Effect of boundary conditions on the dynamic instability and non-linear response of rectangular plates, Part I: Theory

Dynamic instability of rectangular plate with an edge crack

“…Takahashi and Konishi [4] are considered the dynamic stability of a rectangular plate under a linearly distributed period load applied two opposite edges. Ostiguy and Evan-Iwanowski [5], and Nguyen and Ostiguy [6] considered the influence of the aspect ratio and boundary conditions on the dynamic instability and non-linear response of rectangular plates. Duffield and Willens [7] presented an analytical and experimental investigation of parametric instability for a stiffened rectangular plate.…”

Dynamic Stability and Nonlinear Parametric Vibrations of Rectangular Plates

“…A thorough investigation conducted by Nguyen and Ostiguy 28 indicate that the boundary conditions also play a crucial role in determining the stability and resonances of rectangular plates. The results are summarized in Table 1.…”

“…For the combination resonance TJ = 0, + Q 3 , stationary values for the specified combination response are given by 28 where A is the decrement of linear damping, as defined previously. The amplitude of vibration associated with the first mode is determined first by Eq.…”

“…More recently, Ostiguy and Nguyen 1127 have examined the effect of internal resonances and the possibility of simultaneous and combination resonances on the response of parametrically excited rectangular plates. In 1989, Nguyen and Ostiguy 28 have presented the results of an analytical and experimental investigation of the effect of boundary conditions on the dynamic stability and nonlinear parametric response of rectangular plates. Other analytical studies were published by The first experimental studies on plates were conducted by Somerset and Evan-Iwanowski 35 and they pertain mainly to the large amplitude, nonlinear parametric response of simply supported square plates.…”