基于改进Chebyshev级数的层合结构-振动分析新理论
摘要
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 highorder counterpart considered to improve the accuracy of the theory. In each discrete layer, the highorder 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.