In beam theory, constraints can be classified as fixed/pinned depending on whether the rotational stiffness of the support is much greater/less than the rotational stiffness of the freestanding portion. For intermediate values of the rotational stiffness of the support, the boundary conditions must account for the finite rotational stiffness of the constraint. In many applications, particularly in microelectromechanical systems and nanomechanics, the constraints exist only on one side of the beam. In such cases, it may appear at first that the same conditions on the constraint stiffness hold. However, it is the purpose of this paper to demonstrate that even if the beam is perfectly bonded on one side only to a completely rigid constraining surface, the proper model for the boundary conditions for the beam still needs to account for beam deformation in the bonded region. The use of a modified beam theory, which accounts for bending, shear, and extensional deformation in the bonded region, is required in order to model this behavior. Examples are given for cantilever, bridge, and guided structures subjected to either transverse loads or residual stresses. The results show significant differences from the ideal bond case. Comparisons made to a three-dimensional finite element analysis show a good agreement.
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Modeling of a One-Sided Bonded and Rigid Constraint Using Beam Theory
Peter J. Ryan,
Peter J. Ryan
Department of Mechanical and Industrial Engineering,
Northeastern University
, Boston, MA 02115; Department of Electrical and Computer Engineering, Northeastern University
, Boston, MA 02115
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George G. Adams,
George G. Adams
Department of Mechanical and Industrial Engineering,
e-mail: adams@coe.neu.edu
Northeastern University
, Boston, MA 02115
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Nicol E. McGruer
Nicol E. McGruer
Department of Electrical and Computer Engineering,
Northeastern University
, Boston, MA 02115
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Peter J. Ryan
Department of Mechanical and Industrial Engineering,
Northeastern University
, Boston, MA 02115; Department of Electrical and Computer Engineering, Northeastern University
, Boston, MA 02115
George G. Adams
Department of Mechanical and Industrial Engineering,
Northeastern University
, Boston, MA 02115e-mail: adams@coe.neu.edu
Nicol E. McGruer
Department of Electrical and Computer Engineering,
Northeastern University
, Boston, MA 02115J. Appl. Mech. May 2008, 75(3): 031008 (6 pages)
Published Online: April 8, 2008
Article history
Received:
February 9, 2007
Revised:
August 28, 2007
Published:
April 8, 2008
Citation
Ryan, P. J., Adams, G. G., and McGruer, N. E. (April 8, 2008). "Modeling of a One-Sided Bonded and Rigid Constraint Using Beam Theory." ASME. J. Appl. Mech. May 2008; 75(3): 031008. https://doi.org/10.1115/1.2839898
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