Added mass

About: Added mass is a research topic. Over the lifetime, 2849 publications have been published within this topic receiving 47899 citations.

Vortex-induced vibration of a rising and falling cylinder

Abstract: In this study, we investigate the dynamics of a freely rising and falling cylinder. This is, in essence, a vortex-induced vibration (VIV) system comprising both transverse (Y) and streamwise (X) degrees-of-freedom (d.o.f.), but with zero spring stiffness and zero damping. This problem represents a limiting case among studies in VIV, and is an extension of recent research of elastically mounted bodies having very low spring stiffness, as well as bodies with very low mass and damping. We find that if the mass ratio (where m* = cylinder mass/displaced fluid mass) is greater than a critical value, m*crit = 0.545, the body falls or rises with a rectilinear trajectory. As the mass ratio is reduced below m*crit = 0.545, the cylinder suddenly begins to vibrate vigorously and periodically, with a 2P mode of vortex formation, as reported in the preliminary study of Horowitz & Williamson (J. Fluids Struct. vol. 22, 2006, pp. 837–843). The similarity in critical mass between freely rising and elastically mounted bodies is unexpected, as it is known that the addition of streamwise vibration can markedly affect the response and vortex formation in elastically mounted systems, which would be expected to modify the critical mass. However, we show in this paper that the similarity in vortex formation mode (2P) between the freely rising body and the elastically mounted counterpart is consistent with a comparable phase of vortex dynamics, strength of vortices, amplitudes and frequencies of motion and effective added mass (CEA). All of these similarities result in comparable values of critical mass. The principal fact that the 2P mode is observed for the freely rising body is an interesting and consistent result; based on the previous VIV measurements, this is the only mode out of the known set {2S, 2P, 2T} to yield negative effective added mass (CEA < 0), which is a condition for vibration of a freely rising body. In this paper, we deduce that there exists only one possible two degree-of-freedom elastically mounted cylinder system, which can be used to predict the dynamics of freely rising bodies. Because of the symmetry of the vortex wake, this system is one for which the natural frequencies are fNX = 2fNY. Although this seems clear in retrospect, previous attempts to predict critical mass did not take this into account. Implementing such an elastic system, we are able to predict vibration amplitudes and critical mass (m*crit = 0.57) for a freely rising cylinder in reasonable agreement with direct measurements for such a rising body, and even to predict the Lissajous figures representing the streamwise–transverse vibrations for a rising body with very small mass ratios (down to m* = 0.06), unobtainable from our direct measurements.

Exploiting nonlinearity to enhance the sensitivity of mode-localized mass sensor based on electrostatically coupled MEMS resonators

Abstract: An ultrasensitive mass sensor is proposed by combining the benefits of mode localization and nonlinear dynamics in two clamped–clamped microbeams of different lengths. The coupling electrostatic stiffness between the two resonators can be tuned for modulating sensitivity, and the actuation voltage applied to the shorter beam can be adjusted in order to overcome mechanical defects such as geometric asymmetry. The analytical dynamic model considering the quadratic and cubic nonlinearities is established and solved by the asymptotic numerical method (ANM) combined with harmonic balance method (HBM), as well as validated by the long-time integration (LTI) method. A parametric study is performed in order to investigate the effects of the coupling voltage, gap ratio, position of added mass and length ratio on the device sensitivity. Beyond the critical Duffing amplitude and while taking advantage of mode localization, it is shown that the device sensitivity in terms of amplitude ratio is significantly enhanced with up to three orders of magnitude higher than the relative shift in resonance frequencies. The proposed model can be used as a design tool to tune the nonlinearity level enabling the performance improvement of multimodal MEMS mass sensors.