Damping of layered porous composites and an application in machinery

The structured composite can involve the porous materials providing the important internal damping that is usable in mechanical engineering applications. The stiff base material is equipped by layer/s of softer porous material/s covered by constrained layer. Such layered structure is characterized by increased internal damping in vibration process. Paper analyses some either measured or simulated mechanical properties of designed layered porous composites. Novelty provided in paper is a specific application of structured composite for damping the high frequency vibrations in resonance frequency obtaining the beneficial results, e.g. 40-48% of maximum amplitude reduction.

The approximation of the solution of wave problems by spectral expansions connected with elliptic differential operators

In this research, we investigate the spectral expansions connected with elliptic differential operators in the space of singular distributions, which describes the vibration process made of thin elastic membrane stretched tightly over a circular frame. The sufficient conditions for summability of the spectral expansions connected with wave problems on the disk are obtained by taking into account that the deflection of the membrane during the motion remains small compared to the size of the membrane and for wave propagation problems, the disk is made of some thermally conductive material.

An approximate mathematical model for estimating the influence of vibrations on attached elements of a mobile robot video system

The problem of constructing and applying of mathematical model for assessing the influence of vibrations on the attached elements of the video system of a mobile robot is solved. This robot is considered as a mobile platform for placing of the special equipment for various purposes. The analysis of mathematical models and the results of experimental studies of vibrations of multi-support wheeled machine and its structural elements has been conducted. On the basis of this analysis, the form of a stochastic mathematical model of vibrations of the structure of a mobile robot has been substantiated. The vibration model is specified as a correlation function or spectral density of a random process for various conditions of the robot’s movement. Differential equations of the shaping filter for modeling а random vibration process with given characteristics are presented. Differential equations for the probabilistic moments of the vibration process are presented. Based on the equations for the probabilistic moments and the proposed formula, an assessment of events, which consist in exceeding the vibration amplitude of a given level was carried out. These events are named as outliers of a random process and characterize the range within the basic properties of the equipment installed on the mobile platform are preserved. An analytical study of a mathematical model to determine the intensity of emissions of a random vibration process has been carried out. The probabilistic characteristics of the vibration process and the intensity of emissions are determined. The obtained theoretical results make it possible to assess the performance of the elements of a video system installed on a mobile platform and to formulate the basic requirements for tolerances for their parameters. The results of computer modeling clearly showed the efficiency of the proposed mathematical model for assessing the influence of vibrations.

Separation of the Structure Signal by the Maximal Overlap Discrete Wavelet Transform and Fast Fourier Transform

Power spectral density (PSD) is used for evaluating a structure’s vibration process. Moreover, PSD not only shows a discrete form of vibration but also presents various components in a vibration structure. The superposition of multiple vibration patterns on the same spectrum poses difficulty in analyzing the spectral information in the way needed to find the structure’s discrete vibration. This paper proposes a method for separating the synthetic vibration signal into a structure’s discrete vibration and other extraneous vibrations using the maximal overlap discrete wavelet transform (MODWT) method combined with the method of fast Fourier transform (FFT). With the combination of these two algorithms, MODWT and FFT, the signals of the synthesized vibration have been separated into component signals with different frequency ranges. This means that PSD will be formed, which is based on the combination of the single power spectra of the component signals. Thus, the single spectrum of each of these constructed components can be used to evaluate the types of discrete vibrations coexisting in a structure’s vibration process. The survey results in this paper show the sensitivity and suitability of select types of discrete vibrations to be separated out during the assessment of the structural change, so as to achieve the best possible plan for eliminating the unwanted and unexpected noise and vibration components.

HAMILTONIAN-BASED FREQUENCY-AMPLITUDE FORMULATION FOR NONLINEAR OSCILLATORS

Complex mechanical systems usually include nonlinear interactions between their components which can be modeled by nonlinear equations describing the sophisticated motion of the system. In order to interpret the nonlinear dynamics of these systems, it is necessary to compute more precisely their nonlinear frequencies. The nonlinear vibration process of a conservative oscillator always follows the law of energy conservation. A variational formulation is constructed and its Hamiltonian invariant is obtained. This paper suggests a Hamiltonian-based formulation to quickly determine the frequency property of the nonlinear oscillator. An example is given to explicate the solution process.

Research on the Vibration Characteristics of a Track’s Structure Considering the Viscoelastic Properties of Recycled Composite Sleepers

In order to investigate the vibration characteristics of a composite sleeper-ballasted track and provide a basis for further popularization, a vehicle–track dynamic coupling model is established and the viscoelastic properties of the composite sleeper are considered. The power flow method is employed to reveal the power flow distribution characteristics of the composite sleeper. The results show that the viscoelastic properties of the composite sleeper have little influence on the rail power and have a greater influence on the power flow of the sleeper and ballast bed in some frequency ranges. The viscoelastic properties of the composite sleeper can effectively improve the calculation accuracy of the track structure’s power flow. Compared with the type-III pre-stressed concrete sleepers widely used in China, composite sleepers consume more energy in the vibration process due to their own physical characteristics, which reduces the power flow transmitted downward and relieves vibration on the ballast bed, especially in the ranges of 80–125 Hz and 250–400 Hz. The temperature change mainly affects the power flow of the composite sleeper in the frequency range above 50 Hz. As the temperature increases, the modulus of the composite sleeper decreases and the vibration reduction effect of the ballast bed is improved.