Thermo-viscoelastic analysis of high-frequency motions of thin plates
Using the three-dimensional thermo-viscoelastodynamics, the authors derive a hierarchic system of two-dimensional equations 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 Laplace-transformed field variables for fundamental equations of linear, non-isothermal, non-polar and non-local three-dimensional theory. Next a generalized versions of Mindlin's hypothesis for elastic plates is introduced for displacement and temperature fields. Then the hierarchic system of plate equations is systematically derived by means of the differential variational principle. The hierarchic system of two-dimensional equations governs the extensional, thickness-shear, flexural and torsional as well as coupled motions of thermoviscoelastic thin plates of uniform thickness at both low and high frequencies. Finally, the authors study certain cases involving special geometry, motions and materials, and investigate the uniqueness of solutions of the hierarchic system of plate equations.
three-dimensional thermo-viscoelastodynamics
scientific article; zbMATH DE number 1506072
scientific article