ACCELERATION WAVES IN THE VON KARMAN PLATE THEORY V. VASSILEV and P. DJONDJOROV

where ∆ is the Laplace operator with respect to x and x, D = Eh/12(1 − ν) is the bending rigidity, E is Young’s modulus, ν is Poisson’s ratio, h is the thickness of the plate, ρ is the mass per unit area of the plate middle-plane, δ is the Kronecker delta symbol and ε is the alternating symbol. Here and throughout the work: Greek (Latin) indices range over 1, 2 (1, 2, 3), unless explicitly stated otherwise; the usual summation convention over a repeated index is used and subscripts after a comma at a certain function f denote its partial derivatives, that is f,i = ∂f/∂x , f,ij = ∂f/∂x ∂x , etc. The von Kármán equations (1) describe entirely the motion of a plate, the membrane stress tensor N , moment tensor M, shear-force vector Q, strain tensor E and bending tensor Kαβ being given in terms of w and Φ through the following expressions: N = εεΦ,μν , M αβ = −D {