Complete Controllability of One-Dimensional Vibrating Systems with Bang-Bang Controls

1984 ◽  
Vol 22 (5) ◽  
pp. 788-804 ◽  
Author(s):  
Kimiaki Narukawa
Keyword(s):  
Complete Controllability ◽  
One Dimensional ◽  
Vibrating Systems

Modelling of an Electric Circuit’s Type Influence on Dynamic Flexibility of System with Passive Vibration Damping

2014 ◽  
Vol 1036 ◽  
pp. 511-516 ◽  
Author(s):  
Marek Płaczek
Keyword(s):  
Mathematical Model ◽  
Approximate Method ◽  
Piezoelectric Transducer ◽  
Electric Circuit ◽  
Vibration Damping ◽  
Mathematical Tool ◽  
Exact Methods ◽  
One Dimensional ◽  
Mathematical Algorithm ◽  
Vibrating Systems

Paper presents a proposal of mathematical algorithm used for analysis of influence of type of selected passive electric circuit on dynamic flexibility of system with piezoelectric transducer used for shunting vibration damping. Mathematical model of one-dimensional, vibrating system with shunted piezoelectric transducer is proposed and using approximate method the systems dynamic flexibility is calculated. Influence of type of used passive electric circuit on the systems dynamic flexibility are analysed. The purpose of this work is to obtain a functional mathematical tool that can be used to design such kind of systems obtaining the best efficiency of their work. In order to make it possible it is necessary to know the influence of type and parameters of elements of chosen passive electric circuit on the systems characteristic. In order to realize the assumed aims, the discrete-continuous mathematical model of the considered system is created. It is not possible to use an exact methods to analyse such kind of one-dimensional, vibrating systems with piezoelectric transducers, this is why the approximate method is used.

On one-dimensional vibrating systems

1963 ◽  
Vol 276 (1366) ◽  
pp. 418-435 ◽  
Keyword(s):  
Exact Expression ◽  
Frequency Equation ◽  
Alternative Formulation ◽  
Vibration Band ◽  
One Dimensional ◽  
Power Series Expansions ◽  
Wave Region ◽  
Band Spectra ◽  
The Masses ◽  
Vibrating Systems

An exact expression is derived for the frequency equation of a linear vibrating system with arbitrary masses. By considering the particular case in which all the masses are equal but for a few isolated exceptions, the properties of isotopic mass defects in a homogeneous one-dimensional chain are simply deduced. A stochastic model in which the masses follow a given probability distribution is then discussed, and following a method introduced by Weiss & Maradudin (1958) expansions for the spectrum are obtained in terms of moments about the mean mass. Hence power series expansions are derived for the long-wave region of the spectrum, and these are extended to models in which short-range order is present. An alternative formulation offers reasonable hope of calculating spectra over the whole frequency range. Finally, a number of general properties of vibration band spectra in one dimension are obtained.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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