Vibration Behaviour Of In-plane Loaded Thin Rectangular Plates With Initial Geometrical Imperfections

The effect of in-plane loading on the natural frequencies of simply supported thin rectangular plates with initial geometrical imperfection is investigated theoretically and experimentally. It is shown that the natural frequencies depend on applied in-plane load, initial geometrical imperfection and the in-plane boundary conditions.;In the theoretical analysis, the natural frequencies, out-of-plane static displacements and in-plane stress distribution are calculated using the Rayleigh-Ritz minimization technique. A concept of 'connection coefficients' has been used to reduce the computational work. In this concept, the relationship between the out-of-plane and in-plane displacement coefficients are first determined by solving the equations resulting from the minimization of the total potential energy with respect to the in-plane displacement coefficients. This relationship is then substituted into the equations obtained by minimizing the total potential energy with respect to the out-of-plane displacement coefficients.;In the experimental side of the work, tests were carried out on several thin (thickness ranging from 0.56 mm to 1.15 mm) mild steel plates (300 mm x 250 mm). Uniaxial in-plane loading was applied through two 'V' grooved edge beams. The other two edges were supported between two rows of ball bearings placed in 'V' grooves, carefully adjusted to minimize the friction along these edges.;The agreement between the measured and calculated values of natural frequencies, out-of-plane central displacements and static strain distribution is very good. An interesting observation from the result is that a simple approximate linear relationship between a load-frequency parameter (involving the fundamental natural frequency and the state of in-plane stress) and the square of the central deflection is obtained. Further experimental and theoretical work in this field is strongly recommended.