Non-linear non-planar vibrations of geometrically imperfect inextensional beams, Part I: Equations of motion and experimental validation

摘要: Abstract The non-linear equations and boundary conditions of non-planar (two bending one torsional) vibrations inextensional isotropic geometrically imperfect beams (i.e. slightly curved twisted beams) are derived using the extended Hamilton's principle. assumptions Euler–Bernoulli beam theory used. order magnitude natural geometric imperfection is assumed to be same as first amplitude. Although small, in contrast case straight perfect beams), this study shows that vibration linearly coupled have linear quadratic terms addition cubic terms. Also, near-square or near-circular beams, coupling between lateral torsional exist. Furthermore, a problem parametric excitation changes mixed external beams. validity model investigated existing experimental data.