Journal of Vibration and Acoustics Newest Issueen-usFri, 10 Nov 2017 00:00:00 GMTFri, 10 Nov 2017 09:43:30 GMTSilverchaireditor@vibrationacoustics.asmedigitalcollection.asme.orgwebmaster@vibrationacoustics.asmedigitalcollection.asme.orgSuspension Design, Modeling, and Testing of a Thermo-Acoustic-Driven Linear Alternator
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Fri, 10 Nov 2017 00:00:00 GMTSaha CR, Riley PH, Jinks RR, et al. <span class="paragraphSection">The Score-Stove™ generates electricity from a wood-burning cooking stove using a thermo-acoustic engine (TAE) that converts heat to sound through a linear alternator (LA). This paper introduces a prototype hemitoroidal suspension that was refined into a segmented trapezoidal shape that gave a higher cyclic life for the LA and includes a critical evaluation that compares a theoretical analysis with experimental results. The results show an improvement from the 40% efficiency of a standard loudspeaker used in reverse as an LA to 70–80% efficiency with the new suspension and a double Halbach array magnetic topology.</span>//article/140/2/021014/2660904/Suspension-Design-Modeling-and-Testing-of-aOptimal Vibration Absorber With a Friction Damper
//article/140/2/021015/2660905/Optimal-Vibration-Absorber-With-a-Friction-Damper
Fri, 10 Nov 2017 00:00:00 GMTSinha A, Trikutam KT. <span class="paragraphSection">The response of a single degree-of-freedom spring mass system connected to a vibration absorber with a friction damper and subjected to a sinusoidal excitation is considered in this paper. Two possible configurations of the friction damper, rigid and flexible, are explored in details. Optimization of the parameters of absorbers with both these damper configurations to minimize the peak value of the frequency response of the primary system is presented. Results from this minimax optimization approach are compared to the classical solutions for a vibration absorber with linear viscous damper.</span>//article/140/2/021015/2660905/Optimal-Vibration-Absorber-With-a-Friction-DamperTrailing Edge Perforation for Interaction Tonal Noise Reduction of a Contra-Rotating Fan
//article/140/2/021016/2659656/Trailing-Edge-Perforation-for-Interaction-Tonal
Fri, 10 Nov 2017 00:00:00 GMTWang C. <span class="paragraphSection">This study focuses on a passive noise abatement technique in a small contra-rotating fan, aiming at reducing the interaction noise between the two rotors through porous trailing edge (TE) treatment to the forward rotor. A preliminary design with fixed perforation parameters is experimentally investigated, and 6–7 dB overall noise reduction is achieved compared with baseline design under the same aerodynamic output. A three-dimensional (3D), full-wheel, unsteady-flow numerical simulation of the acoustic design is carried out to better understand the noise reduction mechanism. Comparisons of monitored unsteady forces acting on both the forward and the aft rotor between baseline and perforated fan indicate that such treatment reduces all the unsteady forces. Thus, it can be concluded that the noise reduction would be due to not only the mitigation of viscous wake of forward rotor before impinging upon the downstream blades but also the reduction of the response of the upstream rotor to the potential flow interaction with the downstream rotor. Furthermore, a parametric study in a selected range is conducted to minimize the adverse effect of aerodynamic unloading due to TE perforation and to improve the acoustic benefit. The parameters in the parametric study include perforation ratio, aperture diameter, and perforation distribution. Trends are deducted from this, and it is recommended that there exists an optimal perforation ratio; the smallest possible aperture diameter and the decreasing perforation ratio distribution away from the blade TE should be selected in consideration of both aerodynamic and acoustic effects.</span>//article/140/2/021016/2659656/Trailing-Edge-Perforation-for-Interaction-TonalVibrational Response of Initially Deformed Bistable Microbeams under the Combined Effect of Mechanical Shock Loads and Electrostatic Forces
//article/140/2/021013/2657036/Vibrational-Response-of-Initially-Deformed
Fri, 27 Oct 2017 00:00:00 GMTAlqasimi JE, Ouakad HM. <span class="paragraphSection">This paper focuses on the influence of sudden drop tests on the nonlinear structural behavior of electrically actuated bi-table shallow microelectromechanical system (MEMS) arches. The assumed structure consists of an initially bell-shaped doubly clamped microbeam with a rectangular cross section. The Euler–Bernoulli beam theory is assumed to model the nonlinear structural behavior of the bistable system under the combined effect of both the direct current (DC) actuating load and the shaking waves. Moreover, the structural model takes into account both geometric midplane stretching and electric actuation nonlinear terms. A multimode Galerkin-based decomposition is used to discretize the beam equations to extract a reduced-order model (ROM). The convergence of the ROM simulations are first verified and furthermore compared to published experimental data. A thorough ROM parametric study showed that the effect of increasing the shallow arch initial rise alter drastically the system behavior from undergoing a uninterrupted snap-through motion to a sudden snap-through instability. Moreover, the arch rise relationship with its shock spectrum response (SSR) is investigated and it was concluded that as increasing the rise value can cause the system to collapse under the combined DC and shock wave loadings if the shock wave duration is lower or near the system fundamental natural period. All the presented graphs in this investigation represent some robust numerical approaches and design tools to help MEMS designers in improving both the reliability and efficiency of these bistable-based microdevices under shaking dynamic environments.</span>//article/140/2/021013/2657036/Vibrational-Response-of-Initially-DeformedEnergy Harvesting From the Vibrations of Rotating Systems
//article/140/2/021010/2657035/Energy-Harvesting-From-the-Vibrations-of-Rotating
Fri, 20 Oct 2017 00:00:00 GMTCooley CG, Chai T. <span class="paragraphSection">This study investigates the vibration of and power harvested by typical electromagnetic and piezoelectric vibration energy harvesters when applied to vibrating host systems that rotate at constant speed. The governing equations for these electromechanically coupled devices are derived using Newtonian mechanics and Kirchhoff's voltage law. The natural frequency for these devices is speed-dependent due to the centripetal acceleration from their constant rotation. Resonance diagrams are used to identify excitation frequencies and speeds where these energy harvesters have large amplitude vibration and power harvested. Closed-form solutions are derived for the steady-state response and power harvested. These devices have multifrequency dynamic response due to the combined vibration and rotation of the host system. Multiple resonances are possible. The average power harvested over one oscillation cycle is calculated for a wide range of operating conditions. Electromagnetic devices have a local maximum in average harvested power that occurs near a specific excitation frequency and rotation speed. Piezoelectric devices, depending on their mechanical damping, can have two local maxima of average power harvested. Although these maxima are sensitive to small changes in the excitation frequency, they are much less sensitive to small changes in rotation speed.</span>//article/140/2/021010/2657035/Energy-Harvesting-From-the-Vibrations-of-RotatingThe Use of Damping Based Semi-Active Control Algorithms in the Mechanical Smart-Spring System
//article/140/2/021011/2656467/The-Use-of-Damping-Based-SemiActive-Control
Fri, 20 Oct 2017 00:00:00 GMTGustavo Rocha Vieira W, Nitzsche F, De Marqui C, Jr.. <span class="paragraphSection">In recent decades, semi-active control strategies have been investigated for vibration reduction. In general, these techniques provide enhanced control performance when compared to traditional passive techniques and lower energy consumption if compared to active control techniques. In semi-active concepts, vibration attenuation is achieved by modulating inertial, stiffness, or damping properties of a dynamic system. The smart spring is a mechanical device originally employed for the effective modulation of its stiffness through the use of semi-active control strategies. This device has been successfully tested to damp aeroelastic oscillations of fixed and rotary wings. In this paper, the modeling of the smart spring mechanism is presented and two semi-active control algorithms are employed to promote vibration reduction through enhanced damping effects. The first control technique is the smart-spring resetting (SSR), which resembles resetting control techniques developed for vibration reduction of civil structures as well as the piezoelectric synchronized switch damping on short (SSDS) technique. The second control algorithm is referred to as the smart-spring inversion (SSI), which presents some similarities with the synchronized switch damping (SSD) on inductor technique previously presented in the literature of electromechanically coupled systems. The effects of the SSR and SSI control algorithms on the free and forced responses of the smart-spring are investigated in time and frequency domains. An energy flow analysis is also presented in order to explain the enhanced damping behavior when the SSI control algorithm is employed.</span>//article/140/2/021011/2656467/The-Use-of-Damping-Based-SemiActive-ControlAnalytical Modeling of the Vibro-Acoustic Response of a Double-Walled Cylindrical Shell With Microperforation Excited by Turbulent Boundary Layer Pressure Fluctuations
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Fri, 20 Oct 2017 00:00:00 GMTZhang Q, Mao Y, Qi D. <span class="paragraphSection">An analytical model is developed to investigate the vibro-acoustic response of a double-walled cylindrical shell with the inner wall perforated when excited by the external turbulent boundary layer (TBL) pressure fluctuations. The shell motion is governed by the Donnell’s thin shell theory, and the mean particle velocity model is employed to describe the boundary condition between the microperforated shell and fluid media. Numerical results indicate that the transmission loss (TL) for the configuration of microperforating the inner wall could be larger than that for the conventional solid double-walled cylindrical shell with and without the core of porous material over a wide frequency range. Comparison between TL results with excitations from the TBL and the acoustic diffuse field (ADF) shows that with the thought of microperforating the inner shell, to reduce the acoustical excitation will be of more importance than the flow excitation over the ring frequency for a quiet interior space. Parametric studies illustrate that the perforation ratio is the main factor affecting the sound insulation performance through the total reactance.</span>//article/140/2/021012/2656468/Analytical-Modeling-of-the-VibroAcoustic-ResponseErratum: “Optimal Design of Double-Mass Dynamic Vibration Absorbers Arranged in Series or in Parallel” [ASME J. Vib. Acoust., 2017, 139(1), p. 011015; DOI: 10.1115/1.4034776]
//article/140/2/027001/2657034/Erratum-Optimal-Design-of-DoubleMass-Dynamic
Fri, 20 Oct 2017 00:00:00 GMTAsami T. <span class="paragraphSection"><ul><li class="order">Some of the figure numbers are wrong in the text. The corrections are summarized below.</li></ul></span>//article/140/2/027001/2657034/Erratum-Optimal-Design-of-DoubleMass-DynamicComplexification-Averaging Analysis on a Giant Magnetostrictive Harvester Integrated With a Nonlinear Energy Sink
//article/140/2/021009/2656469/ComplexificationAveraging-Analysis-on-a-Giant
Thu, 12 Oct 2017 00:00:00 GMTFang Z, Zhang Y, Li X, et al. <span class="paragraphSection">The present study aims to investigate the steady-state response regimes of a device comprising a nonlinear energy sink (NES) and a giant magnetostrictive energy harvester utilizing analytical approximation. The complexification-averaging (CX-A) technique is generalized to systems defined by differential algebraic equations (DAEs). The amplitude-frequency responses are compared with numerical simulations for validation purposes. The tensile and compressive stresses of giant magnetostrictive material (GMM) are checked to ensure that the material functions properly. The energy harvested is calculated and the comparison of transmissibility of the apparatus with and without NES–GMM is exhibited to reveal the performance of vibration mitigation. Then, the stability and bifurcations are examined. The outcome demonstrates that the steady-state periodic solutions of the system undergo saddle-node (SN) bifurcation at a certain set of parameters. In the meantime, no Hopf bifurcation is observed. The introduction of NES and GMM for vibration reduction and energy harvesting brings about geometric nonlinearity and material nonlinearity. By computing both the responses of the primary system equipped with the NES only and the NES–GMM, it is indicated that the added GMM can dramatically modify the steady-state dynamics. A further optimization with respect to the cubic stiffness, the damper of NES, and the amplitude of excitation is conducted, respectively. The boundary where the giant magnetostrictive energy harvester is out of work is pointed out as well during the process of optimizing.</span>//article/140/2/021009/2656469/ComplexificationAveraging-Analysis-on-a-GiantOptimal Vibration Reduction of Flexible Rotor Systems By the Virtual Bearing Method
//article/140/2/021008/2654994/Optimal-Vibration-Reduction-of-Flexible-Rotor
Mon, 09 Oct 2017 00:00:00 GMTLiu S, Yang B. <span class="paragraphSection">This paper presents a new approach to optimal bearing placement that minimizes the vibration amplitude of a flexible rotor system with a minimum number of bearings. The thrust of the effort is the introduction of a virtual bearing method (VBM), by which a minimum number of bearings can be automatically determined in a rotor design without trial and error. This unique method is useful in dealing with the issue of undetermined number of bearings. In the development, the VBM and a distributed transfer function method (DTFM) for closed-form analytical solutions are integrated to formulate an optimization problem of mixed continuous-and-integer type, in which bearing locations and bearing index numbers (BINs) (specially defined integer variables representing the sizes and properties of all available bearings) are selected as design variables. Solution of the optimization problem by a real-coded genetic algorithm yields an optimal design that satisfies all the rotor design requirements with a minimum number of bearings. Filling a technical gap in the literature, the proposed optimal bearing placement approach is applicable to either redesign of an existing rotor system for improvement of system performance or preliminary design of a new rotor system with the number of bearings to be installed being unforeknown.</span>//article/140/2/021008/2654994/Optimal-Vibration-Reduction-of-Flexible-RotorRotordynamic Stability Effects of Shrouded Centrifugal Impellers With Combined Whirl and Precession
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Fri, 06 Oct 2017 00:00:00 GMTKim E, Palazzolo A. <span class="paragraphSection">Whirling (translational) and precession (tilt) motion of the shrouded centrifugal impeller are possible vibration sources that can cause rotordynamic instability problems. Whirling motion of shrouded impellers and seals has been investigated by test and theory in the literature. However, there has been little study of the effects of coupled motion of whirling and precession of a centrifugal impeller on rotordynamic forces and moments using computational fluid dynamics (CFD). In the present study, the CFD approach for calculating the moment coefficients of the precessing impeller is developed and verified by comparison with the measured data for a precessing centrifugal compressor by Yoshida et al. (1996, “Measurement of the Flow in the Backshroud/Casing Clearance of a Precessing Centrifugal Impeller,” Sixth International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Honolulu, Hawaii, Vol. 2, pp. 151–160). A full set (4 × 4) of rotordynamic coefficient matrices is calculated, using two separate models of (a) a precessing impeller with a tilt angle and (b) a whirling impeller with dynamic eccentricity to investigate the stability of the impeller. Rotordynamic stability is evaluated by using the whirl frequency ratio of the coupled motion, obtained from the full rotordynamic coefficient matrices, to show that the precession motion has a significant impact on rotordynamic stability. A similar conclusion is reached based on the whirling plus precession response of a finite element (FE) structural rotordynamic model including the 4 × 4 rotordynamic coefficient matrices. A stability analysis using the rotordynamic coefficients indicates that the precession motion with the positive tilt angle increases the tendency toward destabilization of the rotor.</span>//article/140/2/021007/2654991/Rotordynamic-Stability-Effects-of-ShroudedNonlinear Finite Element Analysis of Transient Behavior of Delaminated Composite Plate
//article/140/2/021001/2653501/Nonlinear-Finite-Element-Analysis-of-Transient
Wed, 04 Oct 2017 00:00:00 GMTHirwani C, Panda S, Mahapatra T. <span class="paragraphSection">The internal debonding effects on implicit transient responses of the shear deformable layered composite plate under the mechanical transverse (uniform and sinusoidal) loading are analyzed in this article. The physics of the laminated composite plate with internal debonding has been expressed mathematically via two kinds of midplane displacement functions based on Reddy's simple shear deformation kinematic theory. The geometrical nonlinearity of the debonded plate structure is estimated using total Lagrangian method. The time–displacement characteristics are evaluated numerically using the nonlinear finite element method (FEM). The governing equation of motion of the debonded laminated structure has been derived using the total Lagrangian method and solved numerically with the help of Newmark's time integration scheme in association with the direct iterative method. For the computation of output, a suitable <span style="text-transform:lowercase;font-variant:small-caps;">matlab</span> program is written by the use of the presently developed higher order nonlinear model. The consistency and the accuracy of the proposed complex numerical solutions have been established through the appropriate convergence and the comparison study. Finally, a series of numerical examples have been examined to address the influence of the size, the position, and the location of internal damage along with the material and geometrical parameter (modular ratio, side to thickness ratio, aspect ratio, and the boundary condition) on the nonlinear transient responses of delaminated composite plate and discussed in detail.</span>//article/140/2/021001/2653501/Nonlinear-Finite-Element-Analysis-of-TransientOrbit Response Recognition During Touchdowns by Instantaneous Frequency in Active Magnetic Bearings
//article/140/2/021002/2653502/Orbit-Response-Recognition-During-Touchdowns-by
Wed, 04 Oct 2017 00:00:00 GMTLyu M, Liu T, Wang Z, et al. <span class="paragraphSection">During touchdowns of active magnetic bearings (AMB), the violent collision between rotors and touchdown bearings (TDB) can cause damages to both parts. Orbit response recognition provides a way for the AMB controller to automatically switch the control algorithm to actively suppress the rotor–TDB vibration and promptly relevitate the rotor during touchdowns. A novel method based on Hilbert transform (HT) is proposed to recognize the orbit responses (pendulum vibration, combined rub and bouncing, and full rub) in touchdowns. In this method, the rotor suspension status is monitored by the AMB controller in real-time. When touchdown is detected, the rotor displacement signal during the sampling period is intercepted, and the instantaneous frequency (IF) is calculated by HT. Then, the local variance of IF during the sampling period is calculated, and it is compared with the threshold value. Combined rub and bouncing can be identified for it has the largest local variance. Finally, the mean value of IF during the sampling period is calculated and is compared with the other threshold value. Pendulum vibration can be identified for it has a lower and fixed mean value, while full rub has a larger value. The principle of the recognition method is demonstrated by the simulated results of a thermo-dynamic model. The results reveal that the method is feasible in recognizing the orbit responses and can be implemented in the AMB controller to help switch the control algorithms automatically in case of touchdowns.</span>//article/140/2/021002/2653502/Orbit-Response-Recognition-During-Touchdowns-bySurge Vibration-Induced Nonlinear Behavior Regulation of Power Amplifier for Magnetic Bearing in a 315 kW Centrifugal Compressor
//article/140/2/021003/2653503/Surge-VibrationInduced-Nonlinear-Behavior
Wed, 04 Oct 2017 00:00:00 GMTZhang Y, Zheng S, Ma C, et al. <span class="paragraphSection">The severe vibration induced by surge and rotating stall is an obstacle to the stability of a magnetically suspended centrifugal compressor (MSCC). In order to suppress the severe vibration caused by surge instability, this paper focuses on compressor surge performance improvements enabled by power amplifier control improvements which result in increased dynamic load capacity (DLC) of the systems axial thrust magnetic bearing. A complete discrete-time model of the active magnetic bearing (AMB) power amplifier, composed of three piecewise linear intervals, is developed. A comprehensive view of the dynamic evolution process from stable state to bifurcation for the power amplifier is also analyzed. In order to stabilize the unstable periodic orbits in the power amplifier, a time-delay feedback control (TDFC) method is introduced to enhance the stability of the power amplifier, while the MSCC is subjected to the surge instability. Simulation results show that the stable region of the power amplifier is extended significantly using the TDFC method. Finally, the experimental investigations performed by an MSCC test rig demonstrate the effectiveness of the proposed solution under the conditions of modified surge and mild surge.</span>//article/140/2/021003/2653503/Surge-VibrationInduced-Nonlinear-BehaviorBand Gap Characteristics of Nonrotating Passive Periodic Drill String
//article/140/2/021004/2653504/Band-Gap-Characteristics-of-Nonrotating-Passive
Wed, 04 Oct 2017 00:00:00 GMTAlsaffar Y, Sassi S, Baz A. <span class="paragraphSection">A new class of drill strings is investigated whereby strategically designed and placed periodic inserts are utilized to filter out the vibration transmission along the drill strings. Such mechanical filtering capabilities allow the vibrations to propagate along the periodic drill string only within specific frequency bands called the “pass bands” and completely block it within other frequency bands called the “stop bands.” The design and the location of the inserts are selected to confine the dominant modes of vibration of the drill string within the stop bands generated by the periodic arrangement of the inserts in order to completely block the propagation of the vibrations. A finite element model (FEM) that simulates the operation of this new class of drill strings is developed to describe the complex nature of the vibration encountered during drilling operations. Experimental prototype of the passive periodic drill string was built and tested to demonstrate the feasibility and effectiveness of the concept of periodic drill string in mitigating undesirable vibrations. The experimental results are used to validate the developed theoretical model and to develop a scalable design tool that can be used to predict the dynamical behavior of this new class of drill strings.</span>//article/140/2/021004/2653504/Band-Gap-Characteristics-of-Nonrotating-PassiveDynamics of Slightly Curved Pipe Conveying Hot Pressurized Fluid Resting on Linear and Nonlinear Viscoelastic Foundations
//article/140/2/021005/2652341/Dynamics-of-Slightly-Curved-Pipe-Conveying-Hot
Wed, 04 Oct 2017 00:00:00 GMTOwoseni OD, Orolu KO, Oyediran AA. <span class="paragraphSection">One of the most important facilities in the oil and gas industry is the pipeline. These pipelines convey high pressure with high temperature (HPHT) fluids and transit several kilometers traveling through different seafloor soils. The topography of seabed which acts as viscoelastic foundation to the pipeline is rough and irregular, thereby making the pipelines to be slightly curved. This erratic behavior of these soils presents several problems to the constructor and threatens the lifespan of the pipeline. The nonlinear governing partial differential equations (PDEs) were derived and solved using energy and eigenfunction expansion methods, respectively. The resultant ordinary differential equations (ODEs) were truncated after the fourth mode and solved numerically using eighth-seventh order Runge–Kutta code in <span style="text-transform:lowercase;font-variant:small-caps;">matlab</span>. Two types of foundations were investigated: both with viscous damping but one was with linear spring, while the other was with nonlinear spring. Bifurcation and orbit diagrams with their corresponding phase portraits that show periodic and chaotic motions of the system trajectories are generated and presented. It was examined that foundation, initial curvature, and tension could stiffen the pipe, while pressure and temperature did the rule of softening. Nonlinear stiffness made the pipe to undergo chaotic oscillation which was absent in the linear case, meaning that linear foundations could enhance the life span of pipelines than the nonlinear ones.</span>//article/140/2/021005/2652341/Dynamics-of-Slightly-Curved-Pipe-Conveying-HotAcoustic Analogy for Multiphase or Multicomponent Flow
//article/140/2/021006/2654083/Acoustic-Analogy-for-Multiphase-or-Multicomponent
Wed, 04 Oct 2017 00:00:00 GMTMao Y, Hu Z. <span class="paragraphSection">The Ffowcs Williams and Hawkings (FW-H) equation is widely used to predict sound generated from flow and its interaction with impermeable or permeable surfaces. Owing to the Heaviside function used, this equation assumes that sound only propagates outside the surface. In this paper, we develop a generalized acoustic analogy to account for sound generation and propagation both inside and outside the surface. The developed wave equation provides an efficient mathematical approach to predict sound generated from multiphase or multicomponent flow (MMF) and its interaction with solid boundaries. The developed wave equation also clearly interprets the physical mechanisms of sound generation, emphasizing that the monopole and dipole sources are dependent on the jump in physical quantities across the interface of MMF rather than the physical quantities on one-side surface expressed in the FW-H equation. The sound generated from gas bubbles in water is analyzed by the newly developed wave equation to investigate parameters affecting the acoustic power output, showing that the acoustic power feature concluded from the Crighton and Ffowcs Williams (C-FW) equation is only valid in a specific case of all bubbles oscillating in phase.</span>//article/140/2/021006/2654083/Acoustic-Analogy-for-Multiphase-or-MulticomponentActive Control of Viscoelastic Systems by the Method of Receptance
//article/140/2/024501/2654993/Active-Control-of-Viscoelastic-Systems-by-the
Wed, 04 Oct 2017 00:00:00 GMTSingh KV, Ling X. <span class="paragraphSection">Viscoelastic materials have frequency and temperature-dependent properties and they can be used as passive controlling devices in wide range of vibration applications. In order to design active control for viscoelastic systems, an accurate mathematical modeling is needed. In practice, various material models and approximation techniques are used to model the dynamic behavior of viscoelastic systems. These models are then transformed into approximating state-space models, which introduces several challenges such as introduction of nonphysical internal state variables and requirement of observer/state estimator design. In this paper, it is shown that the active control for viscoelastic structures can be designed accurately by only utilizing the available receptance transfer functions (RTF) and hence eliminating the need for state-space modeling for control design. By using the recently developed receptance method, it is shown that active control for poles and zeros assignment of the viscoelastic systems can be achieved. It is also shown that a nested active controller can also be designed for continuous structures (beams/rods) supported by viscoelastic elements. It is highlighted that such a controller design requires modest size of RTF and solution of the set of linear system of equations.</span>//article/140/2/024501/2654993/Active-Control-of-Viscoelastic-Systems-by-the