Optimum Design of Intermediate Support for Raising Fundamental Frequency of a Beam or Column under Compressive Axial Load

The optimum design of an additional intermediate support is investigated for raising the fundamental natural frequency of a beam or column subjected to compressive axial loadings. First, the criterion that constitutes the general characteristic equation of the optimal attachment position is explicitly provided so that an objective value of the fundamental frequency can be achieved with the minimum restraint stiffness of the intermediate support. Then, the optimum design of an intermediate support is performed for three illustrative beams of different classical boundary conditions to demonstrate the effects of the compressive axial loads. Numerical results show that the axial load can remarkably influence the support design of its optimum position and minimum stiffness when using it to increase the beam fundamental frequency.

[1]  Jing-Zhong Xing,et al.  Free vibrations of a beam with elastic end restraints subject to a constant axial load , 2013 .

[2]  W. Cleghorn,et al.  Generalized Orthogonality Condition for Beams with Intermediate Lumped Masses Subjected to Axial Force , 2010 .

[3]  Yoon Young Kim,et al.  Optimization of Support Locations of Beam and Plate Structures Under Self-Weight by Using a Sprung Structure Model , 2009 .

[4]  Ricardo Oscar Grossi,et al.  The transition conditions in the dynamics of elastically restrained beams , 2008 .

[5]  Michael I. Friswell,et al.  Maximizing the natural frequency of a beam with an intermediate elastic support , 2006 .

[6]  D. Wang,et al.  Optimization of support positions to minimize the maximal deflection of structures , 2004 .

[7]  S. Naguleswaran,et al.  Transverse vibration of an uniform Euler–Bernoulli beam under linearly varying axial force , 2004 .

[8]  C. Wang,et al.  BUCKLING OF COLUMNS WITH INTERMEDIATE ELASTIC RESTRAINT , 2003 .

[9]  C. Y. Wang,et al.  MINIMUM STIFFNESS OF AN INTERNAL ELASTIC SUPPORT TO MAXIMIZE THE FUNDAMENTAL FREQUENCY OF A VIBRATING BEAM , 2003 .

[10]  Zhong‐sheng Liu,et al.  DERIVATIVE OF BUCKLING LOAD WITH RESPECT TO SUPPORT LOCATIONS , 2000 .

[11]  M. H. Imam,et al.  Optimum topology of structural supports , 1996 .

[12]  N. Olhoff,et al.  Minimum stiffness of optimally located supports for maximum value of column buckling loads , 1991 .

[13]  A. Bokaian,et al.  Natural frequencies of beams under tensile axial loads , 1990 .

[14]  Lawrence A. Bergman,et al.  Green functions for transversely vibrating uniform Euler-Bernoulli beams subject to constant axial preload , 1989 .

[15]  N. G. Stephen,et al.  Beam vibration under compressive axial load—upper and lower bound approximation , 1989 .

[16]  A. Bokaian,et al.  Natural frequencies of beams under compressive axial loads , 1988 .

[17]  J. Neuringer,et al.  Interesting Instructional Problems in Column Buckling for the Strength of Materials and Mechanics of Solids Courses , 1998 .