Force appropriation of nonlinear structures

Area of Science:

• Mechanical Engineering
• Structural Dynamics
• Nonlinear Dynamics

Background:

• Nonlinear normal modes (NNMs) are crucial for modeling and understanding nonlinear structures.
• Experimental identification of NNMs often relies on a phase quadrature condition.
• Single-input force excitation is a common practical approach in experimental modal analysis.

Purpose of the Study:

• To investigate the accuracy of the phase quadrature condition for identifying NNMs.
• To analyze the impact of single-force excitation on NNM identification.
• To propose improved methods for accurate NNM identification in nonlinear structures.

Main Methods:

• Studied a clamped-clamped cross-beam with closely spaced modes.
• Applied a single input force for excitation.
• Analyzed energy transfer between system modes.
• Evaluated the phase quadrature condition's accuracy.

Main Results:

• The commonly used quadrature condition can yield significantly different results from true NNMs.
• Inaccuracies are pronounced with single-force excitation.
• Energy transfer analysis helps predict regions of quadrature condition inaccuracy.
• The study highlights limitations of the quadrature condition in specific scenarios.

Conclusions:

• The phase quadrature condition is not universally accurate for NNM identification, particularly with limited excitation.
• Energy transfer analysis provides insights into the limitations of the quadrature method.
• Optimal excitation strategies, including the number and location of input forces, are critical for accurate NNM identification.