similar hysteretic systems exhibit a Brownian-like displacement response: asymptotically, the displacement mean vanishes and the displacement variance linearly increases with time. This diverging behavior, often referred to as the drift, is observed even when the excitation power spectrum vanishes at zero frequency, an instance so far lacking a satisfactory modeling within the framework of statistical linearization. The paper presents a linearization-based method which captures the drift in such an instance without requiring any simulation-calibrated parameter. The method combines statistical linearization with stochastic averaging and a generalized van der Pol transformation comprising terms introduced to make allowance for the drift. Model predictions are compared with Monte Carlo estimates for an excitation whose power spectrum vanishes at zero frequency. Good agreement is found for a wide range of excitation levels despite the extremeness of the non-linearity. 相似文献
Expressions for thermodynamic potentials (internal energy, Helmholtz energy, Gibbs energy and enthalpy) of a thermoelastic material are developed under the assumption of small strains and finite changes in the thermal variable (temperature or entropy). The literature provides expressions for the Helmholtz energy in terms of strain and temperature, most often as expansions to the second order in strain and to a higher order in temperature changes, which ensures an affine stress–strain relation and a certain temperature dependence of the moduli of the material. Expressions are here developed for the four potentials in terms of all four possible pairs of independent variables. First, an expression is obtained for each potential as a quadratic function of its natural mechanical variable with coefficients depending on its natural thermal variable that are identified in terms of the moduli of the material. The form of the coefficients’ dependence on the thermal variable is not specified beforehand so as to obtain the most general expressions compatible with an affine stress–strain relation. Then, from each potential expressed in terms of its natural variables, expressions are derived for the other three potentials in terms of these same variables using the Gibbs–Helmholtz equations. The paper provides a thermodynamic framework for the constitutive modeling of thermoelastic materials undergoing small strains but finite changes in the thermal variables, the properties of which are liable to depend on the thermal variables. 相似文献
Micro-moulding is a critical rapid prototyping process chain used for a wide range of applications. This study demonstrates that it is possible to manufacture mould at low excitation frequency plasma (380 kHz), on a silicon substrate using fluorinated chemistry. According to the mask aperture designed and process time, the cavities profile characteristics, depending on the plasma chemistry, were analysed to predict the degree of anisotropy and the curvature. We show the possibility of creating curvature shapes with a desirable conic constant k of 1.25. In particular, we highlighted the smallest aperture sizes are more attractive for replicating optical micro-lens arrays using silicon moulds. Otherwise, the largest aperture sizes gain more attention for optoelectronics, microsystems, and microfluidics applications. 相似文献
Density functional theory method, at the B3LYP/6–311+G(d, p) level has been used to explore the geometries, relative energies, and electronic properties of all hypothetically possible prototropic tautomers of imexon. The specific interactions of the tautomeric forms of imexon with one and two solvating water molecules have been investigated. The relative stability order of the complexes remains unchanged upon interaction with one water molecule. The addition of a second water molecule, however, stabilizes the oxo-amino form more than the oxo-imino structure. The bulk water environment has been simulated by a combination of microhydration and the conductor-like polarizable continuum model. The energy profile corresponding to the prototopic tautomerisms connecting oxo-imino form with oxo-amino, hydroxyl-amino, and one rare tautomer has been studied. We found that the tautomerism activation barriers are high enough as to conclude that only the oxo-imino tautomer should be found in the gas phase. Our results present clear evidence that microhydration with one and two solvating water molecules considerably lower these barriers by a concerted multiple proton transfer mechanism.