An approximate theory for high-frequency vibrations of elastic plates

摘要: Abstract Two-dimensional equations of successively higher orders approximation for elastic, isotropic plates are deduced from the three-dimensional theory elasticity by a series expansion in terms simple thickness-modes infinite plates. For each order zeroth up to fourth, kinetic and strain energy densities, stress-strain relations displacement motion both flexural extensional vibrations presented. Dispersion curves real imaginary as well complex wave numbers an plate explored detail compared with solution Rayleigh-Lamb frequency equation theory.