Abstract
In this article, flexural vibration and its power flow of an axially loaded beam with arbitrary boundary and non-uniform elastic foundation are analyzed via energy principle in conjunction with Rayleigh–Ritz procedure. A general solution is assumed as a modified version of Fourier series supplemented with boundary-smoothing auxiliary terms. Effects of axial load and elastic foundation of the beam are taken into account in terms of potential energy in system Lagrangian. Critical load of this axially loaded beam is obtained under elastic boundary condition and non-uniform foundation. Numerical examples are then presented to demonstrate the reliability and effectiveness of the established model by comparing results with those available in literature or calculated using finite element method. Results show that the current model can make an accurate dynamic analysis for the elastically restrained beam with axial load and non-uniform elastic foundation. Influence of some important factors, including boundary restraint, axial load, and non-uniform foundation, on the vibration characteristics and power flow transmission are studied and addressed. It is found that the supporting condition has a significant influence on power flow distribution across the whole beam, in which the shear force component plays a dominant role for the power flow transmission.
Highlights
As one of the basic structural elements, beam structure has been widely used in almost every field of engineering occasions
Potential energy of beam with axial load and elastic foundation is formulated in system Lagrangian, which allows the analysis of current model through the minimization with respect to all the unknown coefficients
Results show that the current model can make an accurate prediction of modal characteristics of such beam structure, and the axial load and elastic foundation has a significant influence on the beam vibration characteristics and critical load
Summary
As one of the basic structural elements, beam structure has been widely used in almost every field of engineering occasions. For the propulsion system of ships, motor vehicle, and aircraft, vibration analysis of the propulsion shafting is usually performed through the simplification into beam model with elastic foundation and axial load. A good understanding on its dynamic characteristics will be of fundamental significance for the efficient design and operation of such complex system. For this reason, a lot of research effort has been devoted to the flexural vibration analysis of beam structures resting on elastic foundation and/or subjected to axial load.[1,2,3].
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