This paper considers three dynamic systems composed of a mathematical pendulum suspended on a sliding body subjected to harmonic excitation. A comparative dynamic analysis of the studied parametric mutations of the rigid pendulum with inertial suspension point and damping was performed. The examined system with parametric mutations is solved numerically, where phase planes and Poincaré maps were used to observe the system response. Lyapunov exponents were computed in two ways to classify the dynamic behavior at relatively early stage of forced responses using two proven methods. The results show that with some parameters three systems exhibit a very similar dynamic behavior, i.e., quasi-periodic and even chaotic motions. Math. Comput. Appl. 2019, 24, 90 2 of 15 the full spectrum of Lyapunov exponents is presented in [3], the calculation of the largest Lyapunov exponent is given in [5,6], and the determination of the spectrum of Lyapunov exponents can be found in [7].From a practical point of view, Lyapunov exponents are used in various fields of science, such as: rotor systems [8], electricity systems [9], aerodynamics [10]. The Parametric Pendulum and Its Mutations
Increasing popularity of individualised electricity generation from wind by prosumers creates a strong demand for profitable and highly efficient small wind turbines. This paper investigates the influence of rotor blade solidity parameter on device efficiency in hope of determining its optimal value as a part of the development process of the GUST small wind turbine. The study involved experimental analysis in the wind tunnel and numerical simulations performed in QBlade software. Different solidities of the rotor were achieved by alteration of (1) number of blades and (2) chord distribution along the blade span. The increase of rotor solidity resulted in augmentation of the aerodynamic efficiency in both approaches. The elongation of the chord by 33% in a 3-bladed rotor resulted in a bigger power coefficient increment than addition of a 4th blade with original chord distribution. Even though the solidity was the same, the 3-bladed rotor performed better, possibly due to lower form drag. The results emphasize the importance of the rotor solidity optimization during the small wind turbine rotor development and may significantly influence overall power output.
This paper presents an experimental and numerical analysis using the finite element method (FEM) of the bending of honeycomb-core panel. Segments of honeycomb paperboard of several thicknesses were subjected to four-point flexure tests to determine their bending stiffness and maximum load. Several mechanical properties of orthotropic materials were taken into account to account for the experimental results. The numerical analysis of the damage prediction was conducted by using well-known failure criteria such as maximum stress, maximum strain and Tsai-Wu. The present study revealed how to model the honeycomb panel to obtain curves close to experimental ones. This approach can be useful for modelling more complex structures made of honeycomb paperboard. Moreover, thanks to the use of variously shaped cells in numerical models, i.e., the shape of a regular hexagon and models with a real shape of the core cell, results of the calculation were comparable with the results of the measurements. It turned out that the increase of maximum loads and rise in stiffness for studied samples were almost either linearly proportional or quadratically proportional as a function of the panel thickness, respectively. On the basis of failure criteria, slightly lower maximum loads were attained in a comparison to empiric maximum loads.
Small Wind Turbines (SWTs) are an increasingly developing Renewable Energy Source, thanks to the gradual popularisation of the prosumer energy generation approach. This, however, requires maximum safety of the machine, working next to households. Reliability is also necessary from the financial point of view, as SWTs should withstand 20 - 30 years of operation without any serious failure to ensure investment profitability. The weakest SWT element is arguably its most exposed one - the rotor - hence the important role played by the blade strength tests. The experimental analysis becomes preferable with increasing popularity of new materials (composites) and production techniques (additive manufacturing). This paper sets out to develop a test stand for static strength examination of 3D-printed SWT blades. This kind of objects is often considered as more vulnerable to structural failures than those created via machining techniques, due to their anisotropic structure, so ensuring structural integrity is crucial for safety reasons.
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