Out-of-plane free vibrations of curved beams with variable curvature

2008 ◽  
Vol 318 (1-2) ◽  
pp. 227-246 ◽  
Author(s):  
Byoung Koo Lee ◽  
Sang Jin Oh ◽  
Jeong Man Mo ◽  
Tae Eun Lee
Keyword(s):  
Free Vibrations ◽  
Curved Beams ◽  
Variable Curvature ◽  
Out Of Plane

FREE VIBRATIONS OF SHEAR DEFORMABLE CIRCULAR CURVED BEAMS RESTING ON ELASTIC FOUNDATIONS

2002 ◽  
Vol 02 (01) ◽  
pp. 77-97 ◽  
Author(s):  
BYOUNG KOO LEE ◽  
SANG JIN OH ◽  
KWANG KYOU PARK
Keyword(s):  
Shear Deformation ◽  
Natural Frequencies ◽  
Free Vibrations ◽  
Rotary Inertia ◽  
Transverse Shear Deformation ◽  
Curved Beams ◽  
System Parameters ◽  
Elastic Foundations ◽  
Out Of Plane ◽  
Shear Deformable

The governing differential equations for the out-of-plane, free vibration of circular curved beams resting on elastic foundations are derived and solved numerically. The formulation takes into consideration the effects of rotary inertia and transverse shear deformation. The lowest three natural frequencies are calculated for beams with hinged–hinged, hinged-clamped, and clamped–clamped end constraints. The effects of various system parameters as well as rotary inertia and shear deformation on the natural frequencies are investigated.

IN-PLANE AND OUT-OF-PLANE FREE VIBRATIONS OF CURVED BEAMS WITH VARIABLE SECTIONS

1995 ◽  
Vol 187 (3) ◽  
pp. 381-401 ◽  
Author(s):  
M. Kawakami ◽  
T. Sakiyama ◽  
H. Matsuda ◽  
C. Morita
Keyword(s):  
Free Vibrations ◽  
Curved Beams ◽  
Out Of Plane

Stress concentration factors for the torsion of curved beams of arbitrary cross-section

2006 ◽  
Vol 220 (12) ◽  
pp. 1709-1726 ◽  
Author(s):  
R E Cornwell
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Cross Section ◽  
Cross Sections ◽  
Shear Stresses ◽  
Curved Beams ◽  
Finite Element Implementation ◽  
Out Of Plane ◽  
Concentration Factors ◽  
Stress Concentration Factors

There are numerous situations in machine component design in which curved beams with cross-sections of arbitrary geometry are loaded in the plane of curvature, i.e. in flexure. However, there is little guidance in the technical literature concerning how the shear stresses resulting from out-of-plane loading of these same components are effected by the component's curvature. The current literature on out-of-plane loading of curved members relates almost exclusively to the circular and rectangular cross-sections used in springs. This article extends the range of applicability of stress concentration factors for curved beams with circular and rectangular cross-sections and greatly expands the types of cross-sections for which stress concentration factors are available. Wahl's stress concentration factor for circular cross-sections, usually assumed only valid for spring indices above 3.0, is shown to be applicable for spring indices as low as 1.2. The theory applicable to the torsion of curved beams and its finite-element implementation are outlined. Results developed using the finite-element implementation agree with previously available data for circular and rectangular cross-sections while providing stress concentration factors for a wider variety of cross-section geometries and spring indices.

Earthquake response of linear-elastic arch-frames using exact curved beam formulations

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Baran Bozyigit
Keyword(s):  
Dynamic Stiffness ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Opening Angle ◽  
Earthquake Response ◽  
Response Analysis ◽  
Curved Beam ◽  
Curved Beams ◽  
Base Shear ◽  
Content Type

PurposeThis study aims to obtain earthquake responses of linear-elastic multi-span arch-frames by using exact curved beam formulations. For this purpose, the dynamic stiffness method (DSM) which uses exact mode shapes is applied to a three-span arch-frame considering axial extensibility, shear deformation and rotational inertia for both columns and curved beams. Using exact free vibration properties obtained from the DSM approach, the arch-frame model is simplified into an equivalent single degree of freedom (SDOF) system to perform earthquake response analysis.Design/methodology/approachThe dynamic stiffness formulations of curved beams for free vibrations are validated by using the experimental data in the literature. The free vibrations of the arch-frame model are investigated for various span lengths, opening angle and column dimensions to observe their effects on the dynamic behaviour. The calculated natural frequencies via the DSM are presented in comparison with the results of the finite element method (FEM). The mode shapes are presented. The earthquake responses are calculated from the modal equation by using Runge-Kutta algorithm.FindingsThe displacement, base shear, acceleration and internal force time-histories that are obtained from the proposed approach are compared to the results of the finite element approach where a very good agreement is observed. For various span length, opening angle and column dimension values, the displacement and base shear time-histories of the arch-frame are presented. The results show that the proposed approach can be used as an effective tool to calculate earthquake responses of frame structures having curved beam elements.Originality/valueThe earthquake response of arch-frames consisting of curved beams and straight columns using exact formulations is obtained for the first time according to the best of the author’s knowledge. The DSM, which uses exact mode shapes and provides accurate free vibration analysis results considering each structural members as one element, is applied. The complicated structural system is simplified into an equivalent SDOF system using exact mode shapes obtained from the DSM and earthquake responses are calculated by solving the modal equation. The proposed approach is an important alternative to classical FEM for earthquake response analysis of frame structures having curved members.

Energy flow models for the out-of-plane vibration of horizontally curved beams

2014 ◽  
Vol 136 (4) ◽  
pp. 2141-2141 ◽  
Author(s):  
Hyun-Gwon Kil ◽  
Seonghoon Seo ◽  
Suk-Yoon Hong ◽  
Chan Lee
Keyword(s):  
Energy Flow ◽  
Curved Beams ◽  
Flow Models ◽  
Plane Vibration ◽  
Horizontally Curved ◽  
Out Of Plane

Lateral Buckling of Cantilevered Circular Arches Under Various End Moments

2020 ◽  
Vol 20 (07) ◽  
pp. 2071005
Author(s):  
Y. B. Yang ◽  
Y. Z. Liu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Analytical Solutions ◽  
Analytical Approach ◽  
Three Dimensional ◽  
Curved Beams ◽  
Lateral Buckling ◽  
Circular Arch ◽  
Out Of Plane ◽  
The Moment

Lateral buckling of cantilevered circular arches under various end moments is studied using an analytical approach. Three types of conservative moments are considered, i.e. the quasi-tangential moments of the 1st and 2nd kinds, and the semi-tangential moment. The induced moments associated with each of the moment mechanisms undergoing three-dimensional rotations are included in the Newman boundary conditions. Using the differential equations available for the out-of-plane buckling of curved beams, the analytical solutions are derived for a cantilevered circular arch, which can be used as the benchmarks for calibration of other methods of analysis.

Free vibrations of rectangular cantilever plates. Part 1: out-of-plane motion

2004 ◽  
Vol 271 (1-2) ◽  
pp. 131-146 ◽  
Author(s):  
Jongwon Seok ◽  
H.F. Tiersten ◽  
H.A. Scarton
Keyword(s):  
Free Vibrations ◽  
Plane Motion ◽  
Out Of Plane

Modeling of a Rolling Flexible Circular Ring

2015 ◽  
Vol 82 (11) ◽  
Author(s):  
François Robert Hogan ◽  
James Richard Forbes
Keyword(s):  
Numerical Simulations ◽  
Dynamic Model ◽  
Lagrange Multipliers ◽  
Flat Surface ◽  
Ritz Method ◽  
Free Vibrations ◽  
Circular Ring ◽  
Ring Rolling ◽  
Motion Equations ◽  
Out Of Plane

The motion equations of a rolling flexible circular ring are derived using a Lagrangian formulation. The in-plane flexural and out-of-plane twist-bending free vibrations are modeled using the Rayleigh–Ritz method. The motion equations of a flexible circular ring translating and rotating in space are first developed and then constrained to roll on a flat surface by introducing Lagrange multipliers. The motion equations developed capture the nonholonomic nature of the circular ring rolling without slip on a flat surface. Numerical simulations are performed to validate the dynamic model developed and to investigate the effect of the flexibility of the circular ring on its trajectory. The vibrations of the circular ring are observed to impact the ring's motion.

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