A New Layerwise Theory for Vibration Analysis of Laminated Structures Based on Modified Chebyshev Polynomials

YE Tiangui; JIN Guoyong; LIU Zhigang

doi:10.21656/1000-0887.390098

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YE Tiangui, JIN Guoyong, LIU Zhigang. A New Layerwise Theory for Vibration Analysis of Laminated Structures Based on Modified Chebyshev Polynomials[J]. Applied Mathematics and Mechanics, 2019, 40(1): 58-74. doi: 10.21656/1000-0887.390098

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A New Layerwise Theory for Vibration Analysis of Laminated Structures Based on Modified Chebyshev Polynomials

doi: 10.21656/1000-0887.390098

College of Power and Energy Engineering, Harbin Engineering University,Harbin 150001, P.R.China

Funds: The National Natural Science Foundation of China（51709066；51775125）；China Postdoctoral Science Foundation（2017M621252）

Received Date: 2018-03-29
Rev Recd Date: 2018-05-19
Publish Date: 2019-01-01

Abstract

Abstract

A new layerwise theory for vibration analysis of laminated structures based on modified Chebyshev polynomials was proposed. The displacement field in each discrete layer was composed of a global linear component introduced under the layerwise strategy and a local highorder counterpart considered to improve the accuracy of the theory. In each discrete layer, the highorder displacement field distribution through the laminate thickness was determined with the modified Chebyshev polynomials. Therefore, the proposed theory offers an easy analysis operation to realize different modeling precision requirements only by changing the truncation order without the need for reprogramming from case to case. The theory also has the ability of achieving arbitrary modeling precision according to practical requirements. Based on the proposed theory, the general spectral method was combined to formulate the vibration equations of laminated beams, plates and shells. To test the efficiency and accuracy of the present theory, dynamic properties of laminated beams, plates and shells with different dimensions, boundary conditions and lamination schemes were studied. The numerical results obtained from the present theory are in good agreement with exact elasticity solutions published previously.
- modified Chebyshev polynomials,
- laminated structure,
- high-order layerwise theory,
- vibration

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References(30)

References

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