Examining the behavior of a two-connected-spring pendulum according to non-resonance and resonance conditions DOI Creative Commons
T. S. Amer, M. A. Elhagary,

S.S. Hassan

et al.

Journal of low frequency noise, vibration and active control, Journal Year: 2024, Volume and Issue: unknown

Published: Nov. 27, 2024

This paper focuses on the planar forced oscillations of a particle linked to its support point through system comprising two nonlinear springs arranged in series with viscous dampers. The motion this is restricted being an elliptic route. Three degrees-of-freedom (DOF) characterize system’s motion, explained by differential equations (DEs) and another algebraic equation derived using Lagrange’s equations. traditional method multiple-time scales (MMTS) applied context time realm. dynamics damped explored work, highlighting non-resonant conditions along distinct external resonances. Furthermore, stationary periodic states influenced resonances are examined, stability each case evaluated. asymptotic solutions controlling solved up third approximation. classification resonance cases based second order approximate solutions. Therefore, solvability criteria modulation (ME) obtained. Routh–Hurwitz (RHCs) serve as basis for assessing instability criteria. A discussion graphical representations histories, frequency response curves (FRC), regions provided demonstrate beneficial effects different physical parameter inputs performance. obtained outcomes can improve performance spring-based mechanical systems like vibrational isolation devices, shock absorbers, suspension mechanisms. Additionally, they have potential enhance control robotic limbs aircraft landing gear systems, ensuring better stress absorption stability.

Language: Английский

Modified Lindstedt-Poincare transformation for fractal resonance approach in vibration 2-DOF heterogeneous system DOI Creative Commons
Yusry O. El‐Dib, Haifa A. Alyousef

Journal of low frequency noise, vibration and active control, Journal Year: 2025, Volume and Issue: unknown

Published: April 17, 2025

This study looks at the dynamics of a two-degree-of-freedom system subjected to periodic force and describes it with fractal differential derivatives. The applies harmonic equivalent linearized approach (HELA) convert nonlinear equations into linear systems, allowing for derivation analytical solutions extensive numerical comparison. explores use techniques in capturing complex dynamics, particularly resonance scenarios. It proposes novel compares methods, demonstrating high agreement. research also investigates phenomenon, providing visual evidence, enhancing our understanding its significance stability behavior.

Language: Английский

Citations

0
Examining the behavior of a two-connected-spring pendulum according to non-resonance and resonance conditions DOI Creative Commons
T. S. Amer, M. A. Elhagary,

S.S. Hassan

et al.

Journal of low frequency noise, vibration and active control, Journal Year: 2024, Volume and Issue: unknown

Published: Nov. 27, 2024

This paper focuses on the planar forced oscillations of a particle linked to its support point through system comprising two nonlinear springs arranged in series with viscous dampers. The motion this is restricted being an elliptic route. Three degrees-of-freedom (DOF) characterize system’s motion, explained by differential equations (DEs) and another algebraic equation derived using Lagrange’s equations. traditional method multiple-time scales (MMTS) applied context time realm. dynamics damped explored work, highlighting non-resonant conditions along distinct external resonances. Furthermore, stationary periodic states influenced resonances are examined, stability each case evaluated. asymptotic solutions controlling solved up third approximation. classification resonance cases based second order approximate solutions. Therefore, solvability criteria modulation (ME) obtained. Routh–Hurwitz (RHCs) serve as basis for assessing instability criteria. A discussion graphical representations histories, frequency response curves (FRC), regions provided demonstrate beneficial effects different physical parameter inputs performance. obtained outcomes can improve performance spring-based mechanical systems like vibrational isolation devices, shock absorbers, suspension mechanisms. Additionally, they have potential enhance control robotic limbs aircraft landing gear systems, ensuring better stress absorption stability.

Language: Английский

Citations

1