A finite-element analysis is carried out for small-amplitude free vibration of laminated, anisotropic, rectangular plates having arbitrary boundary conditions, finite thickness shear moduli, rotatory inertia, and bimodulus action (different elastic properties depending upon whether the fiber-direction strain is tensile or compressive). The element has five degrees of freedom, three displacements and two slope functions, per node. An exact closed-form solution is also presented for the special case of freely supported single-layer orthotropic and two-layer, cross-ply plates. This solution provides a benchmark to evaluate the validity of the finite-element analysis. Both solutions are compared with numerical results existing in the literature for special cases (all for ordinary, not bimodulus, materials), and good agreement is obtained.
Vibration of Thick Rectangular Plates of Bimodulus Composite Material
Bert, C. W., Reddy, J. N., Chao, W. C., and Reddy, V. S. (June 1, 1981). "Vibration of Thick Rectangular Plates of Bimodulus Composite Material." ASME. J. Appl. Mech. June 1981; 48(2): 371–376. https://doi.org/10.1115/1.3157625
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