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^{2}

^{3}

^{4}

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^{4}

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^{3}

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^{1}

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The effects of stacking sequences of composite laminated optical beams on free vibration frequencies are investigated using two methods: the Boubaker Polynomials Expansion Scheme (pbes) and the Differential Quadrature Method (dqm). In the last decades, these two techniques have been separately performed for obtaining accurate numerical solutions to several initial boundary value problems (Vo et al. 2010, Li et al. 2008, Chen 2003, Hu et al. 2008, Karami et al. 2003, Malekzadeh et al. 2004, Khare et al. 2004, Della and Shu 2005, Ramtekkar et al. 2002, Adam 2003). Conjointly yielded results are compared and discussed.

Free optical vibration of generally laminated beams has been of increasing interest in the last decades’ literature [

Many other analytical methods of analysis have been used to study the vibration of plates, shells, and beams [

In this paper, a model on the vibration analysis of laminated composite beam has been developed and studied using two resolution protocols. For the beam used, it is assumed that Bernoulli-Euler hypothesis is valid. The results obtained by the two methods are compared. It has been concluded that all of the results are very close to each other.

The normal stress in

Cantilever composite laminated optical beam.

The analytical solution of (

DQM method is carried out for the approximate solution of the characteristic value problem in (

A one-dimensional quadrature grid with adjacent

The BPES [

Consequently, it comes for (

Integrating, for a given value of

Determining the set of coefficients where

Deducing the corresponding frequency using (

Incrementing

Ranging the obtained frequencies.

Natural frequencies of the symmetric laminated composite cantilever beam have been estimated using the Boubaker Polynomials Expansion Scheme (PBES) and the Differential Quadrature Method (DQM), and for parameters values indicated in Table

Geometry and material properties of the composite materials.

Descriptions | Present | Unit |
---|---|---|

320 | mm | |

36 | mm | |

8 | mm | |

26950 | MPa | |

21800 | MPa | |

7540 | MPa | |

0.15 | ||

^{3}) | kg/m^{3} |

Comparison of BPES and DQM frequencies for cross-ply laminated beam.

The natural frequency alteration as a direct result of the change in the stacking sequence causes resonance if the changed frequency becomes closer to the working frequency. Hence, selection of the stacking sequences in the laminated composite beams has to be outlined.

This work deals with two protocols for the calculation of natural frequency of the symmetric laminated composite cantilever beam. Calculations performed by means of Boubaker Polynomials Expansion Scheme PBES and Differential Quadrature Method DQM yielded coherent and similar results.

All considered results have been seen to be in accordance with each other. Changes in the stacking sequence, which likely allow tailoring of the material to achieve desired natural frequencies and respective mode shapes without changing its geometry, are the subject of following studies.