use of internally resonant energy transfer from the symmetrical to anti-symmetrical modes of a curved beam isolator for enhancing the isolation performance and reducing the source mass translation vibration: theory and experiment

this study aims to use the internally resonant energy transfer from the symmetrical to anti-symmetrical modes of a simply supported curved beam isolator to enhance the isolation performance and reduce the source mass vibration. the model is setup and based on the differential equation of the euler–bernoulli beam. the dynamic modal displacements and forces are then obtained from the model using a numerical integration method. the numerical and experimental results indicate that when the ratio of the resonant frequencies of the first bending symmetric and anti-symmetric modes is close to 2 and the excitation frequency is equal to the resonant frequency of the first symmetric mode, the contribution of the first anti-symmetric mode is significant, even though the curved beam and excitation are symmetrical. the net modal force induced by the first anti-symmetric mode acting on the ground is much smaller than that of the first symmetric mode because the two reaction forces at the beam ends induced by the first anti-symmetric mode are equal but opposite. further, the source mass translational vibration is significantly reduced because it is placed on the node of the anti-symmetric mode.