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Passive energy dissipation systems are one of the most resilient solutions to mitigate the seismic risk of structures. In case of strong motions, they can confine the eventual damages into easily replaceable anti-seismic devices. The performance characteristics of nonlinear displacement dependent devices (NLD) shall be defined by the force-displacement cyclic behavior, as well as the expected number of cycles related to both the duration of the earthquake and to the fundamental frequency of the structural systems. The aims of this paper are the comparison between the dynamic results of two different experimental campaigns performed on NLDs included in dissipative bracing systems and the assessment of the reliability of quasi-static testing procedures proposed by current seismic codes for type tests and factory production control tests. The number of cycles under the design earthquake of hysteretic dampers were experimentally evaluated through shaking table testing. Two experimental case studies of a two-story steel frame and of a three-story post-tensioned timber frame both with bracing systems including flexural steel dampers, hysteretic dampers (HDs), and U-shaped flexural plates (UFPs) respectively, were analyzed. Controlled-displacement tests of NLDs were performed considering quasi-static loading procedures specified by codes. Shaking table tests were carried out considering almost the same seismic sequence composed by a set of seven natural earthquakes at increasing peak ground acceleration (PGA) levels. More than one hundred inelastic cycles were experimentally recorded from dynamic tests before the failure of devices in both cases. In line with American standards testing requirements, the number of cycles at the design PGA level, estimated from shaking table tests and from non-linear dynamic analyses, shows a decreasing trend with the increase of ductility demand.

This paper discusses the effect of inductive coil shape on the sensing performance of a linear displacement sensor. The linear displacement sensor consists of a thin type inductive coil with a thin pattern guide, thus being suitable for tiny space applications. The position can be detected by measuring the inductance of the inductive coil. At each position due to the change in inductive coil area facing the pattern guide the value of inductance is different. Therefore, the objective of this research is to study various inductive coil pattern shapes and to propose the pattern that can achieve good sensing performance. Various shapes of meander, triangular type meander, square and circle shape with different turn number of inductive coils are examined in this study. The inductance is measured with the sensor sensitivity and linearity as a performance evaluation parameter of the sensor. In conclusion, each inductive coil shape has its own advantages and disadvantages. For instance, the circle shape inductive coil produces high sensitivity with a low linearity response. Meanwhile, the square shape inductive coil has a medium sensitivity with higher linearity.

We developed an optoelectronic sensor capable of quantifying in-plane rotational and linear displacements between two parallel surfaces. The sensor utilizes a photo detector to capture the intensity of red (R), green (G), blue (B), and clear (C, broad visible spectrum) light reflected from a color gradient wheel on the opposing surface. Variations in reflected R, G, B and C light intensities, caused by displacements, were used to predict linear and rotational motion via a polynomial regression algorithm. To train and validate this model, we employed a custom-built positioning stage that produced controlled displacement and rotation while recording corresponding changes in light intensity. The reliability of the predicted linear and rotational displacement results was evaluated using two different color gradient wheels: a wheel with changing color hue, and another wheel with changing color hue and saturation. Benchtop experiments demonstrated high predictive accuracy, with coefficients of determination (R2) exceeding 0.94 for the hue-only wheel and 0.92 for the hue-and-saturation wheel. These results highlight the sensor’s potential for detecting shear displacement and rotation in footwear and wearable medical devices, such as orthotics and prostheses, enabling the detection of slippage, overfitting, or underfitting. This capability is particularly relevant to clinical conditions, including diabetic neuropathy, flat feet, and limb amputations.

In order to satisfy the measurement of objects in compact settings, a miniaturized linear inductive encoder with a measurement range of 15 mm is investigated in this paper. The encoder structure integrates a movable part with conductive plates and a stationary part with planar excitation and inductive coils. When a high-frequency alternating current is applied to the excitation coils, a time-varying magnetic field will be generated. Meanwhile, the conductive plates on the movable element will produce an eddy current magnetic field to reduce or boost the magnetic field. As the movable part moves, two-channel amplitude-modulated electrical signals whose amplitudes vary with displacement are obtained. The CORDIC algorithm is utilized to calculate the displacement. The paper describes the structure and working principle of the encoder, presents corresponding finite element simulations of the magnetic field, and introduces a prototype fabricated by PCB technology. Experiments evaluating stability, resolution, and accuracy show that the encoder reaches the measurement accuracy of 12.8 μm within one pitch, and the resolution is 0.7 μm. Importantly, its minimal dimensions (20 mm × 10 mm × 1 mm) enable installation in highly constrained mechanisms.

This paper presents a method to improve the alignment accuracy of a mask in linear scale projection lithography, in which the adjacent pixel gray square variance method is applied to a charge-coupled device (CCD) image to obtain the best position of the focal length of the motherboard and then realize the alignment of the focal plane. Two image positions in the focal plane of the CCD are compared with the traits overlap according to the image splicing principle, and four typical errors are corrected on the basis of the total grating errors. Simultaneously, the rotation error of the mask is used to summarize the grayscale variation function of the CCD image. Threshold functions are employed to express the factors including the wave crests of the amplitude, period error, and phase error, which govern the rotation accuracy and weight alignment accuracy expression of the established four error factors. Finally, in the experiment, the slope of the mask is corrected and adjusted to the same direction as the slide plate with the assistance of a dual-frequency laser interferometer. The effect of the alignment error on the lithography accuracy is discussed and verified in the static case, and it is found that the CCD maximum resolution pixel is 0.1 μm and accuracy of the scale is 0.79 μm in only a 200-mm-measurement range.

In interferential linear displacement sensors, accurate information about the position of the reading head is calculated out of a pair of quadrature (sine and cosine) signals. In double grating interference schemes, diffraction gratings combine the function of beam splitters and phase retardation devices. Specifically, the reference diffraction grating is located in the reading head and regulates the phase shifts in diffraction orders. Measurement diffraction grating moves along with the object and provides correspondence to the displacement coordinate. To stabilize the phase imbalance in the output quadrature signals of the sensor, we propose to calculate and optimize the parameters of these gratings, based not only on the energetic analysis, but along with phase relationships in diffraction orders. The optimization method is based on rigorous coupled-wave analysis simulation of the phase shifts of light in diffraction orders in the optical system. The phase properties of the reference diffraction grating in the interferential sensor are studied. It is confirmed that the possibility of quadrature modulation depends on parameters of static reference scale. The implemented optimization criteria are formulated in accordance with the signal generation process in the optical branch. Phase imbalance and amplification coefficients are derived from Heydemann elliptic correction and expressed through the diffraction efficiencies and phase retardations of the reference scale. The phase imbalance of the obtained quadrature signals is estimated in ellipticity correction terms depending on the uncertainties of influencing parameters.

The quality of processed workpieces is affected directly by the precision of the linear stage. Therefore, the linear displacement calibration of machine tools must be implemented before delivery and after employment for a period of time. How to perform a precise calibration with high inspection efficiency is a critical issue in the precision mechanical engineering industry. In this study, the self-developed system integrated by the measurement module based on the common path Fabry–Pérot interferometer for linear displacement and the auto-alignment module for optical axes was proposed to realize the automatic linear displacement calibration of the linear stages. The measurement performance of the developed structure was verified experimentally. With the auto-alignment module, the cosine error was reduced to 0.36 nm and the entire procedure accomplished within 75 s without the limitation of the perceived resolution of the human eye, operational experience, and the risk of misalignment and broken cable. According to the comparison of experimental results for the linear displacement, the repeatability of the proposed measurement module was less than 0.171 μm. After the compensation procedure according to the linear displacement calibration, the systematic positional deviation, repeatability, and accuracy of the linear axis could be improved to 4 μm, 1 μm, and 5 μm respectively. Hence, the calibration efficiency can be improved by 80% with the proposed compact system, which is beneficial for the linear displacement calibration of machine tools in the precision mechanical engineering industry.

This paper presents and validates a novel approach to designing an active controller for a small-scale experimental structure subjected to the action of multiple moving loads. Many of the numerically validated active control methods presented in the literature assume that the synthesised control solution can be applied directly to the structure. When a real structure is investigated, the closed-loop stability and performance of the system are affected by the actuators’ dynamics and by the signal-to-noise ratio. In some cases when the structure is complex, the model used for the structure can have controllability and observability problems. In this study, an active control solution is designed using a simplified model, and then, it is experimentally validated. The control voltage dependent on the measured displacement signals is fed back to the structure via electrodynamic actuators. The objective of the control is to reduce the structure’s deflection under the action of the loads at sensors’ locations. Numerical and experimental results prove that using linear or cubic displacement feedback control the vibration amplitudes can be significantly reduced. The controller can tolerate speed variations, but it always needs to include compensation in order to increase the stability margins of the controlled system. The linear displacement feedback has a better performance at low values of the deflection, whereas the cubic displacement feedback shows a better robustness performance at high values of moving masses and speed variations.

Rotational Risley prisms are one of the fastest two-dimensional (2D) optomechanical scanning systems. Their drawback is the strong non-linearity of the scan patterns they produce, in contrast to the most common (but slower) raster scanning modalities of 2D dual axis galvanometer scanners (GSs) or Micro-Electro-Mechanical Systems (MEMS) with oscillatory mirrors. The aim of this work is to develop a graphical method, which, to our knowledge, we have introduced to determine and characterize, using a commercially-available mechanical design program (for example CATIA V5R20 (Dassault Systems, Paris, France)) to simulate the exact scan patterns of rotational Risley prisms. Both the maximum and minimum angular and linear deviations of this type of scanner are deduced theoretically to characterize the outer diameter/Field-of-View (FOV) and the inner diameter (of the blind zone) of its ring-shaped patterns, respectively. This multi-parameter analysis is performed in correlation with the shape of the scan patterns, considering the four possible configurations of laser scanners with a pair of rotational Risley prisms, as well as all their parameters: prisms angles, refractive indexes, rotational speeds, distance between the two prisms, and the distance from the system to the scanned plane. Marshall’s synthetic parameters are also considered, i.e., the ratios of the rotational velocities and of the angles of the prisms. Rules-of-thumb for designing this optomechanical scanner are extracted from this analysis, regarding both shapes and dimensions of the scan patterns to be produced. An example of experimental validation completes the mathematical analysis and the performed simulations.

In spite of the gradual development of three-dimensional analysis packages utilizing finite element models or finite difference algorithms for stress–strain calculations, two-dimensional (2D) analysis is still used as the primary engineering tool for practical analysis of tunnel behavior and tunnel support performance for design—particularly at the preliminary stage of a project. The applicability of 2D finite element analysis or analytical convergence confinement solutions to staged support installation depend on the application of an assumed or validated longitudinal displacement profile. Convergence in commonly applied 2D staged models is controlled by boundary displacement or internal pressure relaxation. While there have been developments to improve this methodology, this often assumes independence between the ground reaction curve and the support resistance, independence between the longitudinal displacement profile to support application, and the assumption that non-isotropic stresses and non-circular geometries can be handled in the same way as circular tunnels in isotropic conditions. This paper examines the validity of these assumptions and the error inherent in these extensions to 2D tunnel analysis. Anisotropic stresses and lagged (staged) excavation present a particular problem. Practical solutions are proposed for support longitudinal displacement LDPs in simplified conditions.