Abstract
Curved beams are used so much in the arches and railway bridges and equipments for amusement parks. There are few reports about the curved beam with the effects of both the shear deformation and rotary inertias. In this paper, a new finite element model investigates to analyze In-Plane vibration of a curved Timoshenko beam. The Stiffness and mass matrices of the curved beam element was obtained from the force-displacement relations and the kinetic energy equations, respectively. Assembly of the elemental property matrices is simple and without need to transformation matrix because of using the local polar coordinate system. The natural frequencies of curved Euler-Bernoulli beam with large thickness are not sufficiently accurate. In this case, using the curved Timoshenko beam element is necessary. Moreover, the influence of vibration absorber is discussed on the natural frequencies of the curved beam.
Highlights
Static or dynamic analysis of curved structures such as arches, rings, shells of rotating machinery, and railway bridges is one of the common engineering issues
2- the method presents in this paper for obtaining the stiffness matrix somewhat similar to the method presented in [31], this paper considers the shear deformation effects, and the mass matrix will be obtained
Equations (9) and (10), which are the solution of equ– ilibrium and stress-strain equations, they can be used to obtain the stiffness matrix of the curved beam element
Summary
Static or dynamic analysis of curved structures such as arches, rings, shells of rotating machinery, and railway bridges is one of the common engineering issues. Wu et al [21] derived the un-coupled equation of motion for the circumferential displacement of an arch structure to analyse the free in-plane vibration In this research, they obtained a frequency equation by using the compatible equations for the displacements and the equilibrium equations for the forces and moments at each intermediate node and two ends of the entire curved beam. Wu and Chen [22] presented a technique to replace all complex coefficients of the eigenvalue equation by the real ones for the natural frequencies and mode shapes of out-of-plane free vibrations of a uniform curved Euler-Bernoulli beam in various boundary conditions They compared the results with the approximate ones obtained from the finite-element method. By using methods described in [30, 31], stiffness and mass matrices of the curved beam element will be obtained from the force-displa– cement relationships and the kinetic energy equations, respectively. It is similar to formulation was derived by Wu et al [35] for analysing the out-of-plane vibrations of curved beams
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