In-plane free vibration and stability of loaded and shear-deformable circular arches

摘要: The first known equations governing vibrations of preloaded, shear-deformable circular arches are derived according to a variational principle for dynamic problems concerning an elastic body under equilibrium initial stresses. three partial differential with variable coefficients. solved statically preloaded uniformly distributed vertical loading, by obtaining static, closed-form solution and analytical from series solutions stiffness matrices. Convergence accurate results is obtained increasing the number elements or both terms in Taylor expansion Graphs non-dimensional frequencies buckling loads presented clamped arches. They clarify effects opening angle thickness-to-radius ratio on vibration loads. static deformations also investigated. This work compares proposed those classical theory neglecting shear deformation.