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This and the next 2 images are from:
Qingshan Wang, Dongyan Shi, Fuzhen Pang and Qian Liang,
“Vibrations of composite laminated circular panels and shells of revolution with general elastic boundary conditions via Fourier-Ritz method”, Curved and Layered Structures, Vol. 3, No. 1, pp 105-136, April 2016, https://doi.org/10.1515/cls-2016-0010
ABSTRACT: A Fourier-Ritz method for predicting the free vibration of composite laminated circular panels and shells of revolution subjected to various combinations of classical and non-classical boundary conditions is presented in this paper. A modified Fourier series approach in conjunction with a Ritz technique is employed to derive the formulation based on the first-order shear deformation theory. The general boundary condition can be achieved by the boundary spring technique in which three types of liner and two types of rotation springs along the edges of the composite laminated circular panels and shells of revolution are set to imitate the boundary force. Besides, the complete shells of revolution can be achieved by using the coupling spring technique to imitate the kinematic compatibility and physical compatibility conditions of composite laminated circular panels at the common meridian with theta = 0 and theta=2pi. The comparisons established in a sufficiently conclusive manner show that the present formulation is capable of yielding highly accurate solutions with little computational effort. The influence of boundary and coupling restraint parameters, circumference angles, stiffness ratios, numbers of layer and fiber orientations on the vibration behavior of the composite laminated circular panels and shells of revolution are also discussed.
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