Variable-Thickness Sandwich Plates: Beam-Like Bending and Vibration of Plates Symmetric About a Middle Surface

摘要

A theory is presented for the beam-like bending and harmonic vibration of linearly elastic sandwich plates that have thickness variation in one direction (the direction of bending) and are symmetric about a middle surface. The theory has the following main parts: (1) a low-order system of differential equations which yields exact solutions by a double integration method analogous to that of conventional beam theory, (2) a higher-order system of differential equations (analogous to the fourth-order differential equation of conventional beam theory) which, in a simple finite-difference form, serves as the basis for harmonic vibration analysis, (3) the total potential energy (TPE) expression, which serves as the basis for static analyses by the finite-difference energy method, and (4) the incorporation of Lagrangian multipliers into the finite-difference energy method permitting the direct evaluation of the reactions associated with any redundant constraints.