Passive method for controlling the nonlinear characteristics in a parametrically excited hinged-hinged beam by the addition of a linear spring

In the present paper, we propose a simple method for controlling the nonlinear characteristics of the frequency response curve in a parametrically excited hinged-hinged beam with a movable end (changing from softening to hardening and decreasing the overhang in the frequency response curve). The proposed method is achieved simply by the attachment of a linear spring in the axial direction to the movable end and does not require any power. By applying the extended Hamilton's principle, the equation of motion of the beam in the lateral direction is derived, and the change in the nonlinear characteristics of the parametric resonance is theoretically analyzed while tuning the linear stiffness of the attached linear spring. The linear spring affects only the nonlinearity in the lateral vibration, but not the linear natural frequency of the beam. That is, the linear unstable region in the parametric resonance is not shifted, but only the frequency response curve can be changed. This is advantageous in applications to resonators, such as mass sensors and mechanical filters. It is shown experimentally that the nonlinear characteristics of the frequency response curve can be changed by tuning the stiffness of a linear spring. Furthermore, the experimental results reveal that quadratic damping plays a dominant role in determining the nonlinear characteristics of the steady-state amplitude for the case in which the nonlinearity in the system is modified to be relatively small. (C) 2015 Elsevier Ltd. All rights reserved.