Transverse vibration of nematic elastomer Timoshenko beams

Area of Science:

• Materials Science
• Mechanical Engineering
• Polymer Physics

Background:

• Nematic elastomers (NEs) are anisotropic viscoelastic materials exhibiting dynamic soft elasticity.
• Understanding the vibrational behavior of NE structures is crucial for their application.
• Timoshenko beam theory is a suitable model for analyzing the transverse vibration of thicker beams.

Purpose of the Study:

• To investigate the transverse vibration of a nematic elastomer Timoshenko beam.
• To derive the governing equation of motion for NE Timoshenko beams.
• To analyze the influence of material properties and director orientation on vibration characteristics.

Main Methods:

• Application of linear viscoelasticity theory for nematic elastomers.
• Derivation of the governing equation of motion for transverse vibration.
• Utilizing complex modal analysis to determine natural frequencies and decrement coefficients.

Main Results:

• The study successfully derived the equation of motion for NE Timoshenko beams.
• Complex modal analysis yielded natural frequencies and decrement coefficients.
• Nematic director rotation, rubber relaxation time, and director rotation time were found to significantly impact vibration characteristics.

Conclusions:

• The dynamic performance of NE Timoshenko beams is sensitive to director initial angle and relaxation times.
• These sensitivities offer potential for intelligent control of the dynamic behavior of NE beams.
• The research provides a foundation for designing and controlling vibration in nematic elastomer structures.