Vibration of pure bending of composite prismatic beams with constant cross section and structural non-uniformity

Abstract

Differential equation for transverse bending vibrations of prismatic beam of finite length for homogeneous linear elastic and viscoelastic uniformly aging materials was obtained. The solution of this equation is a function of Weber. The solution is generalized to the case of flexural vibrations of structurally inhomogeneous composite bodies. The natural frequencies of bending vibrations of prismatic beam depending on the modulus of elasticity for a homogeneous linear elastic material, as well as the instantaneous elastic modulus and creep kernel for hereditary viscoelasticity equations uniformly aging material also were obtained.