Zero and root loci of disturbed spring-mass systems

Area of Science:

• Applied Physics
• Mechanical Engineering
• Vibrational Analysis

Background:

• Particle chain models are crucial in physics and engineering for understanding lattice dynamics, crystal resonances, and bladed disc responses.
• Analyzing the dynamic behavior of these systems, especially with disturbances and damping, is essential for predicting their performance.

Purpose of the Study:

• To analytically investigate the dynamic responses of disturbed chains of springs and masses, including damped systems.
• To identify and prove novel properties concerning the locations of resonances (poles) and anti-resonances (zeros) in the frequency domain.

Main Methods:

• Development of analytical techniques to study the dynamic response of coupled particle chains.
• Frequency domain analysis to locate poles and zeros of displacement.
• Investigation of local disturbances, such as modified springs or dampers.

Main Results:

• Identification of an elliptical region in the frequency-disturbance magnitude plane where zeros are excluded.
• Determination of discrete frequency and disturbance values at which double poles occur.
• Demonstration of the applicability of normalization techniques to complex systems.

Conclusions:

• The study provides significant insights into the vibrational characteristics of disturbed particle chains.
• The findings offer a generalized framework applicable to a wide range of complex physical, chemical, and engineering systems.
• The identified properties of poles and zeros enhance the predictive capabilities for system dynamics.