تعيين الاهتزازات العرضانية اللاخطية لقضيب من مادة مرنة فعالة

The goal of the presented research in this paper is finding a unified way to solve cross vibration problems in nonlinear elastic fields with a biological factor. We obtained the equations of cross vibration for elastic systems by using known mathematical models, and then we solved the nonlinear cross harmonic vibration problem for a finite length of effective bar