scholarly journals A Theorectical Modal Study for the Lateral Vibrations of Bars Having Variable Cross Section and Free End Condition

1969 ◽  
Author(s):  
Arthur F. Witte
Keyword(s):  
Cross Section ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Lateral Vibrations

scholarly journals The lateral vibrations of bars of variable section

1917 ◽  
Vol 93 (654) ◽  
pp. 506-519 ◽  
Keyword(s):  
Cross Section ◽  
Formal Analysis ◽  
Detailed Examination ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Biological Application ◽  
Lateral Vibrations ◽  
Variable Section ◽  
Set Up ◽  
The Impact

The present investigation, though strictly mathematical in character, arose in connection with a suggestion, put forward by Prof. A. Dendy and the present author in another paper communicated to the Society, that the siliceous deposits found on certain sponge spicules occurred at nodes of the spicules, regarded as vibrating rods. These vibrations, being set up and maintained by the impact of currents of water on the spicules, are necessarily of the lateral type. For the detailed examination of such a suggestion, it is necessary to obtain a comprehensive account of the positions of the funda­mental nodes on a free-free bar, as dependent on the law of variation of its cross-section. The present paper contains, in fact, the formal analysis whose results were quoted without proof in the other paper. This analysis is of considerable generality, as will appear, and the particular examples selected for purposes of illustration, together with the manner in which the variable cross-section is dealt with, have been determined by the requirements of the biological application already mentioned. One general problem is in view throughout the work, and it may be stated as follows

Determination of the Natural Frequencies of the Bending Vibrations of Beams

1947 ◽  
Vol 14 (1) ◽  
pp. A1-A6
Author(s):  
A. I. Bellin
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Moment Equation ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Bending Vibrations ◽  
Elastic Beams ◽  
Lateral Vibrations

Abstract This paper presents a method for determining the natural frequencies of lateral vibrations for elastic beams. The beams may be of variable cross section and may have any number of spans. The five-moment equation is developed and is then applied to beams supported in various ways. The author reduces the necessary calculations to a simple tabular scheme. Several illustrative examples are included to demonstrate the method of computation.

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.

Sign in / Sign up

Export Citation Format

Share Document