Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 Pakdemirli Mehmet

2 2024

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Effect of angular speed variations on the nonlinear vibrations of a rotational spring-mass system

Pakdemirli Mehmet

International Journal of Applied Mechanics and Engineering

2024

Vol. 29, no. 1

130--141

A rotating spring-mass system is considered using polar coordinates. The system contains a cubic nonlinear spring with damping. The angular velocity harmonically fluctuates about a mean velocity. The dimensionless equations of motion are derived first. The velocity fluctuations resulted in a direct and parametric forcing terms. Approximate analytical solutions are sought using the Method of Multiple Scales, a perturbation technique. The primary resonance and the principal parametric resonance cases are investigated. The amplitude and frequency modulation equations are derived for each case. By considering the steady state solutions, the frequency response relations are derived. The bifurcation points are discussed for the problems. It is found that speed fluctuations may have substantial effects on the dynamics of the problem and the fluctuation frequency and amplitude can be adjusted as passive control parameters to maintain the desired responses.

Complex exponential method for solving partial differential equations

Pakdemirli Mehmet

Engineering Transactions

2024

Vol. 72, iss. 4

461--474

For constant-coefficient linear partial differential equations solvable by separation of variables, an alternative solution method is proposed. The method employs complex exponential functions to find exact analytical solutions. Examples include the heat conduction equation, homogenous and non-homogenous wave equations, and the beam vibration equation. The method can be effectively used for partial differential equations (PDEs) whose solutions can be expressed as a product of harmonic and/or exponential type series.