Complex oscillation of the Euler-Bernoulli beams with regard geometrically and physically nonlinear

In this paper, we consider the behavior of the inhomogeneous single-layer beam under alternating load (pressure), distributed uniformly over its entire surface. The research is conducted from the perspective of the qualitative theory of differential equations and nonlinear dynamics. Construct a theory of nonlinear dynamics beams taking into account physical geometric nonlinearity. Physical nonlinearity associated with taking into account the relationship between strain and stress, and geometric nonlinearity associated with the relationship between the deformation and displacement. It accepted the formula of Theodore von Karman. The theory is based on the Euler-Bernoulli hypothesis.