Dynamic response of plane anisotropic beams with shear deformation

The effect of constitutive coupling of stretching, bending, and transverse shearing on the free vibration of anisotropic cantilever beams as well as simply supported beams with narrow rectangular cross sections was investigated. To this end, a Timoshenko-type beam theory was constructed for plane deformation of anisotropic beams by incorporating Reissner's semicomplementary energy function in a Hamilton-type principle. By using the resulting beam equations, natural frequencies and mode shapes were computed. The numerical results illustrate the importance of correctly accounting for anisotropy in obtaining natural frequencies and show dramatic normal-shear coupling effects for mode shapes.