Two New Models for Dynamic Linear Elastic Beams and Simplifications for Double Symmetric Cross-Sections

We present two new models for dynamic beams deduced from three dimensional theory of linear elasticity. The first model is virtual work considered small beam sections. For the second model, we suppose a Taylor-Young expansion displacement field up to fourth order in transverse dimensions beam. consider Fourier series considering Neumann lateral boundary conditions together with dynamical equations, obtain system fifteen vector equations coefficients unknown field. fold symmetric cross sections commonly used (for example circular, square, rectangular, elliptical…), unique decomposition any three-dimensional loads proposed and symmetries these introduced. theories, show that initial problem decouples into four subproblems. an orthotropic material, subproblems are completely independent. monoclinic coupled independent other also give detailed expression when approximation model.