Free vibration of a curved beam

Petyt, M.; Fleischer, C.C.

doi:10.1016/0022-460x(71)90627-4

Cited by 114 publications

(56 citation statements)

References 10 publications

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“…Because R?x, higher order terms can be neglected, and Equation (2) becomes similar to Equation (1). In general, a small number of p elements is enough to analyse a structure, reducing possible problems due to inter-element discontinuities.…”

Section: Curved Beam P -Version Hierarchical Finite Elementmentioning

confidence: 98%

“…One of the first works on the linear vibration of arches by the FEM was presented by Petyt and Fleischer [1], who applied three finite element models to study the radial vibrations of curved beams, with different subtended angles and boundary conditions. More recently, in Reference [2], a formulation was proposed to alleviate the problem of shear and membrane locking and three examples-none in dynamics-were presented.…”

Section: Introductionmentioning

confidence: 99%

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A p‐version, first order shear deformation, finite element for geometrically non‐linear vibration of curved beams

Ribeiro

2004

Numerical Meth Engineering

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SUMMARYA p-version, hierarchical finite element for curved, moderately thick, elastic and isotropic beams is introduced. The convergence properties of the element are analysed and some results are compared with results published elsewhere or calculated using a commercial finite element package. It is verified that, with the proposed element, shear locking does not affect the computation of the natural frequencies and that low dimensional, accurate models are obtainable. Geometrically non-linear vibrations due to finite deformations, which occur for harmonic excitations with frequencies close to the first three natural frequencies of vibration, are investigated using Newmark's method. The influence of the thickness, longitudinal inertia and curvature radius on the dynamic behaviour of curved beams are studied.

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Section: Curved Beam P -Version Hierarchical Finite Elementmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

A p‐version, first order shear deformation, finite element for geometrically non‐linear vibration of curved beams

Ribeiro

2004

Numerical Meth Engineering

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“…It is noted that the third term on the right-hand side of Equation (19), I y˙ y 2 , represents the rotary inertia, which is not considered in References [1] and [9].…”

Section: Mass Matrix For Arch Elementmentioning

confidence: 98%

Free vibration analysis of arches using curved beam elements

Chiang

2003

Numerical Meth Engineering

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SUMMARYThe natural frequencies and mode shapes for the radial (in-plane) bending vibrations of the uniform circular arches were investigated by means of the ÿnite arch (curved beam) elements. Instead of the complicated explicit shape functions of the arch element given by the existing literature, the simple implicit shape functions associated with the tangential, radial (or normal) and rotational displacements of the arch element were derived and presented in matrix form. Based on the relationship between the nodal forces and the nodal displacements of a two-node six-degree-of-freedom arch element, the elemental sti ness matrix was derived, and based on the equation of kinetic energy and the implicit shape functions of an arch element the elemental consistent mass matrix with rotary inertia e ect considered was obtained. Assembly of the foregoing elemental property matrices yields the overall sti ness and mass matrices of the complete curved beam. The standard techniques were used to determine the natural frequencies and mode shapes for the curved beam with various boundary conditions and subtended angles. In addition to the typical circular arches with constant curvatures, a hybrid beam constructed by using an arch segment connected with a straight beam segment at each of its two ends was also studied. For simplicity, a lumped mass model for the arch element was also presented. All numerical results were compared with the existing literature or those obtained from the ÿnite element method based on the conventional straight beam element and good agreements were achieved.

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“…Therefore, the accurate prediction of the behavior of curved sandwiches is of fundamental importance in the design of these structures. The effects of curvature on the vibration of a curved beam were determined earlier in references [2,3]. It was shown that even a slight amount of curvature has a significant effect on the fundamental frequency for simply supported and clamped beams.…”

Section: Introductionmentioning

confidence: 98%

Experimental and Numerical Investigation of Free Vibrations of Composite Sandwich Beams with Curvature and Debonds

2010

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In this paper experimental and numerical results concerning the dynamic response of composite sandwich beams with curvature and debonds are reported. Sandwich beams made of carbon/epoxy face sheets and polyurethane foam core material were manufactured with four different radii of curvature and debonds between the top and bottom interface of face sheet and foam core. Dynamic response was obtained using the impulse frequency response technique under clamped-clamped boundary condition. Experimental results were compared with numerical finite element model results. A combined experimental and numerical FE approach was used to determine the material properties of the skin and foam core materials based on modal vibration and static flexure tests. Results indicate that the fundamental frequency increases with increasing curvature angle, however, for higher frequencies; the natural frequencies are not significantly affected. Also, it is found that face/core debond causes reduction of the natural frequencies due to stiffness degradation.

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Free vibration of a curved beam

Cited by 114 publications

References 10 publications

A p‐version, first order shear deformation, finite element for geometrically non‐linear vibration of curved beams

A p‐version, first order shear deformation, finite element for geometrically non‐linear vibration of curved beams

Free vibration analysis of arches using curved beam elements

Experimental and Numerical Investigation of Free Vibrations of Composite Sandwich Beams with Curvature and Debonds

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