On the Natural Frequencies of a Flexible Manipulator with a Tip Payload

Abstract This paper is concerned with the vibrations of an Euler-Bernoulli stepped cantilever, clamped to a hub rotating at a constant speed. The system parameters are: the speed of rotation of the hub, the position of the step, the ratio of the mass per unit length of the two portions of the beam and the ratio of the flexural rigidity. Analytical solution of the mode shape differential equations for out-of-plane vibrations (normal to the plane of rotation) is developed. The frequency equation is expressed as a 4th order determinant equated to zero. A scheme is presented to derive the natural frequencies. The first three frequencies are tabulated for various combinations of the system parameters. Published results (which were obtained via finite element procedure) are compared with the analytical results.

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Natural Frequencies of a Manipulator with Rigid Tip Mass: the Case of Flexural-Flexuraltorsional Coupling

10.32920/ryerson.14653014.v1 ◽

2021 ◽

Author(s):

Mohammad Arshad

Keyword(s):

Finite Element ◽

Characteristic Equation ◽

Natural Frequencies ◽

Slenderness Ratio ◽

Frequency Equation ◽

Flexible Manipulator ◽

Torsional Deformation ◽

Finite Element Software ◽

Centre Of Gravity ◽

Tip Mass

The characteristic (or frequency) equation of a flexible manipulator with a rigid tip mass is derived. The manipulator is modelled as an Euler-Bemoulli beam and it permits flexural (bending) deformation in two planes and torsional deformation. The position of the centroid of the tip mass may not necessarily be coincident with the elastic axis of the beam. This is represented by the use of offset coordinates. The natural frequencies of the manipulator are obtained by solving the characteristic equation. The results are compared to the results in the literature, where possible, and also to those obtained using a commercial finite element software ANSYS. The effects of the magnitude of the tip load, offset of the tip mass centre of gravity from its point of attachment, the length of the beam and slenderness ratio on the natural frequencies are examined.

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Natural Frequencies of a Manipulator with Rigid Tip Mass: the Case of Flexural-Flexuraltorsional Coupling

10.32920/ryerson.14653014 ◽

2021 ◽

Author(s):

Mohammad Arshad

Keyword(s):

Finite Element ◽

Characteristic Equation ◽

Natural Frequencies ◽

Slenderness Ratio ◽

Frequency Equation ◽

Flexible Manipulator ◽

Torsional Deformation ◽

Finite Element Software ◽

Centre Of Gravity ◽

Tip Mass

The characteristic (or frequency) equation of a flexible manipulator with a rigid tip mass is derived. The manipulator is modelled as an Euler-Bemoulli beam and it permits flexural (bending) deformation in two planes and torsional deformation. The position of the centroid of the tip mass may not necessarily be coincident with the elastic axis of the beam. This is represented by the use of offset coordinates. The natural frequencies of the manipulator are obtained by solving the characteristic equation. The results are compared to the results in the literature, where possible, and also to those obtained using a commercial finite element software ANSYS. The effects of the magnitude of the tip load, offset of the tip mass centre of gravity from its point of attachment, the length of the beam and slenderness ratio on the natural frequencies are examined.

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Study on Natural Frequencies of Transverse Free Vibration of Functionally Graded Axis Beams by the Differential Quadrature Method

Acta Acustica united with Acustica ◽

10.3813/aaa.919388 ◽

2019 ◽

Vol 105 (6) ◽

pp. 1095-1104

Author(s):

Jin-lun Zhang ◽

Liao-jun Zhang ◽

Ren-yu Ge ◽

Li Yang ◽

Jun-wu Xia

Keyword(s):

Free Vibration ◽

Natural Frequencies ◽

Differential Quadrature Method ◽

Functionally Graded ◽

Differential Quadrature ◽

Variable Cross ◽

Quadrature Method ◽

Bernoulli Beam ◽

Functionally Graded Beam ◽

Euler Bernoulli Beam

Functionally gradient materials with special mechanical characteristics are more and more widely used in engineering. The functionally graded beam is one of the commonly used components to bear forces in the structure. Accurate analysis of the dynamic characteristics of the axially functionally graded (AFG) beam plays a vital role in the design and safe operation of the whole structure. Based on the Euler-Bernoulli beam theory (EBT), the characteristic equation of transverse free vibration for the AFG Euler-Bernoulli beam with variable cross-section is obtained in the present work, and the governing equations of the beam are transformed into ordinary differential equations with variable coefficients. Using differential quadrature method (DQM), the solution formulas of characteristic equations under different boundary conditions are derived, and the natural frequencies of the AFG beam are calculated, while the node partition of a non-uniform geometric progression is discussed.

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The Effect of Axial Force on the Free Vibration of an Euler-Bernoulli Beam Carrying a Number of Various Concentrated Elements

Shock and Vibration ◽

10.1155/2013/735061 ◽

2013 ◽

Vol 20 (3) ◽

pp. 357-367 ◽

Cited By ~ 5

Author(s):

Gürkan Şcedilakar

Keyword(s):

Free Vibration ◽

Vibration Analysis ◽

Axial Load ◽

Natural Frequencies ◽

Free Vibration Analysis ◽

Mode Shapes ◽

The Finite Element Method ◽

Bernoulli Beam ◽

Euler Beam ◽

Euler Bernoulli Beam

In this study, free vibration analysis of beams carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and spring-mass systems subjected to the axial load was performed. All analyses were performed using an Euler beam assumption and the Finite Element Method. The beam used in the analyses is accepted as pinned-pinned. The axial load applied to the beam from the free ends is either compressive or tensile. The effects of parameters such as the number of spring-mass systems on the beam, their locations and the axial load on the natural frequencies were investigated. The mode shapes of beams under axial load were also obtained.

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FREE VIBRATION ANALYSIS FOR EULER-BERNOULLI BEAM ON PASTERNAK FOUNDATION

10.26678/abcm.cobem2017.cob17-1084 ◽

2017 ◽

Author(s):

Lucas Soares ◽

simone dos santos hoefel ◽

Wallison Bezerra

Keyword(s):

Free Vibration ◽

Vibration Analysis ◽

Free Vibration Analysis ◽

Pasternak Foundation ◽

Bernoulli Beam ◽

Euler Bernoulli Beam

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

Mathematical Problems in Engineering ◽

10.1155/2017/8178703 ◽

2017 ◽

Vol 2017 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Hamdi Alper Özyiğit ◽

Mehmet Yetmez ◽

Utku Uzun

Keyword(s):

Finite Element ◽

Free Vibration ◽

Boundary Conditions ◽

Natural Frequencies ◽

Variable Cross ◽

Additional Mass ◽

Inertia Effects ◽

Tapered Beam ◽

Out Of Plane ◽

Good Agreement

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-of-plane 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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