Academic literature on the topic 'Mass Proportional Dampers'
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Journal articles on the topic "Mass Proportional Dampers"
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Waghmare, Manisha V., Suhasini N. Madhekar, and Vasant A. Matsagar. "Influence of Nonlinear Fluid Viscous Dampers on Seismic Response of RC Elevated Storage Tanks." Civil Engineering Journal 6 (December 9, 2020): 98–118. http://dx.doi.org/10.28991/cej-2020-sp(emce)-09.
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The numerical investigation on the seismic response of RC elevated liquid storage tanks installed with viscous dampers is presented. A discrete two-mass model for the liquid and multi-degree of freedom system for staging, installed with the dampers are developed for Reinforced Concrete (RC) elevated liquid storage tanks. The elevated tank is assessed for seismic response reduction when provided with Linear Viscous Damper (LVD) and Nonlinear Viscous Damper (NLVD), installed in the staging. The RC elevated liquid storage tanks are analyzed for two levels of liquid containment in the tank, 100% and 25% of the tank capacity. Three Configurations of placements of dampers viz. dampers at alternate levels (Configuration I and Configuration II) and dampers at all the panels of the staging of the tank (Configuration III) are considered. To study the effect of peak ground acceleration, eight real earthquake time histories with accelerations varying from 0.1 g to 0.93 g are considered. The nonlinearity in the viscous damper is modified by taking force proportional to various velocity exponents. It is found that the nonlinear viscous dampers with lower damping constant result in a comparable reduction in the response of RC elevated liquid storage tank, to that of linear viscous dampers with higher damping constant. A lower damping constant signifies compact the size of the damper. Doi: 10.28991/cej-2020-SP(EMCE)-09 Full Text: PDF
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TROMBETTI, TOMASO, and STEFANO SILVESTRI. "ADDED VISCOUS DAMPERS IN SHEAR-TYPE STRUCTURES: THE EFFECTIVENESS OF MASS PROPORTIONAL DAMPING." Journal of Earthquake Engineering 8, no. 2 (March 2004): 275–313. http://dx.doi.org/10.1080/13632460409350490.
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Adhar Bagus, Muhammad, Azizan As’arry, Hesham Ahmed Abdul Mutaleb Abas, Abdul Aziz Hairuddin, and Mohd Khair Hassan. "Vibration control of FSAE quarter car suspension test rig using magnetorheological damper." Indonesian Journal of Electrical Engineering and Computer Science 17, no. 3 (March 1, 2020): 1281. http://dx.doi.org/10.11591/ijeecs.v17.i3.pp1281-1288.
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Recently MRF damper -which has a significant controllable damping force - used frequently in many active and semi-active suspension systems. However, MRF damper needs controller to estimate the desired force to dissipate the occurred vibration instantaneously. PID controller is one of the effective feedback controllers which shows robustness and simplicity in control MRF dampers, but still the parameters of the PID controller under study to find out the optimum values. This study focused on the vibration control using Magneto-rheological (MR) damper on a FSAE quarter car suspension test rig to study and obtain the optimum running condition. The test rig was designed, modified and then tested using a P-controller integrated with MR damper, unbalance mass used as disturbance and analyzed using LABVIEW software in time and frequency domains. The natural frequency obtained was 2.2 Hz were similar to the actual FSAE car natural frequency. Based on the acceleration against time graph with different proportional gain value the optimal value for proportional gain, Kp was 1. Hence, the experiment work could be used as the initial stage to study and develop a robust controller to suppress vibration on a car.
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Pawlak, Zdzisław M., and Roman Lewandowski. "The Effectiveness of the Passive Damping System Combining the Viscoelastic Dampers and Inerters." International Journal of Structural Stability and Dynamics 20, no. 12 (October 14, 2020): 2050140. http://dx.doi.org/10.1142/s0219455420501400.
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Passive damping systems are energy dissipating devices that are used in building constructions to reduce excessive vibration caused by wind or earthquakes. Recently, the use of inerters, devices using the inertia of the rotating mass, as a passive damping system has become more and more popular. Inerter, regardless of the construction, generates a resistance force that is proportional to the relative acceleration at the terminal ends of the device. The purpose of this study is to evaluate the effectiveness of the viscoelastic (VE) dampers in combination with the inerter. For the derived equations of motion of structures with VE dampers and inerters, the Laplace transformation is applied, which leads to a nonlinear eigenproblem. The solution to the eigenproblem is obtained using the continuation method, also known as the homotopy or as the path following method. It was found that for some cases of inerter connection with ve damper, there are some additional solutions in relation to the degrees of freedom of the structure. Furthermore, the dynamic characteristics of the structure associated with the above-mentioned additional eigenvalue are strongly dependent on the equivalent inerter mass. Damping efficiency is tested by determining changes in the system’s dynamic characteristics: natural frequencies, non-dimensional damping ratios and displacement transfer functions. The presented approach allows determining the appropriate parameters of the inerter and VE damper and their appropriate location on the structures that correspond to the most effective damping. The obtained numerical results confirm the effectiveness of the proposed approach.
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Szary, Marek L., and Peter Weber. "The Study of Behavior of Vibrating Systems Controllable by Devices with Rheological Fluid." Archives of Acoustics 38, no. 2 (June 1, 2013): 217–22. http://dx.doi.org/10.2478/aoa-2013-0026.
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Abstract The nonlinear mathematical model of behavior of controllable viscosity fluid (CVF) under applied external field is presented. A large family of these fluids is commonly used to control responding forces of dampers in vibration control applications. The responding force of a damper with CVF has two components. The first one - uncontrollable - is proportional to the viscosity of a base fluid and velocity of its motion, the second one, which is controllable, depends on the strength of the applied external field. Both are involved in the process of dissipation of unwanted energy from the vibrating systems. An equivalent damping factor based on the principle of energy dissipated during one cycle of damper work under a constant strength external field was calculated. When mass or stiffness is variable the equivalent damping factor can be set accordingly by adjusting the strength of external field to have vibrating damped system purposely/continuously working in the critical or other chosen state. This paper also presents cases of applying periodically changing strengths of an external field synchronized with cycles of periodical motion of the vibrating system to continuously control the damping force within each cycle.
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KOSTANTAKOPOULOS, T. G., and G. T. MICHALTSOS. "MODELING AND ANALYSIS OF A PLATE ON ELASTIC FOUNDATION SUBJECTED TO LANDING AIRPLANES' FORCES." International Journal of Structural Stability and Dynamics 10, no. 01 (March 2010): 37–54. http://dx.doi.org/10.1142/s0219455410003373.
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This paper deals with the problem of the dynamic behavior of a plate on elastic foundation under the action of forces produced by a landing airplane. A partially plastic impact is postulated for the contact between the airplane and the plate. The Winkler model is used to simulate the ground's elastic behavior, by which the foundation reaction is proportional to the plate deflection, along with dampers for energy dissipation. Two models are used for the airplane, i.e. a simplified mass-load model and a mass-dashpot-spring model, and their influences on the dynamic response of the plate are evaluated. Moreover, various parameters concerning the salient features of the airplane and its landing on the plate are studied with conclusions drawn. The efficiency of the methodology proposed herein was demonstrated in the numerical study.
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Trombetti, T., and S. Silvestri. "Novel schemes for inserting seismic dampers in shear-type systems based upon the mass proportional component of the Rayleigh damping matrix." Journal of Sound and Vibration 302, no. 3 (May 2007): 486–526. http://dx.doi.org/10.1016/j.jsv.2006.11.030.
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Kayabekir, Aylin Ece, Gebrail Bekdaş, Sinan Melih Nigdeli, and Zong Woo Geem. "Optimum Design of PID Controlled Active Tuned Mass Damper via Modified Harmony Search." Applied Sciences 10, no. 8 (April 24, 2020): 2976. http://dx.doi.org/10.3390/app10082976.
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In this study, the music-inspired Harmony Search (HS) algorithm is modified for the optimization of active tuned mass dampers (ATMDs). The modification of HS includes the consideration of the best solution with a defined probability and updating of algorithm parameters such as harmony memory, considering rate and pitch adjusting rate. The design variables include all the mechanical properties of ATMD, such as the mass, stiffness and damping coefficient, and the active controller parameters of the proposed proportional–integral–derivative (PID) type controllers. In the optimization process, the analysis of an ATMD implemented structure is done using the generated Matlab Simulink block diagram. The PID controllers were optimized for velocity feedback control, and the objective of the optimization is the minimization of the top story displacement by using the limitation of the stroke capacity of ATMD. The optimum results are presented for different cases of the stroke capacity limit of ATMD. According to the results, the method is effective in reducing the maximum displacement of the structure by 53.71%, while a passive TMD can only reduce it by 31.22%.
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Venanzi, Ilaria, and Filippo Ubertini. "Free Vibration Response of a Frame Structural Model Controlled by a Nonlinear Active Mass Driver System." Advances in Civil Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/745814.
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Active control devices, such as active mass dampers, are mainly employed for the reduction of wind-induced vibrations in high-rise buildings, with the final aim of satisfying vibration serviceability limit state requirements and of meeting appropriate comfort criteria. When such active devices, normally operating under wind loads associated with short return periods, are subjected to seismic events, they can experience large amplitude vibrations and exceed stroke limits. This may lead to a reduced performance of the control system that can even worsen the performance of the whole structure. In this paper, a nonlinear control strategy based on a modified direct velocity feedback algorithm is proposed for handling stroke limits of an active mass driver (AMD) system. In particular, a suitable nonlinear braking term proportional to the relative AMD velocity is included in the control law in order to slowdown the device in the proximity of the stroke limits. Experimental and numerical free vibration tests are carried out on a scaled-down five-story frame structure equipped with an AMD to demonstrate the effectiveness of the proposed control strategy.
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Hathout, J. P., and A. El-Shafei. "PI Control of HSFDs for Active Control of Rotor-Bearing Systems." Journal of Engineering for Gas Turbines and Power 119, no. 3 (July 1, 1997): 658–67. http://dx.doi.org/10.1115/1.2817035.
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This paper describes the proportional integral (PI) control of hybrid squeeze film dampers (HSFDS) for active control of rotor vibrations. Recently it was shown that the automatically controlled HSFD based on feedback of rotor speed can be a very efficient device for active control of rotor vibration when passing through critical speeds. Although considerable effort has been put into the study of steady-state vibration control, there are few methods in the literature applicable to transient vibration control of rotor-bearing systems. Rotating machinery may experience dangerously high dynamic loading due to the sudden mass unbalance that could be associated with blade loss. Transient run-up and coast down through critical speeds when starting up or shutting down rotating machinery induces excessive bearing loads at criticals. In this paper, PI control is proposed as a regulator for the HSFD system to attenuate transient vibration for both sudden unbalance and transient runup through critical speeds. A complete mathematical model of this closed-loop system is simulated on a digital computer. Results show an overall enhanced behavior for the closed-loop rotor system. Gain scheduling of both the integral gain and the reference input is incorporated into the closed-loop system with the PI regulator and results in an enhanced behavior of the controlled system.
Dissertations / Theses on the topic "Mass Proportional Dampers"
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Mazza, Samuele. "Soluzioni progettuali con dissipatori viscosi per il miglioramento sismico di un edificio ospedaliero." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017.
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Nel presente elaborato si sono analizzate alcune metodologie per il miglioramento sismico dell'Istituto Ortopedico Rizzoli. In particolare sono state elaborate tre differenti soluzioni progettuali contemplanti i dispositivi di smorzamento viscoso. Le soluzioni si diversificano oltre che dal punto di vista applicativo, anche da quello teorico, in quanto gli smorzatori in una soluzione sono stati inseriti all'interno della costruzione stessa venendo quindi modellati in modo proporzionale alle masse di piano, nelle altre due soluzioni sono inseriti al di fuori della struttura, costituendo alcune torri esterne a complemento del progetto di miglioramento; in quest'ultimo caso i dispositivi vengono modellati proporzionalmente alle rigidezze laterali degli elementi verticali interpiano. Il dimensionamento degli smorzatori è stato effettuato seguendo i criteri proposti nella Five-Step Procedure proposta da Silvestri et al. nel 2010. Per ogni soluzione, si è redatto il corrispondente computo metrico estimativo al fine di confrontare i costi delle tre soluzioni.
Conference papers on the topic "Mass Proportional Dampers"
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Tai, Wei-Che. "Optimum Design of a New Tuned Inerter Mass Damper (TIMD) Passive Vibration Control for Stochastically Motion-Excited Structures." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-98044.
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Abstract The inerter that is referred to as a two-terminal device that provides resisting forces proportional to the relative accelerations between its two terminals has been widely applied in vibration control due to its mass amplification effect. In this paper, a new inerter-based damper is proposed to take advantage of the inerter, which consists of a rack-pinion inerter in conjunction with a tuned rotational inertia damper. Unlike any other inerter-based dampers, the rotational inertia damper is connected to the pinion of the inerter via a rotational spring and damper. As a result, the weight of the damper can be significantly reduced. The proposed damper is applied to single-degree-of-freedom primary structures and a two-degree-of-freedom structure and the H2 optimization is conducted to obtain the optimum tuning ratio and damping ratio analytically. When comparing the proposed damper with its counterpart reported in the literature, the proposed damper achieves 20% to 70% improvement when their weights are identical.
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Kashani, Reza. "An Air Suspension System With Adjustable Height, Damping and Stiffness Using No Viscous Dampers." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-10153.
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Abstract Air suspension is gaining more and more popularity with both the auto industry and drivers. Traditionally the height adjustability aspect of air suspension systems has been their main attracting attribute. More recently, resolving the classic conflict of combining comfortable ride with sport handling in a single suspension setup has become the main attraction of air suspension. An air suspension system has been developed which in addition to height adjustment, can adjust its damping and stiffness in real time with using neither viscous dampers nor any additional actuators. This is done by real-time adjustment air flow to and from the air springs using proportional valves. Measured relative displacement and acceleration as well as estimated velocity of the sprung mass with respect to unspring mass at each corner are fedback, thru their corresponding gains, to create the control signal that adjusts the proportional valve with the goal of controlling the height, stiffness, and damping at that corner. In a numerical study followed by laboratory testing, the effectiveness of the proposed air suspension system in terms of its ability to vary the damping and stiffness as well as the height of the suspension system is demonstrated.
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Changsheng, Zhu, Wang Xixuan, and Fu Caigao. "Investigation on the Bistable Jump in Subcritical Speed Range of Rotor Supported on Uncentralized Squeeze Film Dampers." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0255.
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Abstract This paper presents one of bistable jump phenomena observed in rotor system supported on uncentralized squeeze film dampers which occurs in the subcritical speed range of rotor. The jumping tendency of this bistable jump is jumping up in acceleration and jumping down in deceleration and is without the transposition of disk mass centre. The behaviors, especially the latter, are different from the bistable jump behaviors reported to date. The reason for occurrence of the subcritical speed bistable jump is explained by a Duffing equation with the varied stiffness and the exciting force which amplitude is proportional to the square of rotating speed of rotor.
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Hathout, J. P., and A. El-Shafei. "PI Control of HSFDs for Active Control of Rotor-Bearing Systems." In ASME 1996 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-gt-123.
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This paper describes the proportional integral (PI) control of hybrid squeeze film dampers (HSFDs) for active control of vibrations of rotors. Recently it was shown that the automatically controlled HSFD based on feedback of rotor speed can be a very efficient device for active control of rotor vibration when passing through critical speeds. Although considerable effort has been put into the study of steady state vibration control, there are few methods in the literature applicable to transient vibration control of rotor-bearing systems. Rotating machinery may experience dangerously high dynamic loading due to the sudden mass unbalance that could be associated with blade loss. Transient run-up and coast down through critical speeds when starting up or shutting down rotating machinery induces excessive bearing loads at criticals. In this paper, PI control is proposed as a regulator for the HSFD system to attenuate transient vibration for both sudden unbalance and transient run-up through critical speeds. A complete mathematical model of this closed-loop system is simulated on a digital computer. Results show an overall enhanced behavior for the closed-loop rotor system. Gain scheduling of both the integral gain and the reference input is incorporated to the closed-loop system with the PI regulator and results in an enhanced behavior of the controlled system.
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Chesne, S., K. Billon, C. Collette, and G. Zhao. "Power Flow Analysis for Hybrid Mass Damper Design." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85813.
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Tuned Mass Damper (TMD) are largely used in many domains like aerospace or civil engineering. While very simple and robust, their damping capability is proportional to their mass, which represents an important shortcoming. Hybrid-TMDs propose to combine active systems to an optimal passive device. Nevertheless, stability problems can result from this association. In this study, the passivity concept is used to design a control law enforcing the hybrid-TMD to be hyperstable. Consequently, the resulting Hybrid TMD is fail-safe and unconditionally stable. An analysis of the active and reactive powers also illustrates the energy flux in the device and its passive nature. Simulations based on an experimental model show the performance of such system.
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San Andrés, Luis, and Bonjin Koo. "Model and Experimental Verification of the Dynamic Forced Performance of a Tightly Sealed Squeeze Film Damper Supplied With a Bubbly Mixture." In ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gt2019-90330.
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Abstract Practice and experiments with squeeze film dampers (SFDs) sealed with piston rings (PRs) show the lubricant exits through the PR slit, i.e. the gap made by the PR abutted ends when installed, forced as a jet during the portion of a rotor whirl cycle generating a positive squeeze film pressure. In the other portion of a whirl cycle, a sub ambient dynamic pressure ingests air into the film that mixes with the lubricant to produce a bubbly mixture. To reduce persistent air ingestion, commercial air breathing engines utilizing PRSFDs demand of a sufficiently large lubricant supply pressure (Ps), and hence a larger flow rate that is proportional to the journal squeeze velocity (vs = amplitude r × frequency of motion ω). The stringent requirement clearly limits the applicability and usefulness of SFDs. This paper presents a computational physics model for a sealed ends SFD operating with a mixture and delivers predictions benchmarked against profuse laboratory test data. The model implements a Reynolds equation adapted for a homogeneous bubbly mixture, includes temporal fluid inertia effects, and uses physics based inlet and outlet lubricant conditions through feed holes and PR slit, respectively. In the experiments for model validation, a SFD damper, 127 mm in diameter D, film land length L = 25.4 mm (L/D = 0.2), and radial clearance c = 0.371 mm, is supplied with an air in ISO VG2 oil bubbly mixture of known GVF, zero (pure oil) to 50% in steps of 10%. The mixture supply pressure varies from Ps = 2.06 bar-g (30 psig) to 6.20 bar-g (90 psig). Located in grooves at the top and bottom of the journal, a piston ring (PR) and an O-ring (OR) seal the film land. The OR does not allow any oil leakage or air ingestion; hence the supplied mixture discharges thru the PR slit into a vessel submerged within a large volume of lubricant. Dynamic load tests with a single frequency ω, varying from 10 Hz to 60 Hz, produce circular centered orbits with amplitude r = 0.2c. The measurements record the exerted forces and journal motions and an analysis delivers force coefficients, damping and inertia, representative of the exerted frequency range. The model predicts the pressure field and evolution of the gas volume fraction (GVF) within the film land and, in a simulated process replicating the experimental procedure, delivers representative force coefficients. For all Ps conditions, both predictions and tests show the SFD added mass coefficients significantly decrease as the inlet GVF (βs) increases. The experimentally derived damping coefficients do not show a significant change, except for tests with the largest concentration of air (βs = 0.5). The predicted damping differs by 10% with the test derived coefficient which does not readily decrease as the inlet GVF (βs) increases. The added mass coefficients, test and predicted, decrease with βs, both being impervious to the magnitude of supply pressure. The test PRSFD shows a quadrature stiffness due to the sliding friction between the PR being pushed against the journal. An increase in supply pressure exacerbates this unique stiffness that may impair the action of the squeeze film to dissipate mechanical energy. The comprehensive test results, first of their kind, demonstrate that accurate modeling of SFDs operating with air ingestion remains difficult as the flow process and the paths of its major components (air and liquid) are rather complex.
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Hampton, R. David, Nathan S. Wiedenman, and Ting H. Li. "Analytical Determination of Shock Response Spectra for an Impulse-Loaded Proportionally Damped System." In ASME 7th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2004. http://dx.doi.org/10.1115/esda2004-58024.
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Many military systems must be capable of sustained operation in the face of mechanical shocks due to projectile or other impacts. The most widely used method of quantifying a system’s vibratory transient response to shock loading is called the shock response spectrum (SRS). The system response for which the SRS is to be determined can be due, physically, either to a collocated or to a noncollocated shock loading. Taking into account both possibilities, one can define the SRS as follows: the SRS presents graphically the maximum transient response (output) of an imaginary ideal mass-spring-damper system at one point on a flexible structure, to a particular mechanical shock (input) applied to an arbitrary (perhaps noncollocated) point on the structure, as a function of the natural frequency of the imaginary mass-spring-damper system. For a response point sufficiently distant from the impact area, many Army platforms (such as vehicles) can be accurately treated as linear systems with proportional damping. In such cases the output due to an impulsive mechanical-shock input can be decomposed into exponentially decaying sinusoidal components, using normal-mode orthogonalization. Given a shock-induced loading comprising such components, this paper provides analytical expressions for the various common SRS forms. The analytical approach to SRS-determination can serve as a verification of, or an alternative to, the numerical approaches in current use for such systems. No numerical convolution is required, because the convolution integrals have already been accomplished analytically (and exactly), with the results incorporated into the algebraic expressions for the respective SRS forms.
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Frazier, Michael J., and Mahmoud I. Hussein. "Bloch-Theory-Based Analysis of Damped Phononic Materials." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-65662.
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In this paper, we combine Bloch theory with familiar techniques of structural dynamics to study the effects of energy dissipation (i.e., damping) in an acoustic metamaterial. The formulation we present has the novel feature of incorporating a temporal component to wave attenuation in addition to the standard spatial component. The frequency band structure reflects the metamaterial response to the damping intensity. In the context of a lumped parameter nested mass model, increasing the magnitude of damping is shown to cause the band structure to descend the frequency range and reveal an intriguing phenomenon: branch overtaking. This effect occurs as dissipation causes the optical branch to descend below the acoustical branch. The resulting decrease in the width of the band gap would impact vibration minimization and isolation. We also examine the effective properties of the metamaterial, specifically, the effective mass and effective stiffness, and the conditions for these quantities to become negative. Finally, the aforementioned material results are shown to be related to their finite counterpart. For ease of exposition, we consider a special form of Rayleigh damping in which the damping is proportional to the stiffness. The intrinsic presence of dissipation in acoustic metamaterials and the limited scientific literature addressing damped wave propagation in periodic media in general motivates our present study.
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Wanderley, Juan B. V., Luiz F. Soares, Marcelo Vitola, Sergio H. Sphaier, and Carlos Levi. "Reynolds Number Effect on Vortex-Induced Vibration on a Two-Dimensional Circular Cylinder With Low Mass-Damping Parameter." In ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2011. http://dx.doi.org/10.1115/omae2011-49049.
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The vortex induced vibration (VIV) on a circular cylinder with low mass-damping parameter and low Reynolds number is investigated numerically as basis for applications on dynamics of risers used in the offshore oil and gas industry and as a first step before tackling the harder high Reynolds number problem. The cylinder is supported by a spring and a damper and free to vibrate in the transverse direction. The numerical solution of the Reynolds average Navier-Stokes equations written in curvilinear coordinates is obtained using an upwind and Total Variation Diminishing conservative scheme and the k-ε turbulence model is used to simulate the turbulent flow in the wake of the body. Results were obtained for the phase angle, response amplitude, frequency, and lift coefficient for a variation of reduced velocity from 2 to 12 and three different proportional variations of Reynolds number, 2000–6000, 2000–12000, and 2000–24000. The numerical results indicate the strong effect of the Reynolds number range on the response amplitude, lift coefficient, and frequency of oscillation for a low mass-damping parameter.
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Dmitriev, Alexandr S. "Fluctuation Hydrodynamics, Thermophoresis of Nanoparticles and Heat Transfer in Nanofluids." In ASME 2012 Third International Conference on Micro/Nanoscale Heat and Mass Transfer. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/mnhmt2012-75205.
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In this paper we studied in the framework of two-fluid hydrodynamics with fluctuations the behavior of nanoparticles in the liquid with temperature gradient [1, 2]. It is shown that the acoustic long-wave fluctuations are not damped in liquids (long-wavelength phonons) and leads to an additional force acting on the nanoparticles, as well as lead to the emergence of a new force of thermophoresis [3], which is proportional to the temperature in three second degree. It is also shown that such a thermophoresis force arising under the two-fluid hydrodynamics, can lead to instability of an ensemble of nanoparticles in the presence of a temperature gradient. The last effect leads to the possible merger of the nanoparticles in the form of elongated clusters. The appearance of such clusters on the one hand, leads to an increase in effective thermal conductivity of nanofluids, and secondly, appearing elongated clusters contribute to the propagation of long-wavelength phonons along of such clusters. In fact, this new type of heat transfer in nanofluids, which must be considered in addition to the Brownian motion of nanoparticles.