The properties of dense granular systems are analyzed from a hydrodynamical point of view, based on conservation laws for the particle number density and linear momentum. We discuss averaging problems associated with the nature of such systems and the peculiarities of the sources of noise. We perform a quantitative study by combining analytical methods and numerical results obtained by ensemble-averaging of data on creep during compaction and molecular dynamics simulations of convective flow. We show that numerical integration of the hydrodynamic equations gives the expected evolution for the time-dependent fields.

Spacecraft designs are driven by the necessity of the spacecraft to survive being launched into orbit. This launch environment consists of structure-borne vibrations transmitted to the payload through the payload attach fitting (PAF) and acoustic excitation. Here we present a discussion on the need for and benefit of isolating the structure-borne vibrations. If the PAF were replaced with an isolator with the correct characteristics the potential benefits would be significant. These benefits include reduced spacecraft structural weight and cost, as well as increased life and reliability. This paper presents an overview of the problem of vibration on a launch vehicle payload and the benefits that an isolating PAF would provide. The structure-borne vibrations experienced by a spacecraft during launch are made up of transient, shock, and periodic oscillations originating in the engines, pyrotechnic separation systems, and from aerodynamic loading. Any isolation system used by the launch vehicle must satisfy critical launch vehicle constraints on weight, cost, and rattle space. A discussion of these points is presented from the perspective of both a launch vehicle manufacturer and a spacecraft manufacturer/user.

A spacecraft is subjected to very large dynamic forces from its launch vehicle during its ascent into orbit. These large forces place stringent design requirements on the spacecraft and its components to assure that the trip to orbit will be survived. The severe launch environment accounts for much of the expense of designing, qualifying, and testing satellite components. Reduction of launch loads would allow more sensitive equipment to be included in missions, reduce risk of equipment or component failure, and possibly allow the mass of the spacecraft bus to be reduced. These benefits apply to military as well as commercial satellites. This paper reports the design and testing of a prototype whole-spacecraft isolation system which will replace current payload attach fittings, is passive-only in nature, and provides lateral isolation to a spacecraft which is mounted on it. This isolation system is being designed for a medium launch vehicle and a 6500 lb spacecraft, but the isolation technology is applicable to practically all launch vehicles and spacecraft, small and large. The feasibility of such a system on a small launch vehicle has been demonstrated with a system-level analysis which shows great improvements. The isolator significantly reduces the launch loads seen by the spacecraft. Follow-on contracts will produce isolating payload attach fittings for commercial and government launches.

The U.S. Air Force's Phillips Laboratory has sponsored several programs to isolate payloads from mechanical vibrations during launch. This paper details a program called LVIS (for launch vibration isolation system). LVIS's goals are to reduce the rms accelerations felt by an isolated payload by a factor of 5 compared to an unisolated payload while using minimal launch vehicle services, fitting within existing payload attach fittings' dimension and mass envelopes, and providing fail- safe operation. The LVIS system must provide axial isolation while at the same time not allowing its host spacecraft to 'rattle' too much and make contact with the launch vehicle's external payload fairing, which is present to protect against heat, aerodynamic, and acoustic loads. This challenging set of goals will be accomplished using an innovative suspension system specially designed to be relatively soft in the vertical and lateral directions and stiff in the rotational directions to prevent payload fairing contact. An overview of the LVIS design and predicted performance is given.

The theoretical analysis of an improved piezoelectric shunt using a piezoelectric PZT element shunted with a parallel resistor and inductor circuit for passive structural damping and vibration control was studied. In this paper, we report results of the experiments of the improved shunting technique which were performed and demonstrated successfully for passive vibration control in the ARPA consortium SPICES program on several structures including thermoset fiberglass/epoxy composite plates with embedded PZT patches and cantilever beams with surface bonded patches. Vibration reductions on resonant response of more than 17 dB using the single mode shunting have been obtained on an 18' by 18' by 0.5' composite plate with eight embedded PZT patches. When we excite another composite plate with a commercial compressor mounted on top of it and turn on the shunt circuits, the transmitted vibration level measured with a force gauge at a plate mounting post is reduced about 15 dB. The improved piezoelectric shunting technique has been studied further to shunt-damp multiple vibration modes using only a single PZT patch. The experimental result of the multiple mode shunting also is presented.

A shunting method has been developed and experimentally verified for tuning the natural frequency and damping of a piezoceramic inertial actuator (PIA). Without power, a PIA behaves much like a passive vibration absorber (PVA). PVAs typically minimize vibration at a specific frequency often associated with a lightly damped structural mode. Large response reductions, however, may only be achieved if the PVA is accurately tuned to the frequency of concern. Thus, an important feature of a PVA is the ability to be accurately tuned to the possibly varying frequency of a target vibration mode. Tuning an absorber requires a change in either the mass or stiffness of the device. The electromechanical properties of the piezoceramic forcing element within a PIA in conjunction with an external passive electrical shunt circuit can be used to alter the natural frequency and damping of the device. An analytical model of a PIA was created to predict changes in natural frequency and damping due to passive electrical shunting. Capacitive shunting alters the natural frequency of the actuator only, while resistive shunting alters both the natural frequency and damping of the actuator. Experiments using both passive capacitive and passive resistive shunt circuits verified the ability to predictably shift the natural frequencies of the piezoceramic inertial actuator by more than 5%.

To add damping to systems, viscoelastic materials (VEM) are added to structures. In order to enhance the damping effects of the VEM, a constraining layer is attached. When this constraining layer is an active element, the treatment is called active constrained layer damping (ACLD). Recently, the investigation of ACLD treatments has shown it to be an effective method of vibration suppression. In this paper, the treatment of a beam with a separate active element and passive constrained layer (PCLD) element is investigated. A Ritz- Galerkin approach is used to obtain discretized equations of motion. The damping is modeled using the GHM method and the system is analyzed in the time domain. By optimizing on the performance and control effort for both the active and passive case, it is shown that this treatment is capable of lower control effort with more inherent damping, and is therefore a better approach to damp vibration.

This paper is concerned with the investigations of edge elements' effects on a new class of active constrained layer (ACL) treatment, the so-called enhanced active constrained layer (EACL) configurations. Specific interests are on understanding how the edge elements will influence the passive damping ability, the active action transmissibility, and their combined effects in EACL. Analysis results indicate that the edge elements can significantly improve the active action transmissibility of the current ACL treatment. Although the edge elements will slightly reduce the viscoelastic material (VEM) passive damping effect, the EACL will still have significant damping from the VEM. Combining the overall active and passive actions, the new EACL with sufficiently stiff edge elements can achieve better performance with less control effort as compared to systems with purely active or current ACL treatments.

This paper presents new insights obtained from analyzing the active-passive hybrid piezoelectric network (APPN) concept. It is shown that the shunt circuit not only can provide passive damping, it can also enhance the active action authority if tuned correctly. Therefore, the integrated APPN design is more effective than a system with separated active and passive elements. However, it is also recognized that a systematic design/control method is needed to ensure that the passive and active actions are optimally synthesized. Such a method is presented. The bandwidth issue for the APPN configuration is also addressed.

The development of controllable suspension dampers for ground vehicles is the subject of much current research. In this paper the authors describe aspects of a design methodology for controllable dampers which use electro-rheological (ER) fluid as the working medium. This methodology is based upon a non- dimensional characterization of ER fluid data which allows measurements obtained from small-scale tests to be used to predict the behavior of industrial-scale vibration dampers. The ER damper is represented via a Bingham plastic constitutive relationship, augmented by terms to account for fluid inertia and compressibility. An industrial-scale test facility is described and the first available set of experimental results are presented. A comparison is made between model predictions and observed behavior.

A combined theoretical and experimental study of electrorheological (ER) fluid dampers is presented here. A moving electrode ER damper was built and tested for its dynamic characteristics for different electric field strengths and varying displacement amplitudes. Based upon the phenomenology observed in the experimental results, an augmented nonlinear model is proposed to describe the dynamic characteristics of the damper. The six model parameters are estimated from the experimental hysteresis data. The force versus displacement and force versus velocity hysteresis cycles are then reconstructed using these estimated parameters. The results show that the model captures the nonlinear damper behavior quite accurately. The importance of the various components in the model is illustrated.

Electro-rheological fluid (ERF) shock absorbers are semi- active vibration control devices that utilize ERF to control the damping capacity of the dampers. The focus of this work is on the experimental study of a multi-electrode, cylindrical ERF damper designed for in-plane motion. Several three- electrode ERF dampers are built and tested specifically for vibration damping of in-plane motions. The force-velocity loops were obtained and examined for different voltage levels and electrode lengths.

An experimental investigation was performed on a semi-active control scheme that uses the rheological properties of electro-rheological fluids (ER-fluids) in squeeze-flow mode to control the dynamic behavior of single-degree-of-freedom (SDOF) systems. The reversible and very rapid changes in the mechanical properties of the fluid under variable voltage are exploited by using a control scheme that automatically turns 'on' and 'off' the electrical field as loads are applied. This control scheme rapidly adapts to any changes in the mechanical properties of the system, reducing the response of the structure for a wide range of excitation frequencies. The ER- fluid used in this study, Zeolite in silicone oil, was subjected to an electrical field range from one to five kV/mm. Tests were carried out for the 'off' system, the 'on' system, and the controlled system, and the experimental and analytical results were compared. The experimental results show that this control scheme is effective for reducing the vibration of the system. Other types of ER-fluid should be tested using this control scheme to investigate the most effective fluid for vibration suppression.

A large scale electrorheological (ER) damper has been designed, constructed, and tested. The damper consists of a main cylinder and a piston rod that pushes an ER-fluid through a number of stationary annular ducts. This damper is a scaled- up version of a prototype ER-damper which has been developed and extensively studied in the past. In this paper, results from comprehensive testing of the large-scale damper are presented, and the proposed theory developed for predicting the damper response is validated.

The behavior of actuators based on magnetorheological fluids is determined by a variety of parameters. The magnetorheological properties of the MR suspension, the working mode (shear mode, flow mode, squeeze mode) and the design of the magnetic circuit consisting of MR fluid, flux guide and coil all considerably influence the properties of the actuator. This paper presents design rules for MR fluid actuators in different working modes. The behavior of MR fluids in the three working modes was investigated by using a rotational viscometer, a flow mode damper and a new measuring technique working in the squeeze mode. The measurement results for various magnetic flux densities are reported and the results of the different working modes are compared. High dynamic damping forces dependent on the magnetic field can be achieved especially in the squeeze mode. The design of the magnetic circuit of an MR fluid actuator is analyzed by using finite-element-methods. The advantages of integrating permanent magnets into the magnetic circuit of an MR fluid actuator are pointed out. The working point of the actuator can be adjusted by permanent magnets without consuming any power and the maximum power required to drive the actuator can be reduced. From these results design rules for MR fluid actuators are developed.

A fluid surface damping (FSD) technique proposed for vibration suppression of beam-like structures is applied to a generic simply supported aluminum beam. The steady-state frequency response of the FSD-treated beam at the vicinity of one end, due to an applied white noise displacement excitation at the other end, is determined using the finite element method. The response is found over a range of frequency covering the first four resonant frequencies and over a wide temperature range. Comparison of the results with the corresponding ones of a beam treated with the constrained layer damping method indicates that the FSD technique has a much greater potential for the vibration suppression of beam-like structures. Results also indicate that the FSD technique can provide a good vibration suppression over a wider temperature range.

Much of the work done on active and passive constrained-layer beams is done with models using kinematic assumptions proposed by Kerwin, Mead and Markus, and others. The key assumption is that the base and constraining layers undergo identical transverse displacements, which is a reasonable assumption when the middle layer (here a viscoelastic material) is thin and the constraining layer is relatively weak. There are, however, many practical cases where an effective passive damping design requires the stiffness of the constraining layer to be on the order of that of the base layer. If the base structure is stiff to begin with, a constraining layer that will produce good damping is likely to violate the above stated assumption by refusing to follow the base layer exactly. The question arises as to how this affects predictions of damping. In this work the facesheets are treated as independently deforming Timoshenko beams, which results in a more general state of strain in the core material. Expressions for the potential and kinetic energies are developed from basic principles of continuum mechanics, and the assumed modes method is used to predict how levels of strain energy in the core are affected by the assumptions on the relative motions of the facesheets.

Even in this period of large expansion of active control for noise and vibration suppression, passive damping technology is widely accepted and used because of its low cost and high reliability in many common applications. Viscoelastic materials play an important role in vibration reduction both in their free and constrained layer forms. This paper addresses the problem of calculating the modal frequencies and loss factors of beams containing a constrained viscoelastic layer. The problem is approached from an analytical point of view and an approximation is proposed on the mode shapes to simply take into account different boundary conditions. Calculations are performed on the basis of the energy method and compared with the results of the classical RKU theory and a finite elements model. A similar approach is also adapted to the study of partially covered beams; in this situation the RKU theory doesn't fit and only the FE model has been used as reference.

A dynamic model for a multilayered laminated plate is developed. The laminated plate consists of 2n plate layers and 2n - 1 adhesive layers. The layers (both plate and adhesive layers) are assumed to be homogeneous, transversely isotropic and perfectly bonded to one another. In the initial modeling, the Reissner-Mindlin theory of shear deformable plates is applied to each layer, resulting in a high-order plate theory in which the shear motions of the layers are completely independent. Simpler, lower-order models can then be obtained from this initial model from asymptotic limits based upon the assumptions that (1) the adhesive layers are very thin, (2) the elastic modulii of the adhesive layers are small compared to those of the plate layers, (3) the shear stiffnesses of the plate layers are very large, (4) the rotational moments of inertia of the individual plate layers are very small.

By means of the split Hopkinson pressure bar (SHPB) technique, the time domain dynamic mechanical properties of a polyisoprene elastomer were characterized over a range of temperatures. These properties include the dynamic stress- strain and compressional relaxation modulus characteristics of the elastomer. In the SHPB technique employed in the measurements, two identical long steel bars, which are known as the incident and transmitter pressure bars, were used as wave guides. Solid disc specimens of 10 mm diameter by 3 mm and 6 mm thickness of the polyisoprene rubber were sandwiched, in turn, between the bars. Strain pulses were generated in the incident pressure bar by the collinear impact of a hardened steel spherical ball, which was fired from a mechanical launcher, with the plane free end of the incident pressure bar via a small cylindrical anvil which was attached to the impacted end of the incident pressure bar. The strain pulses generated and propagated down the pressure bar were incident on, reflected from and transmitted through the polyisoprene specimen. These pulses were monitored by PZT sensors of dimensions 5 mm by 3 mm, which were bonded to the middle locations of the pressure bars, and were used to derive the dynamic properties of the specimens. It is shown that the stress and compressional relaxation modulus characteristics of this elastomer undergo larger variations and attain higher values at low temperatures than at high temperatures.

Although high-cycle fatigue cracks in secondary structure are often termed 'nuisance cracks,' they are costly to repair. Often the repairs do not last long because the repaired part still responds in a resonant fashion to the environment. Although the use of visco-elastic materials for passive dampening applications is well understood, there have been few applications to high-cycle fatigue problems because the design information: temperature, resonant response frequency, and strain levels are difficult to determine. The damage dosimeter, and the durability patch are an effort to resolve these problems with the application of compact, off-the-shelf electronics, and a damped bonded repair patch. This paper presents the electronics, and patch design concepts as well as damping performance test data from a laboratory patch demonstration experiment.

ACTA has developed and demonstrated a three-dimensional, large amplitude, actively-controlled, multi-cable suspension system for dynamically testing large space structures in a simulated microgravity environment. Tension in the cables is actively controlled by large amplitude rotary actuators designed and built at Texas A&M University. The actuators passively support the weight of the test article on soft spiral springs. Spring stiffness in each actuator is compensated by a torque- controlled direct current motor. Bearing and brush friction and damping are actively compensated as well as the algorithmic damping induced by the control law. Actuator stiffness properties were determined by measuring the torque- deflection characteristics of the actuator. Hysteresis loops are compared for the different spring materials Actuator friction and damping properties (velocity-dependent resistance) are determined by measuring the torque-speed characteristics of the actuator with the spring disconnected. Multiple tests were conducted to establish the degree of randomness in these characteristics for robust control design. This paper describes the characterization of actuator stiffness, kinetic friction, and damping, and describes how these characteristics are used to negate the resulting resistance torques in the suspension system. Conclusions regarding the effectiveness of the system and possible enhancements are discussed.

Dynamic models and simulation results are presented for D- Strut^TM isolators. The D-Strut is a passive spring-damper device with space flight heritage used for vibration isolation. Detailed models are presented for both hydraulically and pneumatically damped D-Struts and the performance achieved by each will be compared. All of the models presented are single degree-of-freedom with a mass isolated from base motion by one isolator element. A simulation program was used to investigate the frequency domain and time domain dynamic response of the D-Strut models. The results are presented.

This paper discusses the results of a project which focused on the development and evaluation of internal damping concepts applicable to damping curved airfoil shaped plates. Thirteen damping concepts were analyzed. The analysis was completed using an FEA. The initial analysis computed modal damping for the first four modes of the structure. As the study progressed, the final analysis on the best two damping concepts calculated the modal damping for the first thirty modes. The system damping results were obtained using various damping materials, Young's moduli, and an assumed damping material loss factor of 1.0. The modal dampen was calculated as the ratio of the strain energy in the damping elements (SED) divided by the total strain energy (TSE) in the structure times the assumed material loss factor. The damping goal was set at 0.04 loss factor. The final designs developed had an average modal damping value which exceeded 0.1. This paper details the damping concepts evaluated, the thought process which led from one design to the next, the analysis used to evaluate the damping concepts, and the results of the trade study.

The performance of constrained layer damping treatments can be enhanced by optimizing the segment length or through active control by inducing strains in the constraining layer. This paper investigates the effect of these methods on the flexural and extensional modes of a ring over a wide frequency range. Finite element models are first verified experimentally and then used in parametric studies. It is shown that segmentation of the constraining layer does not increase the maximum damping obtainable for a particular configuration but alters the mode number at which the maximum occurs. It is also shown that the optimum viscoelastic layer stiffness for active constrained layer damping is higher than that for the passive case.

The fundamentals of controlling the structural vibration of cylindrical shells treated with active constrained layer damping (ACLD) treatments are presented. The effectiveness of the ACLD treatments in enhancing the damping characteristics of thin cylindrical shells is demonstrated theoretically and experimentally. A finite element model (FEM) is developed to describe the dynamic interaction between the shells and the ACLD treatments. The FEM is used to predict the natural frequencies and the modal loss factors of shells which are partially treated with patches of the ACLD treatments. The predictions of the FEM are validated experimentally using stainless steel cylinders which are 20.32 cm in diameter, 30.4 cm in length and 0.05 cm in thickness. The cylinders are treated with ACLD patches of different configurations in order to target single or multi-modes of lobar vibrations. The ACLD patches used are made of DYAD 606 visco-elastic layer which is sandwiched between two layers of PVDF piezo-electric films. Vibration attenuations of 85% are obtained with maximum control voltage of 40 volts. Such attenuations are attributed to the effectiveness of the ACLD treatment in increasing the modal damping ratios by about a factor of four over those of conventional passive constrained layer damping (PCLD) treatments. The obtained results suggest the potential of the ACLD treatments in controlling the vibration of cylindrical shells which constitute the major building block of many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles.

A finite element for planar beams with active constrained layer damping treatments is presented. Features of this non- shear locking element include a time-domain viscoelastic material model, and the ability to readily accommodate segmented (i.e. non-continuous) constraining layers. These features are potentially important in active control applications: the frequency-dependent stiffness and damping of the viscoelastic material directly affects system modal frequencies and damping; the high local damping of the viscoelastic layer can result in complex vibration modes and differences in the relative phase of vibration between points; and segmentation, an effective means of increasing passive damping in long-wavelength vibration modes, affords multiple control inputs and improved performance in an active constrained layer application. The anelastic displacement fields (ADF) method is used to implement the viscoelastic material model, enabling the straightforward development of time-domain finite elements. The performance of the finite element is verified through several sample modal analyses, including proportional-derivative control based on discrete strain sensing. Because of phasing associated with mode shapes, control using a single continuous ACL can be destabilizing. A segmented ACL is more robust than the continuous treatment, in that the damping of modes at least up to the number of independent patches is increased by control action.

We analyze and experimentally validate an analysis of a sandwich plate structure, where anisotropic face plates sandwich a viscoelastic core. Existing analytical models have been modified to incorporate piezo-actuation in anisotropic and 3-layered thin plates, using the variational energy method. The 3-layered sandwich consists of anisotropic face- plates with surface bonded piezo-electric actuators, and a viscoelastic core. The analysis includes the membrane and transverse energies in the face plates, and shear in the viscoelastic core. A constant, complex shear modulus was used for the dissipative core, thus frequency and temperature dependence of viscoelastic properties is neglected in this model. Simplified forms of the equations are stated based on neglecting shear in face-plates. Experiments were conducted on sandwich plates with aluminum face-plates under clamped boundary conditions to validate the simplified model. Symmetric and asymmetric sandwiches were tested. The maximum error in the first eight natural frequency predictions obtained via the assumed modes solution is less than 10%. Analytical studies on the influence of the number of assumed modes in the Galerkin approximation, and the core storage modulus variation, were conducted. The importance of the in- plane extension modes in sandwich plate analysis was demonstrated. Error in the first natural frequency is nearly 100% when in-plane modes are ignored; error reduces and converges to 6.7% as number of modes is increased to 16 in each of the in-plane directions for each face plate.

One of the most difficult tasks in the structural control industry is providing linear, predictable, passive damping over a wide frequency range. This challenge has been worked around successfully in the past, but rarely has it been performed ideally. The subject matter of this paper takes a radical step toward attaining the goal of linear damping performance, while adding very low static stiffness to the system being damped.

Optical tables are typically used in applications that require a very flat, rigid working surface. The grade of the optical table determines the amount of damping augmentation used to attenuate modal vibration. Discrete tuned mass dampers are a popular and effective damping method, however, their narrow effective bandwidth requires precise tuning to the table's resonant frequency. The present research deals with a damping method whereby a large number of small tuned dampers are distributed over the table's surface. In addition to the spatial distribution, the dampers are also distributed in frequency, providing energy dissipation over a wide frequency band. The wide effective bandwidth makes the distributed damping treatment extremely tolerant to variations in the table's dynamics. Test data is presented for a system of 349 dampers applied to a 243.8 cm by 121.9 cm by 20.3 cm optical table. The distributed damper attenuated both the first bending and the first torsion modes of the table, with a mass increase comparable to that realized with conventional discrete tuned dampers. The experimental results compared favorably to analytical predictions obtained using a full domain plate model.