TABLE OF CONTENTS Flat rectangular plates with restrained normal displacement at the four edges exhibit a strong hardening-type nonlinearity for vibration amplitude of the order of the plate thickness. In order to have a behavior correctly described by a linear theory, the vibration amplitude of thin plates must be of the order of 1/10 of the thickness, or smaller. In-plane constraints largely enhance the nonlinear behavior; consequently, in-plane stretching is produced for large-amplitude deflection, differently from what is stated for linear theory.
Rectangular plates with normal displacement that is not restrained at all the edges can present a linear behavior for larger vibration amplitude. This is the case of the cantilever plate (clamped at one edge and free on the other three edges). In fact, quite large displacement w can be associated with very small rotations ? w/ ? x and ? w/ ? y for these boundary conditions, so that nonlinear terms in the strains can be neglected.
Geometric imperfections play an important role; they transform the flat plate in a curved panel (even if very shallow), which exhibits an initial weak softening behavior, turning to strong hardening nonlinearity for larger vibration amplitude.
In this chapter, the linear vibrations of simply supported rectangular plates are first addressed; numerical and experimental results are presented. Then, nonlinear forced vibrations of plates with different boundary conditions are studied by using the Lagrange equations of motion and the von K rm n theory. The effect of geometric imperfections is investigated. Numerical...
