The dynamic stiffness matrix for the spatially coupled free vibration analysis of thin-walled curved beam with non-symmetric cross section on two-types of elastic foundation is newly presented based on the power series method using the technical computing program Mathematica. For this, the elastic strain energy considering the axial/flexural/torsional coupled terms and the kinetic energy including the rotary inertia effect and the energy due to the elastic foundation are introduced. Then, equations of motion and force-displacement relations are derived from the energy principle and explicit expressions for displacement parameters are derived based on power series expansions of displacement components. Finally, the exact dynamic stiffness matrix is determined using force-displacement relations. In order to demonstrate the validity and the accuracy of this study, the natural frequencies of thin-walled curved beams with mono-symmetric and non-symmetric cross sections are evaluated and compared with the analytical solutions and finite element solutions using Hermitian curved beam elements and ABAQUS’s shell elements. In addition, some results by the parametric study are reported.
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