A semi-analytical method for the vibration of cylindrical shells with embedded acoustic black holes

Embedding acoustic black holes (ABHs) on beams and plates has revealed as an appealing passive method for noise and vibration reduction. However, most ABH designs to date only concern straight beams and flat plates, while cylindrical structures are commonly found in the aeronautical and naval sectors. In this work, we suggest a semi-analytical method to compute the vibration field of a cylinder with an ABH indentation. We also show the ABH efficiency in terms of shell vibration reduction. It is proposed to resort to Gaussian basis functions in the framework of the Rayleigh-Ritz method, to reproduce the ABH cylinder vibration field. The ABH shell displacements in the three directions are decomposed in terms of Gaussian functions, which can be dilated and translated analogously to what is done with wavelet transforms. The functions are also forced to satisfy the continuity periodic conditions in the shell circumferential direction. The Gaussian expansion method (GEM) results in high precision at a low computational cost. The suggested semi-analytical method is validated against a detailed finite element (FEM) model. Modal frequencies and modal shapes are recovered very accurately. Besides, the mean square velocity of the annular ABH shell under point external excitation is compared to that of a uniform shell, in the 50-1000 Hz frequency range. Noticeable vibration reduction is achieved.

Informativity of the Vibration Signal of the Spindle Unit of the Metal Cutting Machine

Monitoring the condition of the spindle units of modern metal-cutting machines by methods of non-selective diagnostics involves the possibility of installing monitoring sensors in places with maximum vibration information. In this regard, the assessment of the informative value of the vibration field of the spindle unit, which can be carried out in advance, taking into account the design features, geometric and dimensional characteristics, is an urgent task. Based on the energy approach, a computational model based on the median planes of the walls is proposed using the example of a universal lathe spindle unit. On the basis of the calculated model, the energy balance equations are drawn up taking into account the conditions for the transmission of vibration power between the walls of the housing. The dependences that allow us to calculate the coefficients that take into account the absorption of vibration energy by the walls of the housing are given. The solution of the energy balance equations made it possible, based on the level of the vibration power flow, to rank the walls of the spindle unit body by information content,. The resulting model of the vibration field can be used to determine the reference values of vibration velocities that are formed from sources in the absence of defects. This will allow for non-selective diagnostics to detect the occurrence of a defect at an early stage, and in the presence of a defect to assess the level of its development.

DETERMINATION OF VIBRATION POWER OF VIBRATION SOURCES OF SPINDLE UNITS OF METAL CUTTING MACHINES

Monitoring the state of spindle assemblies of modern metal-cutting machines using CIP methods implies the possibility of installing control sensors in places with maximum vibration information content. In this regard, the assessment of the informativeness of the vibration field of the spindle assembly, which can be carried out in advance, taking into account the design features, geometric and dimensional characteristics, is an urgent task. Based on the energy approach, using the example of the spindle assembly of a universal lathe, a computational model is proposed, built along the median planes of the walls. On the basis of the calculated model, the equations of the energy balance were compiled taking into account the conditions for the transfer of vibration power between the walls of the housing. The method for determining the vibration power of the main sources in the spindle assemblies is given: a spindle with residual unbalance, a drive gear and bearings. It has been established that the most significant factors determining the vibration power introduced into the spindle unit housing are the operation of the bearings, the weight of the spindle and the location of its center of mass. The result obtained makes it possible to detect incipient defects in the bearings, which, as practice shows, are the defining elements of the parametric reliability of spindle assemblies. The resulting model of the vibration field can be used to determine the reference values of vibration velocities that are formed from sources in the absence of defects.

Analysis of Vibration Field Parameters of the City by the Correlation-Regression Method

Analysis of the parameters of the vibration field of the city was carried out on the example of the area of Syktyvkar. The vibroseismic monitoring data were used as a source material. We obtained the estimates of the mathematical expectation, variances and standard deviations, checked the normal distribution of random variables. The values of the correlation coefficient and correlation ratio were determined applying the method of correlation-regression analysis and carrying out the necessary calculations. Distribution diagrams were also constructed and approximating functions and estimated equations were obtained. This approach can be used to predict the parameters of the vibration field on the city territory and made it possible to give recommendations on its application as selection rationale of construction sites and environmental survey in the field of man-induced impact.

DIRECTIONS OF IMPROVING THE EFFICIENCY OF VIBRATION TECHNOLOGICAL MACHINES

The article considers the directions of increasing the efficiency of vibrating technological machines. The processing of information on the development of vibration technologies is quite diverse and is represented by numerous scientific and technical developments related to improving the efficiency of vibration machines and ensuring the reliability of their work. The analytical basis for previous research in the creation of new technology are mathematical models that reflect the properties of mechanical oscillatory systems with several degrees of freedom, which perform small oscillations under the action of a system of periodic external perturbations that create vibration fields of one configuration. The dynamic properties of the working bodies of machines in a detailed form are revealed as the distribution of the amplitudes of oscillations of the points of the working bodies. In many cases, this distribution is linear, which is due to the manifestations of the properties of the simplest movements of the working bodies. Approaches are proposed in which the possible structural mathematical modeling is realized on the idea that a linear mechanical oscillatory system with concentrated parameters and several degrees of freedom can be compared with the structural scheme of the automatic control system. Particular attention is paid to the study and evaluation of the possibility of new dynamic effects associated with the simultaneous action of several working bodies of machines, as well as - modes of dynamic damping of oscillations. An important role in ensuring such developments is played by areas of research focused on the development of methods of mathematical modeling. Based on the research it is shown that the vibration field of the vibrating technological machine is formed under the influence of several factors, which are determined by the simultaneous action of several force perturbations, asymmetry of inertial and elastic properties of the mechanical system, the presence of additional connections. The introduction of additional links in the structure of the mechanical oscillating system of the vibrating machine, can significantly affect the structure of the vibration field, providing the choice of conditions for rational organization of the technological process of vibration processing, such as vibration hardening, crushing, transportation, screening.