Stability of parametric vibrations of laminated composite plates
The dynamic stability of laminated composite plates subjected to arbitrary periodic loads is studied based on the first-order shear deformation plate theory. The in-plane load is taken to be a combination of periodic biaxial and bending stress. A set of second-order ordinary differential equations with periodic coefficients of Mathieu-Hill type is formed to determine the regions of dynamic instability based on Bolotin's method. Numerical results reveal that the dynamic instability is significantly affected by the modulus ratio, number of layer, static and dynamic load parameters. The effects of various important parameters on the instability region and dynamic instability index are investigated.
Initially Stressed Mindlin Plates
Equations of motion for a transversely isotropic plate in a general state of nonuniform initial stress where the effects of transverse shear and rotary inertia are included are derived by two methods. The first method is to perturb the nonlinear equations of elasticity by an incremental deformation. The resulting equations are linearized and integrated through the thickness of the plate to obtain the plate equations. The second method is to derive nonlinear equations of motion for a thick plate variationally by Hamilton's principle. These equations are then perturbed and suitably linearized to obtain the same equations as were obtained by the first method. A reduced set of equations for a thin plate are also given. Finally, the thick plate equations are solved for a simply supported rectangular plate in a state of uniform compressive stress plus a uniform bending stress both acting in the same direction.
Optical rotatory dispersion and absolute configuration—III
Abstract Optical rotatory dispersion measurements on pyrrolidine, piperidine, and tetrahydro-isoquinoline alkaloids indicate that the absolute configuration of the α-asymmetric center may be assigned directly from the dispersion curve, provided either that the nitrogen atom is not protonated, or that the compound contains a chromophore absorbing above 200 mμ.