Vibration Isolation Using Continuous Beams

The Dynamic Antiresonant Vibration Isolator (DAVI) involves an inertially coupled system with a mass-lever combination where the inertial forces cancel spring induced forces, thus permitting a high degree of isolation at a relatively low frequency in discrete dynamic systems. In the absence of damping, this allows for zero transmissibility between the isolated mass and the vibrating base, independent of the isolated mass. This paper shows that a mass lever combination can be extended to a continuous dynamic system to achieve isolation with zero displacement and force transmissibility. A new method to calculate the frequency response is developed based on the Euler Bernoulli beam assumptions. The method is used to model the deflections along the beam for different frequencies, describing the entire beam model with a single transcendental transfer function. The method is applied to a beam with a tip mass under transverse point force input or point displacement input, subject to different combinations of boundary conditions and viscoelastic and air damping. The theoretical model shows that both force transmissibility and displacement transmissibility can be zeroed out at the isolation frequency for every mode, as compared to a finite number of isolation frequencies in the discrete system. Every point on the beam can be independently isolated from dynamic displacements, shear forces, and internal moments, at certain frequencies, for every mode. Furthermore, it is shown that the zero displacement transmissibility frequencies are different than the zero force and moment transmissibility frequencies, unlike DAVI devices, that have the same zero force and displacement transmissibility frequencies. A cantilevered stepped beam with a sliding tip mass model is discussed in detail. Several parametric studies are conducted to investigate isolation sensitivity. It is shown that the location of the force input or displacement input on the beam has a significant effect on the isolation and natural frequencies, the closer the input is to the cantilevered root, the smaller the isolation and natural frequencies become. Thus, the isolation characteristics are highly sensitive to the amplification factor, which is the ratio of the location of the input to the length of the beam. It is also shown that the tip mass has a pronounced effect on the isolation frequency. A larger mass decreases the overall isolation and natural frequencies in all the modes. Results also show that as the length increases, less mass is needed to achieve isolation at a specific frequency. Thus, the mass to length ratio is an important isolation factor in continuous systems.