Mathematical model of a multisectional vibration unit (Q2753413)
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scientific article; zbMATH DE number 1668326
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Mathematical model of a multisectional vibration unit |
scientific article; zbMATH DE number 1668326 |
Statements
4 November 2001
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vibrational machine
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elastic joint
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generalized coordinate
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Lagrange equations
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nonlinear diferential equations
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Mathematical model of a multisectional vibration unit (English)
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The studied unit consists of \(N\) vibrational machines mounted on a common basement framework. The machines are jointed by elastic joints. The technological load is installed on the supporting mass. Equations of motion of the system are written using the Lagrange principle. Generalized coordinates of the system are coordinates of bodies and angles of their rotation. Motion of the unit is represented by a system of nonlinear ordinary diferential equations. Nonlinearity is introduced by dynamic characteristics of the power source, by dry friction in contact zones and periodic collisions of the technological load with working units, by the Sommerfeld effect and by self-synchronization of systems with two or more power sources. An example of construction of the matrix of differential equations for a particular unit is presented.
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