International Journal of Mathematics Trends and Technology
Volume 66 | Issue 7 | Year 2020 | Article Id. IJMTT-V66I7P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I7P507
In acoustics and vibration theory the basic equations are usually linearized. The condition of existence of a nontrivial solution of the linear equations leads to the characteristic transcendental equation with respect to H. Here H is the complex number imaginary part of which is natural frequency of oscillations of the system. Real part is describing the rate of damping of oscillations or instability (in case if real part is positive). The structure of roots of such equations is studied by using argument principle for some specific applied problem from fluid mechanics. It is shown that dispersion equation has two complex-conjugate roots and infinite number of real roots. All roots lie in the left complex half-plane, providing damping of oscillations.
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Nail Suleiman Khabeev, "The Study of Structure of Roots of Transcendental Equation Using Argument Principle," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 7, pp. 65-68, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I7P507
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