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Analytical and Experimental Analysis of the Large Deflection of a Cantilever Beam Subjected to a Constant, Concentrated Force, with a Constant Angle, Applied at the Free End

Visner, John C.
http://rave.ohiolink.edu/etdc/view?acc_num=akron1196090494

Abstract Details

2007, Master of Science, University of Akron, Mechanical Engineering.
Large deflection of a cantilever beam subjected to a constant force is modeled. The motivation for this work is derived from an excellent example of large cantilever beam deflection, the archery limb. With the development of a program that models the deflection of an archery limb comes the possibility to improve upon existing designs, which in turn could have large impacts on a rapidly growing multi-million dollar market. This study investigates a long, slender cantilever beam of constant cross section with homogeneous and isotropic material properties. The beam modeled is subjected to a concentrated force applied at the free end. This force has constant components in two orthogonal directions. For this model, the weight of the beam is assumed to be negligible. It is also assumed that the beam is non-extensible and therefore the strains are negligible. Considering these assumptions, a second order nonlinear differential deflection curve equation is obtained by means of a static analysis. Because an exact analytical solution does not exist, a FORTRAN Program using Euler’s numerical method is created to solve this equation. The first of two boundary conditions, the curvature at the free end, is known to be zero. However, the boundary condition at the fixed end is unknown. A shooting method is employed within the program to obtain the correct curvature at the fixed end to yield the deflected beam shape. Experiments are then performed to verify the numerical results. Comparisons with published numerical results show excellent agreement, and excellent agreement is also obtained between the numerical results and experimental data.
Paul Lam (Advisor)
68 p.
Engineering, Mechanical
Large Deflection of a Cantilever Beam

Recommended Citations

Citations

  • Visner, J. C. (2007). Analytical and Experimental Analysis of the Large Deflection of a Cantilever Beam Subjected to a Constant, Concentrated Force, with a Constant Angle, Applied at the Free End [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1196090494

    APA Style (7th edition)

  • Visner, John. Analytical and Experimental Analysis of the Large Deflection of a Cantilever Beam Subjected to a Constant, Concentrated Force, with a Constant Angle, Applied at the Free End. 2007. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1196090494.

    MLA Style (8th edition)

  • Visner, John. "Analytical and Experimental Analysis of the Large Deflection of a Cantilever Beam Subjected to a Constant, Concentrated Force, with a Constant Angle, Applied at the Free End." Master's thesis, University of Akron, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=akron1196090494

    Chicago Manual of Style (17th edition)

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This open access ETD is published by University of Akron and OhioLINK.