CALCULATION OF PARAMETERS OF BRANCHED MECHANICAL SYSTEMS WITH HARMONIC VIBRATIONS. Continuation

Author(s):  
I. P Popov

Parallel-series and series-parallel connections of mechanical power consumers are considered. According to the known parameters of systems and the disturbing harmonic effect, the velocities of the elements of mechanical systems and the forces applied to them are algebraically determined. For the considered branched mechanical schemes, the classical methods based on solving second-order differential equations become many times more complicated and require solving systems of equations that reduce to higher-order differential equations. The use of a symbolic (complex) description of mechanical processes and systems makes it possible to use instead simple and compact algebraic methods, the complexity of which is ten times less. Vector diagrams, not being a necessary component of the study of mechanical systems, are of significant methodological importance, since they show quantitative and phase relationships between the parameters of systems.

Author(s):  
I.P. POPOV

Parallel-serial and serial-parallel connections of consumers of mechanical power are considered. According to the known parameters of systems and the disturbing harmonic effect, the velocities of the elements of mechanical systems and the forces applied to them are algebraically determined. A comprehensive representation of harmonic and related quantities is used. This approach is widely used in electrical engineering. For the considered branched mechanical schemes, the classical methods based on the solution of second-order differential equations become many times more complicated and require the solution of systems of equations, which are reduced to higher-order differential equations. The use of a symbolic (complex) description of mechanical processes and systems makes it possible to use instead simple and compact algebraic methods, the complexity of which is ten times less.


Author(s):  
I. P. Popov

Parallel and series connections of mechanical power consumers are considered. According to the known parameters of systems and the disturbing harmonic effect, the velocities of the elements of mechanical systems and the forces applied to them are algebraically determined. Attention is paid to resonant modes, incl. resonance of forces and resonance of speeds. The use of a symbolic (complex) description of mechanical systems with forced harmonic vibrations (in a steady state) made it possible to abandon the extremely cumbersome and laborious calculation algorithm associated with solving differential equations and replace it with simple and visual algebraic operations. Due to this, the calculation time is reduced significantly. Vector diagrams, not being a necessary component of the study of mechanical systems, are of significant methodological importance, since they show quantitative and phase relationships between the parameters of systems.


Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 446
Author(s):  
Alanoud Almutairi ◽  
Omar Bazighifan ◽  
Youssef N. Raffoul

The aim of this work is to investigate the oscillation of solutions of higher-order nonlinear differential equations with a middle term. By using the integral averaging technique, Riccati transformation technique and comparison technique, several oscillatory properties are presented that unify the results obtained in the literature. Some examples are presented to demonstrate the main results.


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