Out-of-plane dynamic analysis of beams with arbitrarily varying curvature and cross-section by dynamic stiffness matrix method

Huang, Chiung‐Shiann; Tseng, Yi; Chang, Shao‐Chi; Hung, C. L.

doi:10.1016/s0020-7683(99)00017-7

Cited by 45 publications

(22 citation statements)

References 21 publications

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“…Although there are number of studies about in-plane vibration of curved and symmetrically tapered beams in literature [4,5,15], there is not any about out-of-plane vibration of that kind of structures. In this section, out-of-plane free vibration of symmetrically tapered beams at only C-C end conditions is put into consideration in such a way that (i) the beam is separated into 100 finite elements and (ii) a concentrated mass is located at Figure 5.…”

Section: Symmetrical Tapered Beamsmentioning

confidence: 99%

“…Results of free and forced in-plane vibrations of circular arches with variable crosssections are given by Tong et al [3] using the Kirchhoff assumptions for thin beams and taking the neutral axis as inextensible. Huang et al [4] take into consideration out-ofplane dynamics of beams with arbitrarily varying curvature and cross-section by dynamic stiffness matrix method. Viola et al [5,6] investigate the in-plane linear free vibrations of nonuniform circular arches with damaged configurations by using analytical and generalized differential quadrature (GDQ) methods.…”

Section: Introductionmentioning

confidence: 99%

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Out‐of‐Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

Özyiğit

Yetmez

Uzun

2017

Mathematical Problems in Engineering

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As there is a gap in literature about out-of-plane vibrations of curved and variable cross-sectioned beams, the aim of this study is to analyze the free out-of-plane vibrations of curved beams which are symmetrically and nonsymmetrically tapered. Out-ofplane free vibration of curved uniform and tapered beams with additional mass is also investigated. Finite element method is used for all analyses. Curvature type is assumed to be circular. For the different boundary conditions, natural frequencies of both symmetrical and unsymmetrical tapered beams are given together with that of uniform tapered beam. Bending, torsional, and rotary inertia effects are considered with respect to no-shear effect. Variations of natural frequencies with additional mass and the mass location are examined. Results are given in tabular form. It is concluded that (i) for the uniform tapered beam there is a good agreement between the results of this study and that of literature and (ii) for the symmetrical curved tapered beam there is also a good agreement between the results of this study and that of a finite element model by using MSC.Marc. Results of out-of-plane free vibration of symmetrically tapered beams for specified boundary conditions are addressed.

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Section: Symmetrical Tapered Beamsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Out‐of‐Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

Özyiğit

Yetmez

Uzun

2017

Mathematical Problems in Engineering

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“…The equations can be reduced to the equations in Huang [3] in 2-D in plane analysis. The equations can be reduced to the equations in Huang [23] for the out of plane analysis. It shows the equations discussed here can cover all the 2-D equations of either on plane analysis or out of plane analysis.…”

Section: Journal Of Solid Mechanics and Materials Engineeringmentioning

confidence: 99%

Theory of Three dimensional Helical Curved Beams with Variable Curvatures

Lin¹,

Hung²

2011

JMMP

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The analytical solution are derived for a general 3-D helical curved beam. The equilibrium equations are listed as twelve ordinary differential equations. All force, moment, rotation and displacement components form a set of differential equations of the same pattern. Once the curvature and torsion are specified, the analytical solutions can be derived, if the pattern of differential equations can be solved. Helical curved is found to be solvable. The analytical solutions of 2-D curves of circular, elliptical, cycloid, cantenry, parabolic curves are demonstrated here. The analytical solution of 3-D helical curve with variable curvature is also demonstrated.

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“…They considered the numerical examples for a two-span elliptic beam subjected to a rectangular impulse. Then, Huang et al [9] developed a dynamic stiffness matrix by using the Laplace transform technique for both the free vibration and forced vibration of non-uniform parabolic curved beams with various ratios of rise to span. Tufekci and Dogruer [10] obtained the exact solution of the differential equations for the static behavior of an arch with varying curvature and cross section including the shear deformation effect by using the initial value method.…”

Section: Introductionmentioning

confidence: 99%

Coupled out of plane vibrations of spiral beams for micro-scale applications

Karami

Yardimoglu

Inman

2010

Journal of Sound and Vibration

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a b s t r a c tAn analytical method is proposed to calculate the natural frequencies and the corresponding mode shape functions of an Archimedean spiral beam. The deflection of the beam is due to both bending and torsion, which makes the problem coupled in nature. The governing partial differential equations and the boundary conditions are derived using Hamilton's principle. Two factors make the vibrations of spirals different from oscillations of constant radius arcs. The first is the presence of terms with derivatives of the radius in the governing equations of spirals and the second is the fact that variations of radius of the beam causes the coefficients of the differential equations to be variable. It is demonstrated, using perturbation techniques that the derivative of the radius terms have negligible effect on structure's dynamics. The spiral is then approximated with many merging constant-radius curved sections joined together to approximate the slow change of radius along the spiral. The equations of motion are formulated in non-dimensional form and the effect of all the key parameters on natural frequencies is presented. Non-dimensional curves are used to summarize the results for clarity. We also solve the governing equations using Rayleigh's approximate method. The fundamental frequency results of the exact and Rayleigh's method are in close agreement. This to some extent verifies the exact solutions. The results show that the vibration of spirals is mostly torsional which complicates using the spiral beam as a host for a sensor or energy harvesting device.& 2010 Elsevier Ltd. All rights reserved. IntroductionWe are motivated to look at the vibrations of spiral shaped structures as a prelude to sensing and energy harvesting using the piezoelectric effect in micro-electro-mechanical systems (MEMS) devices. Vibrational energy harvesters convert vibrations available in the environment to electrical energy. The energy generated can be used to power sensor nodes [1]. These energy self-sufficient sensors can be placed in remote places to gather data and wirelessly transmit information. A key challenge in designing MEMS energy harvesters is to make them resonate with low frequency ambient vibrations. Spiral geometry has been suggested as a possible option for compact low frequency substrate in energy harvesting devices [2]. However the vibrational analysis of curved beam with varying radius (spirals) is missing in the literature [3]. Hu et al.[3] approximated the spiral by eccentric constant-radius arcs but only derived the governing equations and did not solve them for vibration characteristics. This paper attempts to solve the free vibrations of spiral beams and pave the way to the modeling of spiral MEMS harvesting devices.

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Out-of-plane dynamic analysis of beams with arbitrarily varying curvature and cross-section by dynamic stiffness matrix method

Cited by 45 publications

References 21 publications

Out‐of‐Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

Out‐of‐Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

Theory of Three dimensional Helical Curved Beams with Variable Curvatures

Coupled out of plane vibrations of spiral beams for micro-scale applications

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