scholarly journals Solving of nonstandard exercises on oscillatory motion

2016 ◽  
Author(s):  
Marat Ruslanovich Mukhamedov ◽  
Keyword(s):  
Oscillatory Motion

Non-Newtonian effects in axially symmetric oscillatory flows of some elastico-viscous liquids

1970 ◽  
Vol 68 (3) ◽  
pp. 731-750 ◽  
Author(s):  
J. R. Jones
Keyword(s):  
Elastic Properties ◽  
Equations Of State ◽  
Time Lag ◽  
Physical Constant ◽  
Oscillatory Motion ◽  
Axially Symmetric ◽  
Metric Tensor ◽  
Oscillatory Flows ◽  
Viscous Liquids ◽  
Deformation Stress

In (general) elastico-viscous liquids the response to stress at any instant will depend on previous rheological history, the equations of state needed to describe the rheological properties of a typical material element at any instant t being expressible in the form of a (properly invariant†) set of integro-differential equations relating its deformation, stress and temperature histories (as defined by a metric tensor (of a convected frame of reference), a stress tensor and the temperature measured in the element as functions of previous time t'( < t)) together with the time lag (t – t') and physical constant tensors associated with the element (1). Thus in any type of oscillatory motion a rheological history will necessarily be a function of the frequency of the forcing agent, the rheological history of a number of different types of elastico-viscous liquids in some simple shearing oscillatory flows being a rather simple oscillatory history (see, for example, (2–4)). It is, therefore, to be expected that a liquid with elastic properties will behave somewhat differently from any inelastic viscous liquid when subjected to any kind of oscillatory motion, and it is for this reason that oscillatory motions have been used extensively to detect and measure the elastic properties of liquids (see, for example, (2–5)).

A Microfluidic Viscometer: Translation of Oscillatory Motion of a Water Microdroplet in Oil under Electric Field

2021 ◽  
Author(s):  
Anvesh Dixit ◽  
Chintak Kamalesh Parashar ◽  
Satarupa Dutta ◽  
Jiwajyoti Mahanta ◽  
Nayanjyoti Kakati ◽  
...  
Keyword(s):  
Electric Field ◽  
Oscillatory Motion

Noncontact optical displacement measurements by dynamic contrast auto focusing for slow oscillatory motion

2021 ◽  
Vol 60 (12) ◽  
Author(s):  
Evgeniy Makagon ◽  
Sergey Khodorov ◽  
Anatoly Frenkel ◽  
Leonid Chernyak ◽  
Igor Lubomirsky
Keyword(s):  
Oscillatory Motion ◽  
Optical Displacement ◽  
Displacement Measurements ◽  
Auto Focusing

scholarly journals Communicating vessels: a non-linear dynamical system

2017 ◽  
Vol 39 (3) ◽  
Author(s):  
Roberto De Luca ◽  
Orazio Faella
Keyword(s):  
Dynamical System ◽  
Fluid Flow ◽  
Ideal Fluid ◽  
Oscillatory Motion ◽  
Linear Dynamical System ◽  
Static Properties ◽  
Bernoulli’S Equation ◽  
Non Linear ◽  
Dynamical Properties

The dynamics of an ideal fluid contained in two communicating vessels is studied. Despite the fact that the static properties of this system have been known since antiquity, the knowledge of the dynamical properties of an ideal fluid flowing in two communicating vessels is not similarly widespread. By means of Bernoulli's equation for non-stationary fluid flow, we study the oscillatory motion of the fluid when dissipation can be neglected.

scholarly journals THE PARAMETRIC OSCILLATIONS OF ROTATING ELASTIC RODS UNDER THE ACTION OF THE PERIODIC AXIAL FORCES

2020 ◽  
pp. 56-64
Author(s):  
Petro Lizunov ◽  
Valentyn Nedin
Keyword(s):  
Differential Equations ◽  
Computer Program ◽  
Block Diagram ◽  
Time Integration ◽  
Numerical Differentiation ◽  
Oscillatory Motion ◽  
Elastic Rods ◽  
Axial Forces ◽  
General Block Diagram ◽  
Rotating Rods

The paper presents the results of numerical investigation of the periodic axial forces’ influence on the transverse oscillations of long rotating rods. The gyroscopic inertia forces are taken to account and space oscillating process of rotating rods is considered with account of geometric nonlinearity. The study has been done with computer program with a graphical interface that is developed by authors. The process of numerical solution of the differential equations of oscillations of rotating rods using the method of numerical differentiation of rod’s bend forms by polynomial spline-functions and the Houbolt time integration method is described. A general block diagram of the algorithm is shown. This algorithm describes the process of repeated (cyclical) solving of the system of differential equations of oscillations for every point of mechanical system in order to find the new coordinates of the positions of these points in each next point of time t+∆t. The computer program in which the shown algorithm is realized allows to monitor for the behavior of moving computer model, which demonstrates the process of oscillatory motion in rotation. Moreover, the program draws the graphics of oscillations and changes of angular speeds and accelerations in different coordinate systems. Using this program, the dynamics of a range of objects which are modeled by long elastic rods have been studied. For investigated objects is shown that on various rotational speeds and beat frequencies the oscillatory motion of the rods occurs with different character of behavior. On certain speeds with different frequencies of axial load the oscillations have definite periodicity and occur with beats of amplitude which are the result of the periodic axial force action.

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