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This paper focuses on the dynamic response, mainly dynamic amplification factors (DAFs), of partial-interaction composite beams (PICBs) based on the Timoshenko beam theory (TBT). By assuming that each sub-beam behaves as an independent Timoshenko beam, the governing differential equations of motion of the PICBs are derived under the action of dynamic load. The natural frequencies and modal shapes for simply supported PICBs are also extracted. For decoupling the governing differential equations of motion, the orthogonality property of two distinct vibration modes is checked and applied for further analysis. The modal superposition method is then utilized to derive the analytical expressions of transverse deflection, interfacial shear slip, and normal stresses of the PICBs subjected to the moving load. Finally, two test beams are organized to validate the proposed methodology. For this purpose, the results which are calculated by ANSYS and obtained from available methods are appropriately compared. The effects of shear connector stiffness and speed of the moving load on the DAFs of the PICB acted upon by the moving constant load are discussed.

The rotary inertia defined by Timoshenko to account for the angular velocity effect in flexural vibration of beams has been questioned by some researchers in recent years, and it caused some confusions. This paper discusses the appropriate rotary inertia in Timoshenko beam theory (TBT) and evaluates the influence of the two forms of the rotary inertia on the prediction of the higher-mode frequencies of transversely vibrating beams. Based on the theory of elasticity and variational principle, this work shows that the rotary inertia in the original TBT, defined in terms of the rotation of beam cross-section induced by bending deformation, is variational consistent and is capable of yielding good results of the phase velocities of transversely vibrating beams even in the case where the wavelength of vibrating beams approaches the beam height. On the other hand, the so-called corrected TBT, in which the rotary inertia is defined in terms of the slope of beam deflection, is neither variational consistent nor accurate when the wavelength of vibrating beams approaches the beam height. Therefore, the rotary inertia in TBT defined by Timoshenko is correct and should be used in the dynamic analysis of beams.