Beam element matrices derived from Vlasov's theory of open thin‐walled elastic beams

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Abstract
A uniform beam element of open thin‐walled cross‐section is studied under stationary harmonic end excitation. An exact dynamic (transcendentally frequency‐dependent) 14 × 14 element stiffness matrix is derived from Vlasov's coupled differential equations. Special attention is paid to the computational problems arising when coefficients vanish in these equations because of symmetric cross‐section, zero warping stiffness, etc. The dynamic element stiffness matrix is established via a generalized linear eigenvalue problem and a system of linear algebraic equations with complex matrices. A static stiffness matrix is also derived and the associated consistent mass and geometric stiffness matrices are given. Modal masses are evaluated. A FORTRAN program and a numerical example are included.

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