Influence of Berger hypothesis on the solution of the problem of the nonlinear vibrations of rectangular plates of varying thickness (Q2730529)

This article deals with the problem of nonlinear vibrations of thin flexible rectangular \((0\leq x\leq l, 0\leq y\leq b)\) isotropic freely fixed plate. The author shows that the considered problem is reduced to a nonlinear second order differential equation according either to the Kirchoff-Love or to the Kirchoff-Love-Berger hypotheses. Corresponding to these hypotheses nonlinear differential equations differ from each other only by coefficient in nonlinear term. For comparison of solutions the author uses the parameter \(\delta=100(\nu_1-\nu_2)/\nu_1\), where \(\nu_1\) is a form of frame curve under the Kirchoff-Love hypothesis, \(\nu_2\) is a form of frame curve under the Kirchoff-Love-Berger hypothesis. The numerical calculations are made for rectangular plate with a constant thickness \(h=h_0\) and with varying thickness \(h(x)=h_0(0.5+x)\).