Propagation of nonlinear acoustic waves and shocks in variable cross‐section resonators

2003 ◽  
Vol 114 (4) ◽  
pp. 2324-2324
Author(s):  
Bart Lipkens
Keyword(s):  
Cross Section ◽  
Acoustic Waves ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Nonlinear Acoustic

scholarly journals DETERMINATION OF DIMENSIONAL PARAMETERS FOR ANNULAR CONCENTRATOR OF ULTRASONIC SYSTEM

2018 ◽  
Vol 17 (1) ◽  
pp. 51-55
Author(s):  
V. P. Lugovoi ◽  
I. V. Lugovoi
Keyword(s):  
Cross Section ◽  
Acoustic Waves ◽  
Visual Analysis ◽  
Variable Cross Section ◽  
Vibrational Amplitude ◽  
External Diameter ◽  
Variable Cross ◽  
Thin Sections ◽  
Dimensional Parameters

Conventional ultrasonic systems contain concentrators of longitudinal type to amplify and transfer vibrations to a tool. Along with them, elastic rings with variable cross section thickness can be used effectively as concentrators for ultrasonic vibrations of acoustic systems. Their practical application requires a scientifically substantiated methodology for determination of geometric parameters. The paper provides substantiation of the method used to determine dimensions of annular concentrators with a variable cross section which can enhance effectiveness of the ultrasound equipment while performing various technological tasks. Visual analysis of acoustic waves radiated by annular concentrators has shown that the most intensive vibrations are produced in the most thin sections. Computer simulation of oscillations in rings with an external diameter of 50 mm and a variable cross section has demonstrated that the largest increase of vibration amplitude is achieved at a certain ratio of ring thicknesses and diameters. An analysis of numerical values for amplication factor of vibrational amplitude Kд has revealed that there is a limit boundary for the ratio of ring wall thicknesses which, in its turn, depends on the ratio of ring outer and inner diameters at certain values of hole axis eccentricity. The ratio of diameters is expressed quantitatively by the coefficient Kд. An analysis of the results concerning numerical calculations of amplitude amplification factor performed for the specified model of the ring having 50 mm diameter have illustrated that this ratio should lie between 1.3 > Kд > 1.15. The obtained results can be used in ultrasonic devices with annular concentrators in order to perform various technological tasks.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

scholarly journals Theoretical and Experimental Studies on MEMS Variable Cross-Section Cantilever Beam Based Piezoelectric Vibration Energy Harvester

Micromachines ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 772
Author(s):  
Xianming He ◽  
Dongxiao Li ◽  
Hong Zhou ◽  
Xindan Hui ◽  
Xiaojing Mu
Keyword(s):  
Power Density ◽  
Cantilever Beam ◽  
Cross Section ◽  
Energy Harvester ◽  
Variable Cross Section ◽  
Vibration Energy ◽  
Variable Cross ◽  
Vibration Energy Harvester ◽  
Piezoelectric Vibration Energy Harvester ◽  
Piezoelectric Vibration

The piezoelectric vibration energy harvester (PVEH) based on the variable cross-section cantilever beam (VCSCB) structure has the advantages of uniform axial strain distribution and high output power density, so it has become a research hotspot of the PVEH. However, its electromechanical model needs to be further studied. In this paper, the bidirectional coupled distributed parameter electromechanical model of the MEMS VCSCB based PVEH is constructed, analytically solved, and verified, which laid an important theoretical foundation for structural design and optimization, performance improvement, and output prediction of the PVEH. Based on the constructed model, the output performances of five kinds of VCSCB based PVEHs with different cross-sectional shapes were compared and analyzed. The results show that the PVEH with the concave quadratic beam shape has the best output due to the uniform surface stress distribution. Additionally, the influence of the main structural parameters of the MEMS trapezoidal cantilever beam (TCB) based PVEH on the output performance of the device is theoretically analyzed. Finally, a prototype of the Aluminum Nitride (AlN) TCB based PVEH is designed and developed. The peak open-circuit voltage and normalized power density of the device can reach 5.64 V and 742 μW/cm3/g2, which is in good agreement with the theoretical model value. The prototype has wide application prospects in the power supply of the wireless sensor network node such as the structural health monitoring system and the Internet of Things.

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