A tutorial on a multi-mode identification procedure based on the complex-curve fitting method

Modal identification is a key step in modal analysis. It enables the researcher to extract modal parameters, such as natural frequency, amplitude, and damping from a given structure. There are a considerable number of techniques in the state of the art aiming to address this problem, where multi-mode approaches arise as an appealing choice due to their ability to deal with mode coupling. This tutorial paper focuses on the complex-curve fitting technique, originally conceived for an application distinct from modal analysis. It aims at guiding other researchers by providing a tutorial-like and in-depth analysis of this important method, associated with a nonlinear weighting procedure for improved precision. Additionally, this paper fills a gap on the original technique, which is limited to the ratio of two polynomials, by proposing an automatic parameter extraction technique. The original and improved methods are applied on both simulated and experimental data, highlighting the effectiveness of the proposed changes. The proposed procedure is also compared with the rational fraction polynomial method.

Neuraxial analgesia interfered with the circadian rhythm of labor: a propensity score matched cohort study

Objectives To investigate whether neuraxial analgesia and other medical interventions have effects on the circadian rhythm of labor. Methods It was a retrospective propensity score matched cohort study. Parturients were recruited, who delivered term singletons in cephalic position, from seven hospitals in Harvard University Partners Healthcare Systems, 2016–2018. The parturients were divided into two groups, neuraxial analgesia delivery and spontaneous vaginal delivery, the stratification was performed according to labor induction, oxytocin, operative delivery. The parturients in each group were divided into 12 periods in every 2 h based on the birth time of babies. Cosine function fitting was used to verify whether the birth time had the characteristic of circadian rhythm. Results In spontaneous vaginal deliveries, the peak of birth time was at 2:00–4:00, and the nadir was at 14:00–16:00, this showed a circadian rhythm presented by a cosine curve fitting with the formula (y = 0.0847 + 0.01711 × cos(− 0.2138 × x + 0.4471). The labor rhythm of NAD (Neuraxial Analgesia Delivery) group changed completely, inconsistent with the cosine curve fitting of the circadian rhythm. The intervention of induction and oxytocin blurred the circadian rhythm of SVD (Spontaneous Vaginal Delivery) group and increased the amplitude of the fluctuation in NAD (Neuraxial Analgesia Delivery) group. The intervention of operative delivery had changed the distribution curve completely both in the SVD (Spontaneous Vaginal Delivery) group and the NAD (Neuraxial Analgesia Delivery) group. Conclusions Neuraxial analgesia did affect on circadian rhythm of labor, changed the cosine rhythm of labor with spontaneous vaginal delivery, and this trend was aggravated by the use of induction, oxytocin and operative delivery.

Research on the law of reflection coefficient of reflective film of traffic sign based on Angle

In this paper, a large number of digital printing reflective film retroreflectivity measurement. Based on the multi-angle test of the reflective film of the mainstream manufacturers in the market, the reverse reflection coefficient of the digital printing reflective film was obtained. Through the curve fitting of the measured values of the backreflection coefficient under different measuring angles by using the scatter plot, the variation law of the luminosity of the digital printing reflective film with incident Angle and observation Angle was obtained. The variation law of backreflection coefficient explored in this paper has certain significance to the application guidance of digital printing reflective film for traffic signs.

Modelling lead-rubber seismic isolation bearings using the unified mechanics theory

Lead-rubber seismic isolation bearings (LRB) have been installed in a number of essential and critical structures, like hospitals, universities and bridges, in order to provide them with period lengthening and the capacity of dissipating a considerable amount of energy to mitigate the effects of strong ground motions. Therefore, studying the damage mechanics of this kind of devices is fundamental to understand and accurately describe their thermo-mechanical behavior, so that seismically isolated structures can be designed more safely. Hitherto, the hysteretic behavior of LRB has been modeled using 1) Newtonian mechanics and empirical curve fitting degradation functions, or 2) heat conduction theories and idealized bilinear curves which include degradation effects. The reason for using models that are essentially phenomenological or that contain some adjusted parameters is the fact that Newton’s universal laws of motion lack the term to account for degradation and energy loss of a system. In this paper, the Unified Mechanics Theory – which integrates laws of Thermodynamics and Newtonian mechanics – is used to model the force-displacement response of LRB. Indeed, there is no need for curve fitting techniques to describe their damage behavior because degradation is calculated at every point using entropy generation along the Thermodynamics State Index (TSI) axis. A finite element model of a lead-rubber bearing was constructed in ABAQUS, where a user material subroutine UMAT was implemented to define the Unified Mechanics Theory equations and the viscoplastic constitutive model for lead. Finite element analysis results were compared with experimental test data.

Prediction of System Parameters of Carbon-Based Composite Structure for Different Carbon Fiber Orientations with Mode Information at Reference Angle Only

The prediction of system parameters is important for understanding the dynamic behavior of composite structures or selecting the configuration of laminated carbon in carbon-based composite (CBC) structures. The dynamic nature of CBC structures allows the representation of system parameters as modal parameters in the frequency domain, where all modal parameters depend on the carbon fiber orientations. In this study, the variation in the system parameters of a carbon fiber was derived from equivalent modal parameters, and the system parameters at a certain carbon fiber orientation were predicted using the modal information at the reference carbon fiber orientation only and a representative curve-fitted function. The target CBC structure was selected as a simple rectangular structure with five different carbon fiber orientations, and the modal parameters were formulated based on a previous study for all modes. Second-order curve-fitted polynomial functions were derived for all possible cases, and representative curve-fitting functions were derived by averaging the polynomial coefficients. The two system parameters were successfully predicted using the representative curve-fitting function and the modal information at only the reference carbon fiber orientation, and the feasibility of parameter prediction was discussed based on an analysis of the error between the measured and predicted parameters.