This research introduces a methodology for data-driven regression modeling of components exhibiting nonlinear characteristics, utilizing the sparse identification of nonlinear dynamics (SINDy) method. The SINDy method is extended to formulate regression models for interconnecting components with nonlinear traits, yielding governing equations with physically interpretable solutions. The proposed methodology focuses on extracting a model that balances accuracy and sparsity among various regression models. In this process, a comprehensive model was generated using linear term weights and an error histogram. The applicability of the proposed approach is demonstrated through a case study involving a sponge gasket with nonlinear characteristics. By contrasting the predictive model with experimental responses, the reliability of the methodology is verified. The results highlight that the regression model, based on the proposed technique, can effectively establish an accurate dynamical system model, accounting for realistic conditions.

OBJECTIVE: It is known that long-term stress leads to trauma and very often to depression. Usually, the diagnosis of depression is dealt with by psychiatrists who, based on conversations and questions, diagnose the patient\'s illness and condition. Unfortunately, this diagnosis is not always reliable. To prevent the development of disease, it is necessary to detect illness in a timely manner. One of the indications of the possibility of the onset of disease is a disturbance in the level of hormones in the body, especially cortisol. The purpose of this study was to develop a mathematical model for cortisol variation resulting from stress which would be useful in making conclusions about depressive states.
METHODS: Rapid changes in cortisol concentration, according to ultradian rhythms, which are much faster than the daily circadian rhythm, is modelled as a truly nonlinear oscillator. The mathematical model contains two coupled first order differential equations. The stress is modeled as a pulsating action, described with a periodic trigonometric function, and cortisol production as a cubic nonlinear one. Three models for cortisol variation are considered: 1) the pure nonlinear model, 2) the periodically excited system, 3) and the chaotic system. The results from the study are supported with experimental measurements.
RESULTS: Without stress, cortisol variation is of an oscillatory type with a constant steady-state amplitude. Intensive stress causes a resonant phenomenon in cortisol oscillatory variation. The occasion is short and is usually without consequences. For long stress periods deterministic chaos occurs which permanently changes the levels of cortisol. This phenomenon is an indicator of depression. Results from the suggested models are compared with experimentally obtained ones and good quantitative agreement is obtained.
CONCLUSIONS: The nonlinear oscillator is a good model for indication of depression. The model provides not only general conclusions, but also individual ones, if personal characteristics are taken into consideration. Response of the model depends not only on the input data related to stress, but also on the system parameters that specify each individual. Findings obtained from this study have implications for the medical diagnosis and treatment of depression.

In engineering, shafting systems are typically subjected to longitudinal vibration excitations, which may result in unwanted vibration. To study the control of longitudinal vibration in shafting systems, they can be simplified to rod structures. Currently, engineers have attempted to apply the nonlinear principle to design nonlinear supports to control the vibration of flexible structures. However, the flexible structures referenced in the literature are usually composed of a single component, which limits the application of nonlinear supports to more complex structures. To explore the potential application of nonlinear supports in marine engineering, this work introduces a longitudinal vibration prediction model for a double-rod system equipped with longitudinal nonlinear supports. The generalized Hamilton principle is used to derive the governing equations for the double-rod system with longitudinal nonlinear supports. The longitudinal vibration responses of the double-rod system are numerically solved using the Galerkin truncation method. The numerical results confirm that a 1-term truncation number guarantees the stability of the longitudinal vibration prediction model. Under certain conditions, the longitudinal vibration responses are significantly affected by longitudinal nonlinear supports. It is recommended to install longitudinal nonlinear supports on both Rod 1 and Rod 2 simultaneously to suppress vibration in the first two main resonance orders. With reasonable excitations, the vibration state and magnitudes of the double-rod system can be effectively controlled by adjusting the longitudinal nonlinear supports. Complex longitudinal vibration responses are more readily induced by altering the parameters of the longitudinal nonlinear support installed on Rod 1. Choosing appropriate parameters for the nonlinear supports on Rod 1 and Rod 2 positively contributes to the reduction of vibration in the double-rod system.

In this study, the coupled ordinary differential equations for the galloping of the first two modes in iced bundled conductors, including in-plane, out-of-plane, and torsional directions, are derived. Furthermore, through numerical analysis, the critical conditions of this modal galloping are determined in the range of wind speed-sag parameters, and the galloping patterns and variation laws in different parameter spaces are analyzed. The parameter space is then divided into five regions according to the different galloping modes. Under the multimodal coupling mechanism of galloping, the impact of single and two kinds of coupled mode galloping on the spatial nonlinear behavior is explored. The results reveal that the system exhibits an elliptical orbit motion during single mode galloping, while an \"8\" motion pattern emerges during coupled mode galloping. Moreover, two patterns of \"8\" motion are displayed under different parameter spaces. This research provides a theoretical foundation for the design of transmission lines.

BACKGROUND: Current voice assessments focus on perceptive evaluation and acoustic analysis. The interaction of vocal tract pressure (PVT) and vocal fold (VF) vibrations are important for volume and pitch control. However, there are currently little non-invasive ways to measure PVT. Limited information has been provided by previous human trials, and interactions between PVT and VF vibrations and the potential clinical application remain unclear. Here, we propose a non-invasive method for monitoring the nonlinear characteristics of PVT and VF vibrations, analyze voices from pathological and healthy individuals, and evaluate treatment efficacy.
METHODS: Healthy volunteers and patients with benign laryngeal lesions were recruited for this study. PVT was estimated using an airflow interruption method, VF vibrational frequency was calculated from accelerometer signals, and nonlinear relationships between PVT and VF vibrations were analyzed. Results from healthy volunteers and patients, as well as pre- and post-operation for the patients, were compared.
RESULTS: For healthy volunteers, nonlinearity was exhibited as an initial increase and then prompt decrease in vibrational frequency at the end of phonation, coinciding with PVT equilibrating with the subglottal pressure upon airflow interruption. For patients, nonlinearity was present throughout the phonation period pre-operatively, but showed a similar trend to healthy volunteers post-operatively.
CONCLUSIONS: This novel method simultaneously monitors PVT and VF vibration and helps clarify the role of PVT. The results demonstrate differences in nonlinear characteristics between healthy volunteers and patients, and pre-/post-operation in patients. The method may serve as an analysis tool for clinicians to assess pathological phonation and treatment efficacy.

Based on the dynamic characteristics of the axle box front cover of high-speed trains in the subharmonic resonance state, the nonlinear single-degree-of-freedom (SDOF) model was proved to be reasonable, and reasons for the ineffectiveness of the common prevention methods for preventing bolt failure were analyzed firstly. Then, dynamic stress of the bolt was simulated by innovatively adopting the linear method based on frequency response analysis. The stress simulation method was verified to be practical under the subharmonic resonance state by analyzing and comparing the experimental and numerical results of the bolted front cover. It was proved that the linear method was accurate enough to simulate the dynamic stress of bolts, which is of great engineering significance. In addition to the transverse resonance stress of bolts caused by drastic vertical vibration of the front cover, the tensile resonance stress at the root of the first engaged thread was too large to be neglected on account of the first-order bending modes of bolts. Next, equivalent stress amplitude of the multiaxial stresses was obtained by means of the octahedral shear stress criterion. Finally, fatigue life of bolts was predicted in terms of S-N curve suitable for bolt fatigue life analysis. It argued that the bolts were prone to multiaxial fatigue failure when the front cover was in subharmonic resonance for more than 26.8 h, and the fatigue life of bolts could be greatly improved when the wheel polygonization was eliminated by shortening the wheel reprofiling interval.

This study aims to enhance conventional vibration energy harvesting systems (VEHs) by repositioning the piezoelectric patch (PZT) in the middle of a fixed-fixed elastic steel sheet instead of the root, as is commonly the case. The system is subjected to an axial simple harmonic force at one end to induce transversal vibration and deformation. To further improve power conversion, a baffle is strategically installed at the point of maximum deflection, introducing a slapping force to augment electrical energy harvesting. Employing the theory of nonlinear beams, the equation of motion for this nonlinear elastic beam is derived, and the method of multiple scales (MOMS) is used to analyze the phenomenon of parametric excitation. This study demonstrates through experiments and theoretical analysis that the second mode yields better power generation benefits than the first mode. Additionally, the voltage generation benefits of the enhanced system with the added baffle (slapping force) surpass those of traditional VEH systems. Overall, the proposed model proves feasible and holds promising potential for efficient vibration energy harvesting applications in various industrial sectors.

Bells are made of bronze, an alloy of copper and tin. Art objects and musical instruments belong to tangible and intangible heritage. The effect of atmospheric alteration on their sound is not well documented. To address this question, alteration cycles of bronze specimens are performed in a chamber reproducing a realistic polluted coastal atmosphere. The corrosion layers are characterized by X-ray diffraction, electron microscopy and X-ray photoelectron spectrometry. The buried interface of the film (alloy-layer interface) is formed by a thin, adherent and micro-cracked layer, mainly composed of sulfates, copper oxide and chloride, on top of tin corrosion products. Near the atmosphere-film interface, less adherent irregular clusters of soot, calcite, gypsum and halite developed. Through these observations, an alteration scenario is proposed. To correlate the bronze corrosion effect on the bell sound, linear and nonlinear resonance experiments are performed on the corroded bronze specimens, where resonance parameters are monitored as a function of increasing driving force using a shaker. Results show that the corrosion effect on the acoustic properties can be monitored through the evolution of the acoustic nonlinear parameters (damping and resonance). These well-calibrated original experiments confirm the effect of corrosion on the acoustic properties of bronze.

Sever vibration will be induced due to the high flow velocity in the pipe. When the flow velocity exceeds the critical value, the static equilibrium configuration of the pipe loses its stability, and the vibration properties change accordingly. In this paper, the free vibration characteristics of the pipe with fixed-fixed ends are revealed in the supercritical regime. Based on the Timoshenko beam theory, the governing equations of the nonlinear vibration near the non-trivial static equilibrium configuration are established. The influences of system parameters on equilibrium configuration, critical velocity, and free vibration frequency is analyzed. The effects of supercritical velocity in different ranges on the natural frequencies are revealed. In addition, the comparison with the Euler-Bernoulli pipe model shows that the differences in critical velocity, equilibrium configuration, and frequency are still significant even the length-diameter ratio is large. The increase of the flow velocity reduces the difference of non-trivial static equilibrium configurations, but eventually aggravates the difference of natural frequencies. Within a certain supercritical velocity range, the vibration difference between the two pipe models is small, beyond this range, the vibration difference increases significantly.

Although small-scale effect or thermal stress significantly impact the mechanical properties of nanobeams, their combined effects and the temperature dependence of the elastic parameters have yet to attract the attention of researchers. In the present paper, we propose a new nonlocal nonlinear Euler-Bernoulli theory to model the mechanical properties of nanobeams. We considered the small-scale effect, thermal stress, and the temperature dependence of Young\'s modulus. A single-walled carbon nanotube (SWCNT) was used to demonstrate the influence of the three factors on elastic buckling and forced bending vibrations. The results indicate that thermal stress and the temperature dependence of Young\'s modulus have a remarkable influence on the mechanical properties of slender SWCNTs as compared to the small-scale effect induced by the nonlocal effect. Ignoring the temperature effect of slender SWCNTs may cause qualitative mistakes.