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Size-dependent free vibration analysis of composite laminated Timoshenko beam based on new modified couple stress theory

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Abstract

A micro-scale free vibration analysis of composite laminated Timoshenko beam (CLTB) model is developed based on the new modified couple stress theory. In this theory, a new anisotropic constitutive relation is defined for modeling the CLTB. This theory uses rotation–displacement as dependent variable and contains only one material length scale parameter. Hamilton’s principle is employed to derive the governing equations of motion and boundary conditions. This new model can be reduced to composite laminated Bernoulli–Euler beam model of the couple stress theory. An example analysis of free vibration of the cross-ply simply supported CLTB model is adopted, and an explicit expression of analysis solution is given. Additionally, the numerical results show that the present beam models can capture the scale effects of the natural frequencies of the micro-structure.

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Authors and Affiliations

  1. Key Laboratory of Liaoning Province for CompositeStructural Analysis of Aerocraft and Simulation, Shenyang Aerospace University, Shenyang, Liaoning, 110136, China

    Wan Ji Chen & Xiao Peng Li

Authors
  1. Wan Ji Chen
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  2. Xiao Peng Li
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Correspondence to Wan Ji Chen.

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Contract/grant sponsor: National Natural Sciences Foundation of China (No. 11072156).

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Chen, W.J., Li, X.P. Size-dependent free vibration analysis of composite laminated Timoshenko beam based on new modified couple stress theory. Arch Appl Mech 83, 431–444 (2013). https://doi.org/10.1007/s00419-012-0689-2

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  • DOI: https://doi.org/10.1007/s00419-012-0689-2

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