On the out-of-plane dynamic response of horizontally curved beams resting on elastic foundation traversed by a moving mass

As a first endeavor, the out-of-plane free vibration analysis of thin-to-moderately thick functionally graded (FG) circular curved beams supported on two-parameter elastic foundation is presented. The formulation is derived based on the first-order shear deformation theory (FSDT), which includes the effects of shear deformation and rotary inertia due to both torsional and flexural vibrations. The material properties are assumed to be graded in the direction normal to the plane of the beam curvature. The differential quadrature method (DQM), as an efficient and accurate method, is employed to discretize the equations of motion and the related boundary conditions. In order to assure the accuracy of the formulation and the method of solution, convergence behavior of the nondimensional natural frequencies is examined for FG circular curved beams and comparison studies with those of isotropic curved beams, available in the literature, are performed. The effects of the elastic foundation coefficients, boundary conditions, the material graded index and different geometrical parameters on the natural frequency parameters of the FG circular curved beams are investigated. The new results can be used as benchmark solutions for future research works.

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

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/0954406jmes303 ◽

2006 ◽

Vol 220 (12) ◽

pp. 1709-1726 ◽

Cited By ~ 1

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.

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Application of active piezoelectric patches in controlling the dynamic response of a thin rectangular plate under a moving mass

International Journal of Solids and Structures ◽

10.1016/j.ijsolstr.2009.01.034 ◽

2009 ◽

Vol 46 (11-12) ◽

pp. 2429-2443 ◽

Cited By ~ 26

Author(s):

Fayaz R. Rofooei ◽

Ali Nikkhoo

Keyword(s):

Dynamic Response ◽

Rectangular Plate ◽

Moving Mass ◽

Thin Rectangular Plate

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Dynamic response of systems subject to moving mass excitations

Journal of the Franklin Institute ◽

10.1016/0016-0032(69)90004-0 ◽

1969 ◽

Vol 287 (4) ◽

pp. 319-331 ◽

Cited By ~ 1

Author(s):

M.H. Skeer ◽

J.A. Hribar

Keyword(s):

Dynamic Response ◽

Moving Mass

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An Investigation on the Dynamic Response and Strength of Very Long Floating Structures by Beam Modeling on an Elastic Foundation

Journal of the Society of Naval Architects of Japan ◽

10.2534/jjasnaoe1968.1997.289 ◽

1997 ◽

Vol 1997 (181) ◽

pp. 289-298 ◽

Cited By ~ 1

Author(s):

Takashi Tsubogo ◽

Hiroo Okada

Keyword(s):

Dynamic Response ◽

Elastic Foundation ◽

Floating Structures ◽

Beam Modeling

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Multi-moving Loads Induced Vibration of FG Sandwich Beams Resting on Pasternak Elastic Foundation

Walailak Journal of Science and Technology (WJST) ◽

10.48048/wjst.2021.9260 ◽

2021 ◽

Vol 18 (9) ◽

Author(s):

Wachirawit SONGSUWAN ◽

Monsak PIMSARN ◽

Nuttawit WATTANASAKULPONG

Keyword(s):

Dynamic Response ◽

Elastic Foundation ◽

Excitation Frequency ◽

Beam Theory ◽

Equation Of Motion ◽

Functionally Graded ◽

Sandwich Beams ◽

Moving Loads ◽

Layer Thickness Ratio ◽

Pasternak Elastic Foundation

The dynamic behavior of functionally graded (FG) sandwich beams resting on the Pasternak elastic foundation under an arbitrary number of harmonic moving loads is presented by using Timoshenko beam theory, including the significant effects of shear deformation and rotary inertia. The equation of motion governing the dynamic response of the beams is derived from Lagrange’s equations. The Ritz and Newmark methods are implemented to solve the equation of motion for obtaining free and forced vibration results of the beams with different boundary conditions. The influences of several parametric studies such as layer thickness ratio, boundary condition, spring constants, length to height ratio, velocity, excitation frequency, phase angle, etc., on the dynamic response of the beams are examined and discussed in detail. According to the present investigation, it is revealed that with an increase of the velocity of the moving loads, the dynamic deflection initially increases with fluctuations and then drops considerably after reaching the peak value at the critical velocity. Moreover, the distance between the loads is also one of the important parameters that affect the beams’ deflection results under a number of moving loads.

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