scholarly journals AIMED CONTROL OF THE FREQUENCY SPECTRUM OF EIGENVIBRATIONS OF ELASTIC PLATES WITH A FINITE NUMBER OF DEGREES OF MASS FREEDOM BY INTRODUCING ADDITIONAL GENERALIZED KINEMATIC DEVICES

2021 ◽  
Vol 17 (4) ◽  
pp. 181-187
Author(s):  
Pavel Akimov ◽  
Leonid Lyakhovich
Keyword(s):  
Finite Number ◽  
Frequency Spectrum ◽  
Degrees Of Freedom ◽  
Mass Movement ◽  
Subsequent Paper ◽  
Elastic Plates ◽  
Natural Vibrations ◽  
Elastic Systems ◽  
The Creation ◽  
Generalized Constraint

As is known, targeted regulation of the frequency spectrum of natural vibrations of elastic systems with a finite number of degrees of mass freedom can be performed by introducing additional generalized constraints and generalized kinematic devices. Each targeted generalized constraint increases, and each generalized kinematic device reduces the value of only one selected natural frequency to a predetermined value, without changing the remaining natural frequencies and all forms of natural vibrations (natural modes). To date, for some elastic systems with a finite number of degrees of freedom of masses, in which the directions of mass movement are parallel and lie in the same plane, special methods have been already developed for creating additional constraints and generalized kinematic devices that change the frequency spectrum of natural vibrations in a targeted manner. In particular, a theory and an algorithm for the creation of targeted generalized constraints and generalized kinematic devices have been developed for rods. It was previously proved that the method of forming a matrix of additional stiffness coefficients, specifying targeted generalized constraint, in the problem of natural vibrations of rods can also be applied to solving a similar problem for elastic systems with a finite number of degrees of freedom, in which the directions of mass movement are parallel, but do not lie in the same plane. In particular, such systems include plates. The distinctive paper shows that the method of forming a matrix for taking into account the action of additional inertial forces, specifying targeted kinematic devices in the problem of natural vibrations of rods can also be applied to solving a similar problem for elastic systems with a finite number of degrees of freedom, in which the directions of mass movement are parallel, but do not lie in the same plane. However, the algorithms for the creation of targeted generalized kinematic devices developed for rods based on the properties of rope polygons cannot be used without significant changes in a similar problem for plates. The method of creation of computational schemes of kinematic devices that precisely change the frequency spectrum of natural vibrations of elastic plates with a finite number of degrees of mass freedom is a separate problem and will be considered in a subsequent paper.

scholarly journals AIMED CONTROL OF THE FREQUENCY SPECTRUM OF EIGENVIBRATIONS OF ELASTIC PLATES WITH A FINITE NUMBER OF DEGREES OF FREEDOM OF MASSES BY SUPERIMPOSING ADDITIONAL CONSTRAINTS

2021 ◽  
Vol 17 (2) ◽  
pp. 76-82
Author(s):  
Leonid Lyakhovich ◽  
Pavel Akimov
Keyword(s):  
Finite Number ◽  
Frequency Spectrum ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Elastic Plates ◽  
Natural Vibrations ◽  
Design Constraint ◽  
Elastic Systems ◽  
The Masses ◽  
Additional Constraints

As is known, for some elastic systems with a finite number of degrees of freedom of masses, for which thedirections of motion of the masses are parallel and lie in the same plane, methods have been developed for creatingadditional constraints that purposefully change the spectrum of natural frequencies. In particular, theory and algorithm forthe formation of aimed additional constraints have been developed for the rods, the introduction of each of which doesnot change any of the modes of natural vibrations, but only increases the value of only one frequency, without changingthe values of the remaining frequencies. The distinctive paper is devoted to the method of forming a matrix of additionalstiffness coefficients corresponding to such aimed constraint in the problem of natural vibrations of rods. This method canalso be applied to solving a similar problem for elastic systems with a finite number of degrees of freedom, in which thedirections of motion of the masses are parallel, but not lie in the same plane. In particular, such systems include plates.However, the algorithms for the formation of aimed additional constraints, developed for rods and based on the propertiesof rope polygons, cannot be used without significant changes in a similar problem for plates. The method for the formationof design constraint schemes that purposefully change the spectrum of frequencies of natural vibrations of elastic plateswith a finite number of degrees of freedom of masses, will be considered in the next work.

Stability of Dynamic Systems

1983 ◽  
Vol 50 (4b) ◽  
pp. 1086-1096 ◽  
Author(s):  
H. H. E. Leipholz
Keyword(s):  
Finite Number ◽  
Infinite Number ◽  
Dynamic Systems ◽  
Stability Theory ◽  
Degrees Of Freedom ◽  
Continuous Systems ◽  
Specific Nature ◽  
Stability Problems ◽  
Comprehensive Theory ◽  
Elastic Systems

It is shown how stability theory of dynamic systems, emerging from various beginnings strewn over the realm of mechanics, developed into a unified, comprehensive theory for dynamic systems with a finite number of degrees of freedom. It is then demonstrated, how such theory could be adapted over the last five decades to the specific nature of stability problems involving continuous elastic systems. The need for such adaption is stressed by pointing to systems with follower forces. The difficulties arising from the fact that continuous systems are systems with an infinite number of degrees of freedom are emphasized, and an adequate approach to a unified stability theory including also continuous systems is outlined.

Study of some rheological models with a finite number of degrees of freedom

2000 ◽  
Vol 19 (2) ◽  
pp. 277-307 ◽  
Author(s):  
Jérôme Bastien ◽  
Michelle Schatzman ◽  
Claude-Henri Lamarque
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Rheological Models

CRYSTALLINE GRAVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3243-3255 ◽  
Author(s):  
GERARD 't HOOFT
Keyword(s):  
Finite Number ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Holonomy Group ◽  
Discrete Subgroup ◽  
Analytic Solutions ◽  
Space Time ◽  
Exact Analytic Solutions ◽  
Finite Domains ◽  
Dimensional Crystal

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.

On the Dynamic Isotropy of Mechanisms With Two Degrees of Freedom

2005 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Closed Curves ◽  
Special Cases ◽  
Dynamic Performances ◽  
Definition Of ◽  
Geometric Locus

The comparison of mechanisms with different topology or with different geometry, but with the same topology, is a necessary operation during the design of a machine sized for a given task. Therefore, tools that evaluate the dynamic performances of a mechanism are welcomed. This paper deals with the dynamic isotropy of 2-dof mechanisms starting from the definition introduced in a previous paper. In particular, starting from the condition that identifies the dynamically isotropic configurations, it shows that, provided some special cases are not considered, 2-dof mechanisms have at most a finite number of isotropic configurations. Moreover, it shows that, provided the dynamically isotropic configurations are excluded, the geometric locus of the configuration space that collects the points associated to configurations with the same dynamic isotropy is constituted by closed curves. This results will allow the classification of 2-dof mechanisms from the dynamic-isotropy point of view, and the definition of some methodologies for the characterization of the dynamic isotropy of these mechanisms. Finally, examples of applications of the obtained results will be given.

scholarly journals Full Control of Virtual Objects Manipulation Based on the Images of Real Ones

2011 ◽  
Vol 10 (3) ◽  
pp. 51-60
Author(s):  
Brahim Nini
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Moving Object ◽  
Real Object ◽  
Virtual Object ◽  
Analytical Geometry ◽  
Six Degrees Of Freedom ◽  
Virtual Objects ◽  
Simulation Process ◽  
Full Control

This work deals with the virtual manipulation of a real object through its images. The results presented in this paper give a movie-based solution to the simulation process. We show how the simulation of infinite virtual views of a moving object can be reached using a finite number of object's taken images stored in an organized way. The basis of this solution is an analytical geometry-based method that links explicit applied user's actions, resulting in an object's views change, and images that match the best such views. This paper presents an overall solution for these three intertwined parts of the virtual manipulation that involves six degrees of freedom. Hence, a user is able to freely manipulate a virtual object in a scene in whatever manner s/he likes. In this case, the actions are transformed into rotations and/or translations which lead to some changes in object's appearance, both covered by two viewing features: zoom and/or rotations

scholarly journals Research and training car driving simulator with weight up to 3.5 tons dedicated to physical disabled drivers

Mechanik ◽  
2019 ◽  
Vol 92 (8-9) ◽  
pp. 571-573
Author(s):  
Jarosław Jankowski
Keyword(s):  
Degrees Of Freedom ◽  
Driving Simulator ◽  
Physical Disabilities ◽  
Motion Platform ◽  
Six Degrees Of Freedom ◽  
Work Related ◽  
The Creation ◽  
People With Physical Disabilities ◽  
Car Driving ◽  
And Training

The article presents the continuation of work related to the creation of a car driving simulator with a weight of up to 3.5 tons adapted to selected disabilities. The article contains a description of the developed motion platform with six degrees of freedom and the cockpit. In order to ensure the possibility of being managed by the largest group of people with physical disabilities, selected support solutions were implemented. These devices can be easily dismantled to test others. The platform together with the cockpit is controlled from the simulator application and the image is presented to the simulation participant in 3D projection glasses and optionally on a three-segment screen.

Aeroelastic Stability of Lifting Surfaces in High-Density Fluids

1959 ◽  
Vol 3 (01) ◽  
pp. 10-21 ◽  
Author(s):  
Charles J. Henry ◽  
John Dugundji ◽  
Holt Ashley
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Separated Flow ◽  
High Density ◽  
Aeroelastic Stability ◽  
Free Surfaces ◽  
Elastic Systems ◽  
Static Instability ◽  
Theoretical Evidence ◽  
Lifting Surfaces

The large increases anticipated in speeds of vehicles towed or propelled underwater suggests a re-examination of the problem of stability of flexible lifting surfaces mounted thereon. Experimental and theoretical evidence is assembled which suggests that oscillatory aeroelastic instability (flutter) is very unlikely at the structural-to-fluid mass ratios typical of hydrodynamic operation. It is shown that static instability (divergence) is the more important practical problem but that its occurrence can be predicted with greater confidence. Flutter data obtained in high-density fluids are reviewed, and various sources of inaccuracy in their theoretical prediction are analyzed. The need is expressed for more precise means of analytically representing both dynamic-elastic systems and three-dimensional unsteady hydrodynamic loads. For a simple hydrofoil with single degrees of freedom in bending and torsion, the theoretical influence of several significant parameters on high-density flutter is calculated and discussed. Recommendations are made for refinements to existing techniques of analysis to include the presence of channel boundaries, free surfaces, cavitation or separated flow.

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