Invariant solutions and constitutive laws for a nonlinear elastic rod of variable cross-section

1986 ◽  
Vol 37 (2) ◽  
pp. 244-255 ◽  
Author(s):  
C. Curr� ◽  
D. Fusco
Keyword(s):  
Cross Section ◽  
Variable Cross Section ◽  
Constitutive Laws ◽  
Variable Cross ◽  
Invariant Solutions ◽  
Elastic Rod ◽  
Nonlinear Elastic

The Analysis of Longitudinal Impact Response for Variable Cross-Section Rod

2016 ◽  
Vol 693 ◽  
pp. 504-510
Author(s):  
Xiao Juan Jiao ◽  
Jian Min Ma
Keyword(s):  
Stress Distribution ◽  
Cross Section ◽  
Influencing Factor ◽  
Variable Cross Section ◽  
Longitudinal Impact ◽  
Variable Cross ◽  
Elastic Rod ◽  
Distribution Law ◽  
Change Rate ◽  
Cross Section Change

s The longitudinal impact between rigid body and variable cross-section elastic rod with fixed boundary condition was studied, the velocity and stress distribution law during 1st impact wave period was derived for the variable cross-section rod, the influence of cross-section change rate on rod response was discussed. Some examples calculations were carried on, It is shown that the cross-section change rate is a significant influencing factor for the velocity and stress distribution in the rod during impact.

scholarly journals About waveguide modeling (transmissions of ultrasonic technological machines)

2019 ◽  
Vol 287 ◽  
pp. 03002
Author(s):  
Vitaly Krupenin ◽  
Vladimir Astashev
Keyword(s):  
Cross Section ◽  
Variable Cross Section ◽  
Vibration Exciter ◽  
Variable Cross ◽  
Core System ◽  
Energy Delivery ◽  
Lumped Parameter ◽  
Additional Equipment ◽  
Nonlinear Elastic ◽  
Waveguide Core

The modeling of energy transfer systems in ultrasonic technological machines is considered. As such systems rod waveguides are usually used. These are, as a rule, distributed systems of variable cross-section, which must transmit energy from an electromechanical vibration exciter to a working body. Sometimes additional equipment is attached to the waveguide (core system), which should be modeled using lumped-parameter subsystems. This article discusses the problems related to the modeling and calculation of the so-called ultrasonic concentrators - waveguides that have a heterogeneous shape and are made to ensure optimal energy delivery to the working body (instrument). Examples of calculations are given that consider the influence of a nonlinear elastic-dissipative load, determined by the nature of the technological process. The analysis of real models is described.

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.

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