Dynamic Characteristics of a Small-Size Beam Mounted on an Accelerating Structure

Area of Science:

• Mechanical Engineering
• Solid Mechanics
• Vibrational Analysis

Background:

• High-speed moving structures present unique challenges for component vibration analysis.
• Small-sized beams are crucial components in various advanced engineering applications.
• Understanding nonlinear dynamics is essential for ensuring structural integrity and performance.

Purpose of the Study:

• To investigate the nonlinear vibration of a small-sized beam under high-speed moving conditions.
• To analyze the influence of small-size effects using modified coupled stress theory.
• To explore the impact of various parameters on the beam's dynamic response and stability.

Main Methods:

• Derivation of the equation of motion using coordinate transformation.
• Incorporation of small-size effects via modified coupled stress theory.
• Discretization using the Galerkin method and analysis via bifurcation diagrams.

Main Results:

• Nonlinear hardening behavior observed with increasing applied force.
• Response transitions from chaotic to period-doubling to stable oscillations with increasing length scale parameter.
• Axial acceleration of the moving structure significantly impacts stability and nonlinearity.

Conclusions:

• The study provides critical insights into the complex nonlinear dynamics of small-sized beams in moving structures.
• Findings are crucial for designing robust systems operating under dynamic and high-speed conditions.
• The modified coupled stress theory effectively captures small-size effects in nonlinear vibration analysis.