Linearization of nonautonomous models describing fluid filled elastic tubes and nonlinear elastic rods with variable cross-section

1993 ◽  
Vol 100 (1-2) ◽  
pp. 95-103 ◽  
Author(s):  
N. Manganaro
Keyword(s):  
Cross Section ◽  
Variable Cross Section ◽  
Elastic Rods ◽  
Variable Cross ◽  
Elastic Tubes ◽  
Nonlinear Elastic

On the theory of rods II. Developments by direct approach

1974 ◽  
Vol 337 (1611) ◽  
pp. 485-507 ◽  
Keyword(s):  
Cross Section ◽  
Variable Cross Section ◽  
Direct Approach ◽  
Elastic Rods ◽  
Variable Cross ◽  
Uniform Cross Section ◽  
Axes Of Symmetry

This paper, which may be regarded as a companion to part I under the same title, is concerned with some aspects of both the nonlinear and the linear theories of elastic rods by a direct approach based on the theory of a Cosserat curve with two directors. Special attention is given to the development of the linear isothermal theory of straight isotropic rods of variable cross-section possessing two axes of symmetry. The resulting equations, which are applicable to rods of non-uniform section, separate into those appropriate for extensional, torsional and flexural modes of deformation. Application of these results to torsion and flexure of non-uniform rods are considered, and the problem of identification of constitutive coefficients for rods of uniform cross-section is dealt with at some length.

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.

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