## Abstract

For the laminated composite beams without elastic symmetry about mid-plane, the in-plane and out-of-plane bending deformation would be coupled together, and the transverse shear deformation would be also significantly induced, especially for thick beams. To implement the associated free vibration analysis for laminated composite beam with coupled stretching-bending and transverse shear deformation, based upon the first order shear deformation beam theory we construct the displacement-based governing partial differential equations in a simple matrix form. Through the separation of spatial and time variables and by taking the time variation as a harmonic function with unknown frequency, the governing equations can be reorganized into ordinary differential equations of spatial functions. The spatial displacement functions can be derived through the use of state-space approach and are expressed in terms of matrix exponential related to the unknown frequency. By enforcing the boundary conditions in the obtained spatial functions, the eigen-relation for solving the natural frequency and corresponding mode shape can be finalized. The zero of determinant of coefficient matrix in eigen-relation would then determine the natural frequency. Since such eigen-relation is highly transcendental, finding exact values of natural frequency may be extremely difficult. In this study, the bisection method is employed to find the natural frequency, and the corresponding nontrivial mode shape is solved through the least-squares technique. To investigate the influences of boundary conditions, stacking sequence and beam width/thickness on the natural frequencies, several numerical examples are demonstrated. Without any limitation of the layer anisotropy and stacking sequence in our formulation, the presented solutions of free vibration analysis are widely applicable and powerful, especially for general arbitrarily laminated composite thick beams.

Original language | English |
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Title of host publication | Proceedings of the 29th International Congress on Sound and Vibration, ICSV 2023 |

Editors | Eleonora Carletti |

Publisher | Society of Acoustics |

ISBN (Electronic) | 9788011034238 |

Publication status | Published - 2023 |

Event | 29th International Congress on Sound and Vibration, ICSV 2023 - Prague, Czech Republic Duration: 2023 Jul 9 → 2023 Jul 13 |

### Publication series

Name | Proceedings of the International Congress on Sound and Vibration |
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ISSN (Electronic) | 2329-3675 |

### Conference

Conference | 29th International Congress on Sound and Vibration, ICSV 2023 |
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Country/Territory | Czech Republic |

City | Prague |

Period | 23-07-09 → 23-07-13 |

## All Science Journal Classification (ASJC) codes

- Acoustics and Ultrasonics