An Equivalent Non-uniform Beam-like Model for Dynamic Analysis of Multi-storey Irregular Buildings

Dynamic analyses and seismic assessments of multi-storey buildings at urban level require large-scale simulations and computational procedures based on simplified but accurate numerical models. At this aim the present paper propos-es an equivalent non-uniform beam-like model, suitable for the dynamic analysis of buildings with asymmetric plan and non-uniform vertical distribution of mass and stiffness. The equations of motion of this beam-like model, which pre-sents only shear and torsional deformability, are derived through the application of Hamilton’s principle. The linear dy-namic behaviour is evaluated by discretizing the continuous non-uniform model according to a Rayleigh-Ritz approach based on a suitable number of modal shapes of the uniform shear-torsional beam. In spite of its simplicity, the model is able to reproduce the dynamic behaviour of low- and mid-rise buildings with a significant reduction of the computa-tional burden with respect to that required by more general models. The efficacy of the proposed approach has been tested, by means of comparisons with linear FEM simulations, on three multi-storey buildings characterized by different irregularities. The satisfactory agreement, in terms of natural frequencies, modes of vibration and seismic response, proves the capability of the proposed approach to reproduce the dynamic response of complex spatial multi storey frames.

A Miniature Resonant and Torsional Magnetometer Based on Lorentz Force

A microelectromechanical system (MEMS) torsional resonant magnetometer based on Lorentz force was investigated, consisting of torsional structures, torsional beams, metal plates, a coil, and a glass substrate. The Lorentz force, introduced by the interaction between the current in the MEMS coil and an external horizontal magnetic field, leads to displacement of the torsional structure. The strength of the magnetic field is proportional to this displacement, and can be detected with two sensing capacitors fabricated on the torsion structure and the substrate. To improve sensor sensitivity, a folded torsional beam and a double-layer excitation coil were introduced. The fabrication processes included lift-off, anodic bonding, chemical mechanical planarization, silicon nitride (SiNx) deposition, plasma-enhanced chemical vapor deposition, and inductively coupled plasma release. The prototype of the magnetometer was finished and packaged. The sensor performance, including its sensitivity and repeatability, was tested in a low-pressure environment. Additionally, the influences of structural parameters were analyzed, including the resistance of the excitation coil, the initial value of the capacitors, the elastic coefficient of the torsional beam, and the number of layers in the excitation coil. The test results demonstrated that this sensor could meet the requirements for attitude determination systems in low earth orbit satellites.

Gravity-Insensitive Flexure Pivot Oscillators

Classical mechanical watch plain bearing pivots have frictional losses limiting the quality factor of the hairspring-balance wheel oscillator. Replacement by flexure pivots leads to a drastic reduction in friction and an order of magnitude increase in quality factor. However, flexure pivots have drawbacks including gravity sensitivity, nonlinearity, and limited stroke. This paper analyzes these issues in the case of the cross-spring flexure pivot (CSFP) and presents an improved version addressing them. We first show that the cross-spring pivot cannot be simultaneously linear, insensitive to gravity, and have a long stroke: the 10 ppm accuracy required for mechanical watches holds independently of orientation with respect to gravity only when the leaf springs cross at 12.7% of their length. But in this case, the pivot is nonlinear and the stroke is only 30% of the symmetrical (50% crossing) cross-spring pivot's stroke. The symmetrical pivot is also unsatisfactory as its gravity sensitivity is of order 104 ppm. This paper introduces the codifferential concept which we show is gravity-insensitive. It is used to construct a gravity-insensitive flexure pivot (GIFP) consisting of a main rigid body, two codifferentials, and a torsional beam. We show that this novel pivot achieves linearity or the maximum stroke of symmetrical pivots while retaining gravity insensitivity.

Damping of Torsional Beam Vibrations by Control of Warping Displacement

Supplemental damping of torsional beam vibrations is considered by viscous bimoments acting on the axial warping displacement at the beam supports. The concept is illustrated by solving the governing eigenvalue problem for various support configurations with the applied bimoments represented as viscous boundary conditions. It is demonstrated that properly calibrated viscous bimoments introduce a significant level of supplemental damping to the targeted vibration mode and that the attainable damping can be accurately estimated from the two undamped problems associated with vanishing and infinite viscous parameters, respectively.