| The elastic behavior of prismatic nonhomogeneous, anisotropic beams with arbitrary cross-sectional geometry is studied. A basis for development of improved 1-D theory is the dispersion curve analysis. A computer code is developed to calculate the dispersion curves, as well as corresponding mode shapes. Use of this code provides benchmark results for the testing of any existing 1-D theory, as well facilitating the construction of a new 1-D theory. End effects for prismatic anisotropic beams with thin-walled, open cross sections are analyzed by the variational-asymptotic method. The decay rates for disturbances at the ends of prismatic beams are evaluated, and the most influential end disturbances are incorporated into a refined beam theory. Thus, the foundations of Vlasov's theory, as well as restrictions on its applicability, are obtained from the variational-asymptotic point of view. The asymptotically correct generalization of Vlasov's theory for static behavior of anisotropic beams is presented. Comparisons with a numerical 3-D analysis are provided, showing that the present approach gives the closest agreement of all published theories. The outline for construction of general dynamic model for high-frequency vibrations based on the developed in the thesis tools is further presented. |
