Vibrations of a Cylindrical Sandwich Shell with a Honeycomb Core Made Using FDM technology

Presented is a model of the dynamic deformation of a three-layer cylindrical shell with a honeycomb core, manufactured by fused deposition modeling (FDM), and skins reinforced with oriented carbon nano-tubes (CNT). A ULTEM 9085 thermoplastic-based honeycomb core is considered. To analyze the stress-strain state of the honeycomb core, a finite element homogenization procedure was used. As a result of this procedure, the dynamic response of the honeycomb core is modeled by a homogeneous orthotropic material, whose mechanical properties correspond to those of the core. The proposed model is based on the high-order theory, extended for the analysis of sandwich structures. The skin displacement projections are expanded along the transverse coordinate up to quadratic terms. The honeycomb core displacement projections are expanded along the transverse coordinate up to cubic terms. To ensure the integrity of the structure, shell displacement continuity conditions at the junction of the layers are used. The investigation of linear vibrations of the shell is carried out using the Rayleigh-Ritz method. For its application, the potential and kinetic energies of the structure are derived. Considered are the natural frequencies and modes of vibrations of a one-side clamped cylindrical sandwich shell. The dependence of the forms and frequencies of vibrations on the honeycomb core thickness and the direction of reinforcement of the shell skins have been investigated. It was found that the eigenforms of a sandwich shell are characterized by a smaller number of waves in the circumferential direction, as well as a much earlier appearance of axisymmetric forms. This means that when analyzing the resonant vibrations of a sandwich shell, it is necessary to take into account axisymmetric shapes. Changing the direction of reinforcement of the skins with CNTs makes it possible to significantly influence the frequencies of the natural vibrations of the shell, which are characterized by a nonzero number of waves in the circumferential direction. It was found that this parameter does not affect the frequencies of the axisymmetric shapes of the shell under consideration.

Cyclic dynamic patterns of Russian macroeconomic indicators found by spectral analysis

The paper proposes a contemporary interdisciplinary method to identify consistent patterns within cyclical dynamics of GDP and its macroeconomics determinants in the Russian Federation. This method may contribute to better recognition of the stages of economic cycle and of potential early predicators to recessions and crises. We first identify the trend component of Russian GDP and then apply the spectral data analysis to its cyclical component which reveals its multi-frequency, and non-linear vibrations. These vibrations are then further investigated by transforming time series data on GDP and its determinants into a frequency spectrum series via Fourier transform techniques. Wavelength scanning of selected macroeconomic indicators shows the basic economic cycle of real GDP with duration time of approx. 3.13 years. Other procyclical indicators nevertheless discover asynchronous behavior towards GDP due to the relative autonomy of the sectors standing behind these indicators. Their autonomy lies behind differences in reaction forces (shifts) and periods (lags) to both internal and external shocks. We estimate differentials between the dynamics of GDP and its determinants by evaluating phase deviations of their pairwise harmonic components, mutual pairwise phase shifts, and by comparison of their pairwise cross-spectrum. The one of output is the quantification of time lags between GDP and key macroeconomic indicators of individual economic sectors. This result reveals the complexity of GDP dynamics that sends an aliased rather than a unit signal to economic agents. Our decomposition of this signal into signals from key economic sectors and quantification of phase discrepancies between sectoral signals may contribute to findings in early crisis predicators. We also estimate the depth and velocity of shocks penetrations into both economy as a whole and its particular sectors.

Numerical Assessment and Parametric Optimization of a Piezoelectric Wind Energy Harvester for IoT-Based Applications

In the 21st century, researchers have been showing keen interest in the areas of wireless networking and internet of things (IoT) devices. Conventionally, batteries have been used to power these networks; however, due to the limited lifespan of batteries and with the recent advancements in piezoelectric technology, there is a dramatic increase in renewable energy harvesting devices. In this research, an eco-friendly wind energy harvesting device based on the piezoelectric technique is analytically modeled, numerically simulated, and statistically optimized for low power applications. MATLAB toolbox SIMSCAPE is utilized to simulate the proposed wind energy harvester in which a windmill is used to produce rotational motion due to the kinetic energy of wind. The windmill’s rotational shaft is further connected to the rotary to linear converter (RLC) and vibration enhancement mechanism (VEM) for the generation of translational mechanical vibration. Consequently, due to these alternative linear vibrations, the piezoelectric stack produces sufficient electrical output. The output response of the energy harvester is analyzed for the various conditions of piezoelectric thickness, wind speed, rotor angular velocity, and VEM stiffness. It is observed that the electrical power of the proposed harvester is proportional to the cube of wind speed and is inversely proportional to the number of rotor blades. Furthermore, an optimization strategy based on the full factorial design of the experiment is developed and implemented on MINITAB 18.0 for evaluating the statistical performance of the proposed harvester. It is noticed that a design with 3 rotor-blades, having 3 mm piezoelectric thickness, and 40 Nm−1 stiffness generates the optimum electrical response of the harvester.

Application of a Novel Picard-Type Time-Integration Technique to the Linear and Non-Linear Dynamics of Mechanical Structures: An Exemplary Study

Applications of a novel time-integration technique to the non-linear and linear dynamics of mechanical structures are presented, using an extended Picard-type iteration. Explicit discrete-mechanics approximations are taken as starting guess for the iteration. Iteration and necessary symbolic operations need to be performed only before time-stepping procedure starts. In a previous investigation, we demonstrated computational advantages for free vibrations of a hanging pendulum. In the present paper, we first study forced non-linear vibrations of a tower-like mechanical structure, modeled by a standing pendulum with a non-linear restoring moment, due to harmonic excitation in primary parametric vertical resonance, and due to excitation recordings from a real earthquake. Our technique is realized in the symbolic computer languages Mathematica and Maple, and outcomes are successfully compared against the numerical time-integration tool NDSolve of Mathematica. For out method, substantially smaller computation times, smaller also than the real observation time, are found on a standard computer. We finally present the application to free vibrations of a hanging double pendulum. Excellent accuracy with respect to the exact solution is found for comparatively large observation periods.

Interpreting the Main Power Characteristics Choice of the Wheel Vehicles Guided Cushioning System

The method of investigation of the non-linear vibrations of the wheel vehicles with the guided cushioning system has been developed. It is based on the idea of the perturbation methods combined with the theory of special periodic Atebfunctions. All these made possible to obtain analytical relations, which describe the characteristic features of the cushioning area vibrations. These relations can be the basis for creation of the software product of the guided cushioning system with the purpose to minimize the dynamic loadings on the transported people and cargo and to increase the stability characteristics of the vehicle movement along the curvilinear areas of the bump road.