Akademik Veri Yönetim Sistemi
ACTA MECHANICA, cilt.143, ss.91-111, 2000 (SCI-Expanded)
Within the frame of the 3D-theory of thermo-viscoelastodynamics, a hierarchic system of 2D-equations is consistently derived in invariant differential and variational forms for the analysis of high-frequency motions of thin plates. First, a differential type of variational principles is presented in terms of the Laplace transformed field variables for the fundamental equations of linear, non-isothermal, nonpolar and non-local, 3D-theory. Next, a generalized version of Mindlin's hypothesis for elastic plates is introduced for the displacement and temperature fields. Then, the hierarchic system of plate equations is systematically established by means of the differential variational principle. The hierarchic system of 2D-equations governs the extensional, thickness-shear, flexural and torsional as well as coupled motions of thermo-viscoelastic thin plates of uniform thickness at both low- and high-frequencies. Lastly, certain cases involving special geometry, motions and material are indicated. Also, the uniqueness is investigated in solutions of the hierarchic system of plate equations.