Low-velocity impact response of agglomerated FG-CNTRC beams with general boundary conditions using Gram-Schmidt-Ritz method

作者：Wang, Yuewu^*; Zhang, Zhipeng; Chen, Jie; Fu, Tairan^*

来源：Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2022, 44(11): 537.

DOI：10.1007/s40430-022-03843-x

• FG-CNTRC beam
• Agglomeration effect
• Low-velocity impact
• Damped response
• Hyperbolic shear deformation theory
• Gram-Schmidt-Ritz method

This paper is determined to investigate the low-velocity impact responses of functionally graded carbon nanotube reinforced composite viscoelastic beams with general boundary constraints. The beams considered are constructed by a multiplayer beam model with layer-wise CNT weight fraction in each individual layer in the thickness direction. The Mori-Tanaka micromechanics model with inclusions of CNT agglomerations is used to determine the effective elastic moduli and Poisson's ratio of nanocomposites. The viscoelastic properties are assumed based on Kelvin-Voigt theory. An impactor drops vertically on the upper surface of the beams, and the contact force between impactor and beam is simulated based on the Hertz contact law. A new hyperbolic shear deformation theory in conjunction with the artificial spring method of quantifiably accounting for the elastic boundary conditions is developed to present energy expressions of the system. Governing equations of motions are derived by means of Lagrange method with the help of Gram-Schmidt process that used to produce admissible functions in a general orthogonal polynomial form. The low-velocity impact responses are solved using the Newmark-beta method in time domain. Numerical examples are carried out to reveal the effects of CNT weight fractions, CNT distribution patterns, CNT agglomeration and artificial spring parameters as well as the impactor velocities on the damped dynamic responses of the beams.

• 单位
  清华大学; 北京工业大学