A study of internal and distributed damping for vibrating turbomachiner blades

Internal and distributed damping as possible methods for reducing the vibration response of turbomachine blades and theoretical methods for analyzing damped vibration were studied. It is demonstrated how the Ritz-Galerkin methods may be used to straightforwardly to analyze forced vibrations with damping. This is done directly without requiring the free vibration eigenfunctions. The Galerkin method is an effective technique for these types of problems. The Ritz method has the further advantage of not needing to satisfy the force type boundary conditions, which is particularly important for plates and shells. But proper functionals representing the forcing and damping terms must be developed, and this is done. Two types of damping--viscous and material (hysteretic) are considered. Both distributed and concentrated exciting forces are treated. Numerical results are obtained for cantilevered beams and rectangular plates. Studies showing the rates of convergence of the solutions are made. In the case of the cantilever beam, approximate solutions from the present methods are compared with the exact solutions

Control of Material Damping in High-Q Membrane Microresonators

We study the mechanical quality factors of bilayer aluminum/silicon-nitride membranes. By coating ultrahigh-Q Si3N4 membranes with a more lossy metal, we can precisely measure the effect of material loss on Q's of tensioned resonator modes over a large range of frequencies. We develop a theoretical model that interprets our results and predicts the damping can be reduced significantly by patterning the metal film. Using such patterning, we fabricate Al-Si3N4 membranes with ultrahigh Q at room temperature. Our work elucidates the role of material loss in the Q of membrane resonators and informs the design of hybrid mechanical oscillators for optical-electrical-mechanical quantum interfaces

On the flexural vibration of cylinders under axial loads:Numerical and experimental study

The flexural vibration of a homogeneous isotropic linearly elastic cylinder of any aspect ratio is analysed in this paper. Natural frequencies of a cylinder under uniformly distributed axial loads acting on its bases are calculated numerically by the Ritz method with terms of power series in the coordinate directions as approximating functions. The effect of axial loads on the flexural vibration cannot be described by applying infinitesimal strain theory, therefore, geometrically nonlinear strain–displacement relations with second-order terms are considered here. The natural frequencies of free–free, clamped–clamped, and sliding–sliding cylinders subjected to axial loads are calculated using the proposed three-dimensional Ritz approach and are compared with those obtained with the finite element method and the Bernoulli–Euler theory. Different experiments with cylinders axially compressed by a hydraulic press are carried out and the experimental results for the lowest flexural frequency are compared with the numerical results. An approach based on the Ritz formulation is proposed for the flexural vibration of a cylinder between the platens of the press with constraints varying with the intensity of the compression. The results show that for low compressions the cylinder behaves similarly to a sliding–sliding cylinder, whereas for high compressions the cylinder vibrates as a clamped–clamped one

Damping of optomechanical disks resonators vibrating in air

We report on miniature GaAs disk optomechanical resonators vibrating in air in the radiofrequency range. The flexural modes of the disks are studied by scanning electron microscopy and optical interferometry, and correctly modeled with the elasticity theory for annular plates. The mechanical damping is systematically measured, and confronted with original analytical models for air damping. Formulas are derived that correctly reproduce both the mechanical modes and the damping behavior, and can serve as design tools for optomechanical applications in fluidic environment

Ultrasound sensing using the acousto-optic effect in polymer dispersed liquid crystals

Acousto-optic effects are demonstrated in polymer dispersed liquid crystal (PDLC) films, showing promise for applications in ultrasound sensing. The PDLC films are used to image two displacement profiles of an air-coupled flexural transducers resonant modes at 295 kHz and 730 kHz. Results are confirmed using laser vibrometry. The regions on the transducers with the largest displacements are clearly imaged by the PDLC films, with the resolution agreeing well with laser vibrometry scanning. Imaging takes significantly less time than a scanning system (switching time of a few seconds, as compared to 8 hours for laser vibrometry). Heating effects are carefully monitored using thermal imaging, and are found not to be the main cause of PDLC clearing

Transformation cloaking and radial approximations for flexural waves in elastic plates

It is known that design of elastic cloaks is much more challenging than that of acoustic cloaks, cloaks of electromagnetic waves or scalar problems of antiplane shear. In this paper, we address fully the fourth-order problem and develop a model of a broadband invisibility cloak for channelling flexural waves in thin plates around finite inclusions. We also discuss an option to employ efficiently an elastic pre-stress and body forces to achieve such a result. An asymptotic derivation provides a rigorous link between the model in question and elastic wave propagation in thin solids. This is discussed in detail to show connection with non-symmetric formulations in vector elasticity studied in earlier work

A time-varying inertia pendulum: Analytical modelling and experimental identification

In this paper two of the main sources of non-stationary dynamics, namely the time-variability and the presence of nonlinearity, are analysed through the analytical and experimental study of a time-varying inertia pendulum. The pendulum undergoes large swinging amplitudes, so that its equation of motion is definitely nonlinear, and hence becomes a nonlinear time-varying system. The analysis is carried out through two subspace-based techniques for the identification of both the linear time-varying system and the nonlinear system. The flexural and the nonlinear swinging motions of the pendulum are uncoupled and are considered separately: for each of them an analytical model is built for comparisons and the identification procedures are developed. The results demonstrate that a good agreement between the predicted and the identified frequencies can be achieved, for both the considered motions. In particular, the estimates of the swinging frequency are very accurate for the entire domain of possible configurations, in terms of swinging amplitude and mass positio

Omnidirectional broadband insulating device for flexural waves in thin plates

This work presents a gradient index device for insulating from vibrations a circular area of a thin plate. The gradient of the refractive index is achieved exploiting the thickness-dependence of the dispersion relation of flexural waves in thin plates. A well-like thickness profile in an annular region of the plate is used to mimic the combination of an attractive and repulsive potentials, focusing waves at its bottom and dissipating them by means of an absorptive layer placed on top. The central area is therefore isolated from vibrations, while they are dissipated at the bottom of the well. Simulations have been done using the multilayer multiple scattering method and the results prove their broadband efficiency and omnidirectional properties.This work has been supported by the U.S. Office of Naval Research under Grant No. N000140910554.Climente Alarcón, A.; Torrent Martí, D.; Sánchez-Dehesa Moreno-Cid, J. (2013). Omnidirectional broadband insulating device for flexural waves in thin plates. Journal of Applied Physics. 114(21):214903-214912. https://doi.org/10.1063/1.4839375S21490321491211421Hsu, J.-C., & Wu, T.-T. (2006). Efficient formulation for band-structure calculations of two-dimensional phononic-crystal plates. Physical Review B, 74(14). doi:10.1103/physrevb.74.144303McPhedran, R. C., Movchan, A. B., & Movchan, N. V. (2009). Platonic crystals: Bloch bands, neutrality and defects. Mechanics of Materials, 41(4), 356-363. doi:10.1016/j.mechmat.2009.01.005Farhat, M., Guenneau, S., Enoch, S., Movchan, A. B., & Petursson, G. G. (2010). Focussing bending waves via negative refraction in perforated thin plates. Applied Physics Letters, 96(8), 081909. doi:10.1063/1.3327813Pierre, J., Boyko, O., Belliard, L., Vasseur, J. O., & Bonello, B. (2010). Negative refraction of zero order flexural Lamb waves through a two-dimensional phononic crystal. Applied Physics Letters, 97(12), 121919. doi:10.1063/1.3491290Wu, T.-T., Chen, Y.-T., Sun, J.-H., Lin, S.-C. S., & Huang, T. J. (2011). Focusing of the lowest antisymmetric Lamb wave in a gradient-index phononic crystal plate. Applied Physics Letters, 98(17), 171911. doi:10.1063/1.3583660Farhat, M., Guenneau, S., & Enoch, S. (2010). High directivity and confinement of flexural waves through ultra-refraction in thin perforated plates. EPL (Europhysics Letters), 91(5), 54003. doi:10.1209/0295-5075/91/54003Oudich, M., Li, Y., Assouar, B. M., & Hou, Z. (2010). A sonic band gap based on the locally resonant phononic plates with stubs. New Journal of Physics, 12(8), 083049. doi:10.1088/1367-2630/12/8/083049Xiao, Y., Wen, J., & Wen, X. (2012). Flexural wave band gaps in locally resonant thin plates with periodically attached spring–mass resonators. Journal of Physics D: Applied Physics, 45(19), 195401. doi:10.1088/0022-3727/45/19/195401Torrent, D., Mayou, D., & Sánchez-Dehesa, J. (2013). Elastic analog of graphene: Dirac cones and edge states for flexural waves in thin plates. Physical Review B, 87(11). doi:10.1103/physrevb.87.115143Farhat, M., Guenneau, S., Enoch, S., & Movchan, A. B. (2009). Cloaking bending waves propagating in thin elastic plates. Physical Review B, 79(3). doi:10.1103/physrevb.79.033102Farhat, M., Guenneau, S., & Enoch, S. (2009). Ultrabroadband Elastic Cloaking in Thin Plates. Physical Review Letters, 103(2). doi:10.1103/physrevlett.103.024301Stenger, N., Wilhelm, M., & Wegener, M. (2012). Experiments on Elastic Cloaking in Thin Plates. Physical Review Letters, 108(1). doi:10.1103/physrevlett.108.014301Bramhavar, S., Prada, C., Maznev, A. A., Every, A. G., Norris, T. B., & Murray, T. W. (2011). Negative refraction and focusing of elastic Lamb waves at an interface. Physical Review B, 83(1). doi:10.1103/physrevb.83.014106Krylov, V. V., & Tilman, F. J. B. S. (2004). Acoustic ‘black holes’ for flexural waves as effective vibration dampers. Journal of Sound and Vibration, 274(3-5), 605-619. doi:10.1016/j.jsv.2003.05.010Krylov, V. V., & Winward, R. E. T. B. (2007). Experimental investigation of the acoustic black hole effect for flexural waves in tapered plates. Journal of Sound and Vibration, 300(1-2), 43-49. doi:10.1016/j.jsv.2006.07.035O’Boy, D. J., Krylov, V. V., & Kralovic, V. (2010). Damping of flexural vibrations in rectangular plates using the acoustic black hole effect. Journal of Sound and Vibration, 329(22), 4672-4688. doi:10.1016/j.jsv.2010.05.019Georgiev, V. B., Cuenca, J., Gautier, F., Simon, L., & Krylov, V. V. (2011). Damping of structural vibrations in beams and elliptical plates using the acoustic black hole effect. Journal of Sound and Vibration, 330(11), 2497-2508. doi:10.1016/j.jsv.2010.12.001D. Ross, E. E. Ungar, and E. Kerwin, in Proceedings of Structural Damping, Section 3, edited by J. E. Ruzicka (1959), pp. 49–87.O’Boy, D. J., & Krylov, V. V. (2011). Damping of flexural vibrations in circular plates with tapered central holes. Journal of Sound and Vibration, 330(10), 2220-2236. doi:10.1016/j.jsv.2010.11.017Bowyer, E. P., O’Boy, D. J., Krylov, V. V., & Horner, J. L. (2012). Effect of geometrical and material imperfections on damping flexural vibrations in plates with attached wedges of power law profile. Applied Acoustics, 73(5), 514-523. doi:10.1016/j.apacoust.2011.12.010Bowyer, E. P., O’Boy, D. J., Krylov, V. V., & Gautier, F. (2013). Experimental investigation of damping flexural vibrations in plates containing tapered indentations of power-law profile. Applied Acoustics, 74(4), 553-560. doi:10.1016/j.apacoust.2012.10.004V. Krylov, in Proceedings of the International Conference on Noise and Vibration Engineering (ISMA), edited by P. Sas, D. Moens, and S. Jonckheer (2012), pp. 933–944.Narimanov, E. E., & Kildishev, A. V. (2009). Optical black hole: Broadband omnidirectional light absorber. Applied Physics Letters, 95(4), 041106. doi:10.1063/1.3184594Climente, A., Torrent, D., & Sánchez-Dehesa, J. (2012). Omnidirectional broadband acoustic absorber based on metamaterials. Applied Physics Letters, 100(14), 144103. doi:10.1063/1.3701611Cai, L.-W., & Sánchez-Dehesa, J. (2008). Acoustical scattering by radially stratified scatterers. The Journal of the Acoustical Society of America, 124(5), 2715-2726. doi:10.1121/1.2967825Norris, A. N., & Vemula, C. (1995). Scattering of flexural waves on thin plates. Journal of Sound and Vibration, 181(1), 115-125. doi:10.1006/jsvi.1995.012