Consistent DOF reduction of tall steel frames

This paper presents an energy‐consistent approach for reducing the number of degrees‐of‐freedom (DOFs) in tall steel frames. In the present approach, the moment resistance of beams and columns in each story is represented by the moment resistance of a rotational spring and a beam‐column element, respectively. The shear resistance provided by braces in each story is represented by the shear resistance of a shear spring. Furthermore, the resistance to the overturning moment provided by axial resistance of columns in each story is represented by the moment resistance of a rotational spring. These representations are carried out by achieving the equivalence between the strain energy stored and dissipated in the elements in the full (unreduced) DOF models and the strain energy stored and dissipated in the corresponding elements in the reduced DOF models. The accuracy of the present approach is demonstrated through numerical examples, which compare the results of nonlinear time history analyses obtained using the full and reduced DOF models. In the numerical examples, the response is estimated for 20‐story and 40‐story steel frames with and without buckling‐restraint braces subjected to a suite of near‐fault and far‐fault ground motions. The present approach is useful in estimating the response of tall steel frames having non‐regular member arrangements to a suite of intense ground motions including near‐fault ones, where it is crucial to capture the influence of higher mode effects on collapse mechanisms. Copyright © 2017 John Wiley & Sons, Ltd.     

Adjustable vertical vibration isolator with a variable ellipse curve mechanism

This paper presents a passive vertical quasi‐zero‐stiffness vibration isolator intended for relatively small objects. The present isolator has features of compactness, long stroke, and adjustability to various load capabilities. To realize these features, we use constant‐force springs, which sustain constant load regardless of their elongation, and propose a variable ellipse curve mechanism that is inspired by the principle of ellipsographs. The variable ellipse curve mechanism can convert the restoring force of the horizontally placed constant‐force springs to the vertical restoring force of the vibration isolator. At the same time as converting the direction, the vertical restoring force can be adjusted by changing the ratio of the semi‐minor axis to the semi‐major one of the ellipse. In this study, a prototype of a class of quasi‐zero‐stiffness vibration isolator with the proposed variable ellipse curve mechanism is created. Shaking table tests are performed to demonstrate the efficacy of the present mechanism, where the prototype is subjected to various sinusoidal and earthquake ground motions. It is demonstrated through the shaking table tests that the prototype can reduce the response acceleration within the same specified tolerance even when the mass of the vibration isolated object is changed. Copyright © 2017 John Wiley & Sons, Ltd.     

A derivation of the scaling law, the power law and the scaling relation for fetch-limited wind waves using the renormalization group theory

A state of wind waves at a fetch is assumed to be transformed into another state of wind waves at a different fetch by the renormalization group transformation. The scaling laws for the covariance of water surface displacement and for the one-dimensional and two-dimensional spectrum and the power law for the growth relation are derived from the fact that the renormalization group transformation constitutes a semigroup. The scaling relation or the relation among the exponents of the power law is also derived, using the two assumptions that the renormalization group transformation is applicable to fetch-limited wind waves and that the saturated range exists, which implies that the directional distribution function of energy in the wave number region much larger than the peak wave number does not depend on wave number.     

A New Empirical Formula for the Aerodynamic Roughness of Water Surface Waves

A new empirical formula for the aerodynamic roughness of water surface waves has been derived from laboratory experimental results using dimensional analysis. The formula has different forms according to wind speed: at moderate wind speeds the formula is a function of the friction velocity of wind, the surface tension, the water density, the kinematic viscosity of water and the acceleration of gravity; at strong winds the formula is expressed by the Charnock relation. The aerodynamic roughness does not depend on such wave state parameters as the spectral peak frequency or the steepness of waves, unlike almost all parameterizations that have been proposed to date. The drag coefficient at moderate winds depends on the surface tension of water and the water temperature through the temperature dependence of the kinematic viscosity of water.