On the modeling of tilted fixed-guided flexible beams under tension
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We derive explicit solutions for a fixed-guided slender suspension beam that is initially straight and tilted with respect to the moving direction of its sliding end. The beam experiences substantial axial forces during the tension, resulting in a nonlinear boundary value problem. We consider sliding end displacements in the direction that cause longitudinal tension along the beam. We first propose an exact approach, leading to analytical solutions for various physical variables such as the transverse force and deflection profile, in terms of the axial force and the positive real solution of a third-order algebraic equation. We also propose an alternative approximate solution based on a second-order equation, which provides closed-form analytical solutions for the physical variables. We also introduce analytical validation techniques for the underlying assumptions. Consistency with nonlinear finite-element analysis is also addressed. Moreover, the results of the approximate method are represented by dimensionless formulas, generating charts to predict solutions for arbitrarily assigned beam parameters. Magnitudes of the normal and shear stress values are also included to consider the effects of yield and shear strengths as the limiting factors at large deflection conditions.
KeywordsAxial Force Transverse Force Beam Length Exact Approach Approximate Approach
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- 1.Aldraihem, O., Wetherhold, R.C., Singh, T.: Intelligent beam structures: Timoshenko theory versus Euler-Bernoulli theory. In: IEEE International Conference on Control Applications, pp. 976–981 (1996)Google Scholar
- 5.Dao D.V., Toriyama T., Wells J., Sugiyama S.: Silicon piezoresistive six-degree of freedom force-moment micro sensor. Sens. Mater. 15(3), 113–135 (2003)Google Scholar
- 9.Gere J.M., Timoshenko S.P.: Mechanics of Materials. PWS Publishing Company, Boston (1997)Google Scholar
- 16.Midha, A., Bapat, S.G., Mavanthoor, A., Chinta, V.: Analysis of a fixed-guided compliant beam with an inflection point using the pseudo-rigid-body model (PRBM) concept. In: ASME International Design Engineering Technical Conferences (IDETC/CIE), 36th Mechanisms and Robotics Conference, vol. 4, pp. 351–361. ASME Proceedings (2012)Google Scholar
- 18.Ogawa, M., Isono, Y.: Novel shear strength evaluation of MEMS materials using asymmetrical four-point bending technique. In: IEEE 20th International Conference on Micro Electro Mechanical Systems, 2007. MEMS, pp. 259–262 (2007)Google Scholar
- 20.Popov E.P.: Engineering Mechanics of Solids, 2 edn. Prentice-Hall, Englewood Cliffs (1998)Google Scholar