Abhijit Sarkar

In this paper, a semi-analytical model is derived to calculate the anchor loss of TPoS resonators operating in higher-order length extensional modes. This model provides valuable insights on the effect of order, device dimensions, position and number of anchors on the quality factor (Q) of these resonators. Results from this model are in close agreement with the FEM simulations. The optimum position, dimension, and the number of anchors to deliver the highest Q are also discussed. Predictions of the model are validated through characterization of TPoS resonators fabricated to operate at a resonant frequency of around 1 GHz with different number of anchor pairs and position. A 23rd order resonator with a W/L ratio of 1.5 with three pairs of anchors placed at positions suggested by the model gave a loaded Q of 4431, which is 65% more than the conventional case where anchors are uniformly placed towards the edge, and also an improvement in the insertion loss by 5.5 dB compared to the latter. For resonators where the anchor loss is predominant, our results show that the performance can be improved by placing the anchors at the optimum position, closer to the middle of the resonator than the conventional scheme where anchors are uniformly placed towards the edge.

Ladder frame structures are used as models for multistorey buildings. These periodic structures exhibit alternating propagating and attenuating frequency bands. Of the six different wave modes of propagation, two modes strongly attenuate at all frequencies. The other four modes have nonoverlapping stop band characteristics. Thus, it is challenging to isolate such structures when subjected to broadband, multimodal base excitation. In this study, we seek to synthesize a periodic ladder frame structure that has attenuation characteristics over the maximal range of frequencies for all the modes of wave propagation. We synthesize a unit cell of the periodic structure, which comprises two distinct regions having different inertial, stiffness, and geometric properties. The eigenvalues of the transfer matrix of the unit cell determines the attenuating or the nonattenuating characteristics of the structure. A novel pictorial presentation in the form of eigenvalue map is developed. This is used to synthesize the optimal unit cell. Also, design guidelines for suitable selection of the design parameters are presented. It is shown that a large finite periodic structure comprising a unit cell synthesized using the present approach has significantly better isolation characteristics in comparison to the homogeneous or any other arbitrarily chosen periodic structure.

Rotating blades are widely used in turbomachinery applications. In these applications, blades fail frequently because of large amplitude vibrations. These large amplitude vibrations are related to the resonances of the blade structure. Thus, accurate estimation of natural frequencies of such rotating structures is of utmost importance. As documented in the literature, a widely used model of such blade structures consists of rotating beams or plates. The objective of this work is to determine the natural frequencies of rotating plate structures. Starting from the non-dimensional governing equation of the rotating staggered cantilever plate as presented by Sun et al. (J Sound Vib 332(5):1355–1371, 2013) [1], the corresponding weighted residual statement is derived. In the present study, a Galerkin-based methodology is implemented to obtain the modal characteristics. Towards this end, we choose six linearly independent shape functions in the form of product of Clamped-Free (C-F) and Free-Free (F-F) beam mode shapes. The characteristic equation for the determination of the natural frequencies is formulated. This sixth-order polynomial equation is solved numerically to obtain the natural frequencies of the rotating staggered cantilever plate. The results for the non-dimensional natural frequencies as a function of the non-dimensional rotating speed are presented in the form of natural frequency maps. Further, these results are validated using Finite Element (FE) simulation. Towards this end, a pre-stressed modal analysis is performed in ANSYS. It is noted that the results obtained by the two methods are in good correlation.

Analytical expressions are found for the wavenumbers and resonance frequencies in flexible, orthotropic shells using the asymptotic methods. These expressions are valid for arbitrary circumferential orders n. The DonnellMushtari shell theory is used to model the dynamics of the cylindrical shell. Initially, an in vacuo cylindrical isotropic shell is considered and expressions for all the wavenumbers (bending, near-field bending, longitudinal and torsional) are found. Subsequently, defining a suitable orthotropy parameter , the problem of wave propagation in an orthotropic shell is posed as a perturbation on the corresponding problem for an isotropic shell. Asymptotic expressions for the wavenumbers in the in vacuo orthotropic shell are then obtained by treating as an expansion parameter. In both cases (isotropy and orthotropy), a frequency-scaling parameter (η) and Poissons ratio (ν) are used to find elegant expansions in the different frequency regimes. The asymptotic expansions are compared with numerical solutions in each of the cases and the match is found to be good. The main contribution of this work lies in the extension of the existing literature by developing closed-form expressions for wavenumbers with arbitrary circumferential orders n in the case of both, isotropic and orthotropic shells. Finally, we present natural frequency expressions in finite shells (isotropic and orthotropic) for the axisymmetric mode and compare them with numerical and ANSYS results. Here also, the comparison is found to be good. © 2011 Elsevier Ltd. All rights reserved.

Rotating plate structures frequently arise in turbo machinery applications. In such cases, the plate is rigidly attached at the rotor hub while the other ends are free. Thus, such structures can be well-represented as a rotating cantilever plate. The high centrifugal forces arising in such cases leads to stiffening and thus changes the modal characteristics of a rotating structure in comparison to its non-rotating counterpart. Experimental Modal Analysis on rotating structures require sophisticated infrastructure. However, the centrifugal effect arising due to rotation can be accommodated in a Finite Element Method solution. The resulting natural frequency characteristics are generally presented in a Campbell diagram format. However, not much published work is available regarding the effect of rotation on the mode shape characteristics. This is important as the mode shape characteristics determine the forced response of the structure. Towards this end, in the present work we use a variational principle based approach in formulating the free and forced vibration characteristics of a rotating cantilever plate. The mode shapes of the non-rotating plate is used as basis functions in a Galerkin method implementation of the problem. In addition to the natural frequency characteristics of the rotating structure, such an approach brings out the manner in which non-rotating structural modes are combined to give the modes under the rotating conditions. The deviation between the rotating and non-rotating mode shapes are quantified using the Modal Assurance Criteria (MAC). MAC between the lower order modal pairs is presented as a function of the rotational speed. Finally, the rotational mode shapes obtained are used to arrive at the forced vibration response of the rotating cantilever plate subjected to a uniform pressure load. The solutions obtained using the above process are verified through a Finite Element Analysis conducted in a commercial software.

Analytical expressions are found for the wavenumbers in an in vacuo, infinite, flexible, orthotropic cylindrical shell using asymptotic methods. These expressions are valid for arbitrary circumferential orders n as they are obtained by treating n as a parameter in the derivation. The Donnell-Mushtari shell theory is used to model the dynamics of the cylindrical shell. Initially, an isotropic cylindrical shell is considered and expressions for all the wavenumbers (bending, near-field bending, longitudinal and torsional) are found. Subsequently, defining a suitable orthotropy parameter, the problem of wave-propagation in an orthotropic shell is posed as a perturbation on the corresponding problem for an isotropic shell. Asymptotic expressions for these wavenumbers in the orthotropic shell are then obtained in the limit of small ?. Wherever necessary, a frequency-scaling approach is used to find elegant expansions in the different frequency regimes following the method of Matched Asymptotic Expansions (MAE). The asymptotic expansions are compared with numerical solutions in each of the cases and the match is found to be good. The main contribution of this work lies in the extension of the existing literature by developing closed-form expressions for wavenumbers with arbitrary circumferential orders n in the case of both, isotropic and orthotropic shells. A secondary contribution is in illustrating a convenient approach to study the problem of wave-propagation in anisotropic shells in general, starting with orthotropy in this case. The advantage of using asymptotic methods is that it is possible to track the continuous transition of the wavenumber as a chosen parameter is varied within the limits of validity of the asymptotic expansion. This adds to the physical understanding of the problem and is not easily possible in a numerical study.

This article investigates the nonlinear normal modes (NNMs) of a three degrees-of-freedom cyclically symmetric system with bilinear contact springs. Further, two different cases of zero and nonzero clearance are assumed for the contact model. These systems are found to exhibit qualitatively different characteristics. Interestingly, the former system admits positive-scaling of solutions, which is reminiscent of linear systems. Four classes of NNMs are found for both zero and nonzero clearance. The NNM solutions are calculated using analytical or numerical techniques. The analytical solution involves solving the equations of motion using appropriate ansatzes, while the numerical solution uses a shooting-based continuation scheme. The NNMs' features and their variations with contact spring stiffness and system energy are also studied. This study highlights certain simplifications applicable to cyclically symmetric structures with contact. These simplifications will be of practical interest for designing real-life structures.

A defect-free rolling element bearing has a varying stiffness. The variation of stiffness depends on number of rolling elements, their configuration and cage frequency. The time-varying characteristics of the stiffness results in a parametric excitation. This may lead to instability which is manifested as high vibration levels. An FEM simulation is performed to evaluate stiffness in each configuration of rolling elements and is used to study the variation of direct stiffness and cross coupled stiffness. The obtained stiffness variation is expanded into a Fourier series to form the equation of motion for the bearing vibration. As the stiffness varies with cage frequency, stiffness term in the equation of motion is periodic with parametric excitation. Hence, the equation of motion is a 2-DOF coupled Mathieu equation. Based on Mathieu parameters and cage frequency there exists unstable rpm ranges for a particular bearing. Floquet theory is employed to find out the stable and unstable regions. This involves finding out maximum Floquet exponent using Monodromy matrix. The results obtained through Floquet theory are in agreement with the numerical solution of the governing equations.

The objective of present work is to improve the transmission loss of a barrier separating two acoustic spaces and subjected to low frequency harmonic excitation. A novel concept of achieving this is proposed through addition of point mass at the optimal location over the barrier surface. This allows for a local control of the radiated noise at the target location through the directivity pattern. Analytical expressions to find the structural response to the normally incident acoustic excitation on the planar barrier is derived and validated by a finite element simulation. Rayleigh integral is then used to calculate the sound pressure. The complete procedure is non-dimensionalized for generalization. The optimal location of mass to minimize sound radiation at a receiver location is obtained using numerical optimization. Point mass attachment at the optimal location results in major sound pressure reduction at the target location which is much more than those obtained by uniform distribution of mass over the plate. The total energy radiated over the entire transmission region is also reduced. However, the reduction in total transmitted energy is smaller than the reduction achieved at the specific target location. Passive techniques to improve the transmission loss of a barrier in global sense works well for high frequency whereas, active techniques spans the low frequency range. But active control methods are costly and difficult to implement and hence local control in the transmitted sound using passive techniques could be an alternative. Copyright© (2013) by Austrian Noise Abatement Association (OAL).

In the present study, a lumped parameter model for vortex-induced vibrations is analysed. In this work, the vortex-induced vibrations of an elastically mounted rigid cylinder are able to move in-line and transverse to the flow with equal mass ratio and natural frequencies. A simplified lumped mass model is proposed to study the two degree of freedom (dof) structural oscillator. A classical van der Pol equation along with acceleration coupling, models the near wake dynamics describing the fluctuating nature of vortex shedding. The model dynamics is investigated analytically and the results are compared for moderate mass ratios. The results predicted using this model show a good agreement with the experimental data. The dependence of stream-wise displacement on mass and damping is explored. The cause of cross-flow displacement magnification due to freedom to move in stream-wise direction is also explored using the proposed model. Apart from these two degrees of freedom, the cylinder can also undergo rotation about its centre of mass. The effect of freedom to move in this rotational degree of freedom is exploited to our advantage by applying it to the VIVACE (Vortex induced vibration aquatic clean energy) design which was originally proposed by Bernitsas et al. (2008). The original design was not reported to be the optimal one and the set-up was shown to work only for a given flow velocity. But, the flow environment keeps changing and hence there is a need to bring in robustness and optimize the proposed design. The values of optimized spring stiffness have been found using the lumped mass model. The design is made robust by exploiting the rotational mode. This mode is triggered by varying the overhang lengths in accordance with the varying flow velocity in order to strike resonance for a certain flow regime. © 2013 Elsevier Ltd.