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The Very‐Low Shear Modulus of Multi‐Walled Carbon Nanotubes Determined Simultaneously with the Axial Young's Modulus via in situ Experiments

The natural frequencies (f) as a function of the length (L) of single, multi‐walled carbon nanotubes (CNTs) are measured using the electric‐field‐induced resonance method together with the “nanoknife” technique for cutting nanotubes to the desired length. The experimental f‐L data for short CNTs are found to be adequately described by the Timoshenko beam model, but not by the widely‐used Euler‐Bernouilli beam model. The failure of the Euler‐Bernouilli beam model is due to its neglect of the significant effect of shear deformation caused by the extremely‐anisotropic mechanical properties of CNTs. The axial Young's modulus and radial shear modulus of CNTs are obtained simultaneously through fitting the experimental f‐L data with the Timoshenko beam model.