The relaxation spectra, from which other material functions used to describe mechanical properties of materials can be uniquely determined, are important for modeling the rheological properties of polymers used in chemistry, food technology, medicine, cosmetics, and many other industries. The spectrum, being not directly accessible by measurement, is recovered from relaxation stress or oscillatory shear data. Only a few models and identification methods take into account the non-negativity of the real spectra. In this paper, the problem of recovery of non-negative definite relaxation spectra from discrete-time noise-corrupted measurements of relaxation modulus obtained in the stress relaxation test is considered. A new hierarchical identification scheme is developed, being applicable both for relaxation time and frequency spectra. Finite-dimensional parametric classes of models are assumed for the relaxation spectra, described by a finite series of power-exponential and square-exponential basis functions. The related models of relaxation modulus are given by compact analytical formula, described by the products of power of time and the modified Bessel functions of the second kind for the time spectrum, and by recurrence formulas based on products of power of time and complementary error functions for frequency spectrum. The basis functions are non-negative. In result, the identification task was reduced to a finite-dimensional linear-quadratic problem with non-negative unknown model parameters. To stabilize the solution, an additional smoothing constraint is introduced. Dual approach was used to solve the stated optimal identification task resulting in the hierarchical two-stage identification scheme. In the first stage, dual problem is solved in two levels and the vector of non-negative model parameters is computed to provide the best fit of the relaxation modulus to experiment data. Next, in second stage, the optimal non-negative spectrum model is determined. A complete scheme of the hierarchical computations is outlined; it can be easily implemented in available computing environments. The model smoothness is analytically studied, and the applicability ranges are numerically examined. The numerical studies have proved that using developed models and algorithm, it is possible to determine non-negative definite unimodal and bimodal relaxation spectra for a wide class of polymers. However, the examples also demonstrated that if the basis functions are non-negative and the model is properly selected for a given type of the real spectrum (unimodal, multimodal), the optimal model determined without non-negativity constraint can be non-negative in the dominant range of its arguments, especially in the wide neighborhood of the spectrum peaks.

This paper focuses on the vibration analysis of a prototype helicopter rotor test stand, with particular attention to the dynamic response of its electric propulsion system. The stand is driven by an induction motor and equipped with composite rotor blades of various geometries, including blades with shape memory alloy (SMA)-based torsion actuators for angle of attack (AoA) adjustment. These variable geometries significantly influence the system’s dynamic behavior, where resonance phenomena may pose risks to structural integrity. The objective was to investigate how selected operational parameters specifically motor speed and AoA affect the vibration response of the propulsion system. Structural vibrations were measured using a tri-axial piezoelectric accelerometer system integrated with calibrated signal conditioning and high-resolution data acquisition modules. This setup enabled precise, time-synchronized recording of dynamic responses along all three axes. Fast Fourier Transform (FFT) and Power Spectral Density (PSD) methods were applied to identify dominant frequency components, including those associated with rotor harmonics and SMA activation. The highest vibration amplitudes were observed at an AoA of 16°, but all results remained within the vibration limits defined by MIL-STD-810H for rotorcraft drive systems. The study confirms the importance of sensor-based diagnostics in evaluating electromechanical propulsion systems operating under dynamic loading conditions.

In Poland, as in the global energy market, the popularity of renewable energy sources, whose main advantage over fossil fuels is climate neutrality, is growing. An alternative to dedicating land exclusively to renewable energy is agrivoltaics, which involves dual use of land: for agricultural production and for photovoltaic installations that convert solar energy into usable energy simultaneously. The study's main purpose was to answer two questions: to what extent are the agricultural lands of eastern Poland suitable for the development of agrivoltaics, and how does the selection of criteria affect the final result of the analysis in light of the Analytic Hierarchy Process. The study area was the Lublin Voivodeship, whose potential was evaluated based on 8 orography and land use criteria. The study focuses on spatial conditions, whereas legal and economic conditions have not been considered. The analysis showed that implementing agrivoltaics is theoretically feasible on 79% of the Voivodeship’s total agricultural land, of which 9,961 km2 can be considered at least moderately highly suitable. Additionally, two alternative scenarios were analysed: in the first, only orography criteria were assessed, and in the second, only land use. The comparative analysis revealed that the choice of criteria significantly impacts the results. The highest area suitability was obtained in the assessment considering land use only, and the lowest for orography.