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Review Our Complete Collection of Industry Technical Papers

We have compiled an extensive list of useful information and industry technical papers for your convenience. Whether you are interested in a case study from a recent projects, want to learn more about the latest trends from a white paper written by one of our engineers, or you’re a numbers junky and looking for technical brief, we have something for everyone.  
White Paper

71. Seismic Protection with Fluid Viscous Dampers for the Torre Mayor, a 57-Story Office Tower in Mexico City, Mexico

The new 57 story Torre Mayor Building is the now the dominant structure in the Mexico City skyline. It is also the first tall building to utilize large Fluid Viscous Dampers as a primary means of seismic energy dissipation. A total of 98 dampers are used, including 24 large dampers, each rated at 570 tonnes of output force, located in the long walls of the building. The short walls utilize 74 smaller dampers, each rated at 280 tonnes of output force. The damping technology successfully implemented for Torre Mayor is now being used on five other tall buildings, including three in the USA, and two in Japan.

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Case Study

70. Seismic Rehabilitation of Historic Concrete Structure with Fluid Visco-Elastic Dampers

This paper presents the nonlinear seismic analysis, development, and implementation of an innovative seismic retrofit strategy for a six story nonductile reinforced concrete 145,000 square foot historic building. Dynamic and nonlinear static analytical results verified that the building had a weak soft story with inadequate post yield capacity and large torsional response. Hotel Stockton, in Stockton, CA, is also torsionally irregular. The analysis indicated that the existing building was not seismically adequate to withstand anticipated lateral forces generated by earthquake excitations at the site. A “collapse prevention” performance upgrade for a 475-year return event was developed. Nonlinear fluid viscous dampers were placed at the first story level to reduce the seismic demand and obtain a more uniform response. Viscoelastic fluid viscous dampers were strategically placed at one side of the building to reduce the torsional irregularity of the building. This cost effective retrofit significantly improved the seismic performance of the building.

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White Paper

69. Analysis, Optimization, and Development of a Specialized Passive Shock Isolation System for High Speed Planing Boat Seats

The Mk V Special Operations Craft (SOC) is used to carry Special Operations Forces (SOF) into and out of combat operations. During operation, particularly during extended training missions, the passengers and crew have reported numerous cases of musculoskeletal injuries from operation in high sea states. This paper describes the analysis, development and operational testing of a highly specialized, non-linear, passive shock isolated seat for this craft. Initial sea trial testing of the isolation system resulted in positive operator feedback that correlated well with earlier field measurements and also validated the analytical predictions.

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Case Study

67. U.S. Design of Structures with Damping Systems

This paper presents an earthquake design procedure and a case study of the Vacaville Police Headquarters. The design goal for this essential facility was to provide immediate occupancy after a 475-year return seismic event. The project also required construction cost within typical code conforming buildings. A combination of Special Moment Resisting Frames (SMRF) and Fluid Viscous Dampers (FVDs) was used as the lateral force resistance system. This system, as described by Gimmel, Lindorfer, and Miyamoto, (2002) results in cost efficiency and superior seismic performance. The 2000 NEHRP (FEMA, 2000) guideline was used to design the project, since it is considered to be a state-of-art procedure for seismic damping devices. This project was the first structure in the United States to use this advanced procedure.

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Case Study

66. Damper Retrofit of the London Millennium Footbridge

The Millennium Footbridge was opened to the public on June 10, 2000 – the first new bridge across the River Thames in historic London in more than a century. Nearly 100,000 people used the new bridge in its first day of operation. On June 12, 2000, the Millennium Bridge was ordered closed, due to hazardous deck motions. Seemingly random pedestrian footfalls were causing resonance of the bridge deck, with lateral accelerations measuring up to 0.25 g. The selected method of retrofit was to add fluid damping to the bridge. This paper describes how this was done, including testing of the bridge with groups of up to 2,000 people.

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White Paper

65. Viscous Damper Development and Future Trends

Viscous dampers can protect structures against wind excitation, blast and earthquakes. Viscous damper technology originated with military and aerospace applications. Approximately 20 years ago it was found that the same fluid viscous dampers that protect missiles against nuclear attack and guard submarines against near miss underwater explosions could also protect buildings, bridges and other structures from destructive shock and vibration. This paper describes fluid damper technology, analysis considerations, installation methods and development work in progress.

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Case Study

64. Virtual Base Isolation by Building Softening with Drift Control Provided by Fluid Viscous Dampers

In many metropolitan areas, mid rise buildings are constructed adjacent to existing buildings, and incorporate concrete shear walls to act as a barrier between the two buildings. The orientation of these shear walls often causes severe torsional response within the building. The addition of a few well placed nonlinear Fluid Viscous Dampers (FVD’s) can significantly decrease the torsional excitation, thereby increasing building performance. This paper describes the retrofit of an 18-story steel frame building that exhibits severe torsional response from the “property line” condition at the lower two stories. FVD’s significantly reduce the displacement and acceleration of the second and third floors of the building, where sensitive telecommunications equipment is being housed. They reduce the demand and drift on the stories above with no additional construction required on these floors. FVD’s offer a very economical and effective means of mitigating undesirable building response due to torsional irregularities. Their use would be effective in the retrofit of many existing buildings with similar “property line” conditions.

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White Paper

63. Virtual Base Isolation by Building Softening with Drift Control Provided by Fluid Viscous Dampers

The paper describes “virtual isolation” for buildings with one or more soft stories. Using the 1999 SEAOC Blue Book (SEAOC, 1999) recommendations for passive energy dissipation, the building’s Lateral Force Resisting System (LFRS) is designed for strength requirements only, resulting in a relatively flexible LFRS, while Fluid Viscous Dampers (FVD) are incorporated to limit story drifts to acceptable levels. There are many benefits to this “virtual isolation” system. With the elimination of the maximum drift requirements, the moment frames are substantially lighter than a traditionally framed building, thus lowering the structural steel cost of the LFRS. The long period structure also produces significantly reduced forces in the foundation elements. Velocity and displacement are reduced significantly through the use of the FVDs, which protects the sensitive contents of the building. These benefits lead to a reduced response resulting in an enhanced performance level during a major seismic event.

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White Paper

62. Structural Control of High Rise Building Using a Tuned Mass with Integral Hermetically Sealed, Frictionless Hydraulic Dampers

Structural control of large buildings using tuned mass damper systems has gained wide acceptance in recent years. Significant structural performance improvements during wind storms have been realized using both active and passive systems. Disadvantages of employing active systems include high engineering and implementation costs, high maintenance costs, unnecessary system complexities, and the requirement for a continuous and non-interrupted power supply. A design for a passive tuned mass damper system is presented with analytical simulations and component test results. These demonstrate the effectiveness of using a tuned mass in conjunction with a maintenance free, hydraulic damper, having frictionless flexural seals to successfully attenuate the response of a high rise building subject to severe wind inputs.

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White Paper

61. A Numerical Investigation of Combined Shock and Vibration Isolation Through the Semi-Active Control of Magnetorheological Fluid Damper in Parallel with an Air Spring

Combining shock and vibration isolation into a single isolation mount is investigated numerically through the use of the Bouc-Wen model of a magnetorheological fluid damper in parallel with an air spring. The stability and dissipative capabilities of the Bouc-Wen model are proven mathematically. The response characteristic of this hybrid isolator to shock and vibration inputs is explored. The advantages of combining shock and vibration isolation into a single package is discussed. It is possible, using this technique, for a single device to perform equally well as a shock and a vibration isolator.

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White Paper

60. Fluid Lock-up Devices

Fluid Lock-up Devices have recently become popular for passive control of large structures subjected to earthquake or wind storm effects. The Lock-up Device, a variation of the Fluid Viscous Damper, allows unrestricted motion at low translational speeds. When a transient event occurs the Lock-up Device activates and forms a rigid connection. After the transient event the Lock-up Device reverts to low force output, permitting structural sections to thermally expand or contract without added stress. The operation of the device is completely passive. It enables multi-mass structures to be dynamically braced without resorting to the cost and complexity of an active actuator system..

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Case Study

58. Viscous Damper with Motion Amplification Device for High Rise Building Applications

Adding damping by the use of various damping devices has become an accepted method to reduce wind induced vibrations in tall buildings. An interesting example of a 39 story office tower is presented where large projected accelerations are the result of vortex shedding of an adjacent existing 52-story building. Viscous dampers and a toggle brace type motion amplification system are used to suppress the anticipated accelerations. A description of the damping system and its analytical simulation are discussed. This paper includes a nonlinear analysis of the tower, with time history forcing functions derived from wind tunnel testing. Cost data for the damper system is also presented.

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White Paper

57. Structural Control of Dynamic Blast Loading Using Fluid Viscous Dampers

This paper evaluates the effectiveness of Fluid Viscous Dampers to reduce blast loading responses in steel buildings. The paper addresses the following issues: (1) development of a blast loading time history from a 3,000 pound explosive charge, (2) characteristics and historical applications of fluid Viscous Dampers for blast and weapon effects, and (3) blast effects and performance comparisons of a conventional steel building frame with and without dampers, and a conventional concrete shear wall building. Simulation results indicate that Fluid Viscous Dampers provide a cost effective way to greatly improve the performance of steel building frames under blast loading.

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Product Info

56. Buildings: Design for Damping

The end of the Cold War in 1990 heralded a restructuring period for the American military and defense industry. In the civil engineering field, high capacity fluid dampers have transitioned from defense related structures to commercial applications on buildings and bridges subjected to seismic and/or wind storm inputs. Because fluid damping technology was proven thoroughly reliable and robust through decades of Cold War usage, implementation on commercial structures has taken place very quickly. This paper provides a broad overview as well as a guide to implementation; with specific case studies for four of the more than 300 major buildings and bridges equipped with fluid dampers by Taylor Devices, Inc., a defense contractor from the Cold War years.

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White Paper

55. Experimental Study of Bridge Elastomer and Other Isolation and Energy Dissipation Systems with Emphasis on Uplift Prevention and High Velocity Near-Source Seismic Excitation

A series of shake table tests on an isolated bridge model included low and high damping elastomeric isolation systems, and low damping elastomeric systems with added linear and nonlinear viscous dampers. Each of these configurations could withstand much stronger seismic excitations than the non-isolated configurations. A set of low intensity tests was conducted to form a basis for comparison with the non-isolated configurations and also to test the effectiveness of these systems under low intensity excitation. The results of these tests are presented, followed by a discussion of the effects of scragging, the benefits of seismic isolation, and the significance of damping, the importance of added damping in near source seismic excitation and on the benefits and drawbacks of using nonlinear viscous damping.

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White Paper

53. SEAOC Energy Dissipation Committee Appendix A: Guidelines for Buildings Using Passive Energy Dissipation Systems

This set of provisions provides minimum design requirements for the incorporation of passive energy dissipation devices in buildings. Energy dissipation devices (also termed damping devices) reduce global and interstory seismic displacement response of structural systems, but may either increase or decrease seismic stresses and accelerations within structural systems. They provide a controlled increase in structural damping, and may also result in an increase in structural stiffness or change in participating mass. Passive energy dissipation systems do not require active control by electrical, pneumatic or hydraulic systems. Buildings designed in conformance with these provisions must also be designed in accordance with all other applicable provisions of the Uniform Building Code, except as specifically defined in this appendix. Design must consider the combined behavior of all elements of both the Lateral Force Resisting System (LFRS) and the Energy Dissipation System (EDS). Energy dissipation devices must not form part of the gravity load – resisting system.

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White Paper

52. Development and Testing of an Improved Fluid Damper Configuration for Structures Having High Rigidity

Structures with high rigidity experience relatively small deflections and interstructural velocities under seismic shock. This means that conventional energy dissipation devices may not be feasible or cost effective. An improved damper configuration has been investigated, utilizing a toggle mechanism to magnify internal structural deflections. This provides a more effective way to add damping to a stiff structure. Experimental results were obtained from a 32,000 lb. test structure utilizing two fluid dampers and two toggle brace elements. Test inputs included around eighty individual earthquake transients, varying both in wave form and intensity. The results demonstrated the ability of the toggle mechanism to magnify displacements significantly. The toggle brace damping system appears to be an excellent solution to the addition of supplemental damping devices to rigid structures of all types. Advantages include relatively low damper cost, a simple bracing element design, and low installation cost.

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White Paper

51. Applications of Hermetically Sealed Fluid Dampers for Low Level, Wide Bandwidth Vibration Isolation

Vibration isolation of sensitive components like high resolution cameras requires extremely low friction in the isolator system. Hydraulic dampers for these systems must be leak-free, which equates to relatively high friction seals. There is always a trade-off between allowable leakage and allowable friction in this type of application. This paper describes the isolation performance of a new hermetically sealed damper with essentially zero friction. It contains both an analytical representation of damper performance and dynamic test results.

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Technical Brief

50. Testing and Modeling of an Improved Damper Configuration for Stiff Structural Systems

This report describes a toggle brace damper system that adds significant damping to stiff structures, like reinforced concrete shear wall buildings. It is generally recognized that these stiff structural systems, such as reinforced concrete shear walls and steel braced dual systems, are characterized by small drifts and small relative velocities that make the implementation of seismic energy dissipation devices difficult. This report presents a study on a toggle brace damper system that magnifies the damper displacement and reduces the required damper force to produce the desired damping. The reports presents the concept, describes the theoretical treatment, and includes an experimental study with cyclic and shake table testing of a model structure along with procedures for response history and simplified analysis.

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Technical Brief

49. Seismic Testing of a Building Structure with a Semi-Active Fluid Damper Control System

This paper describes shaking table tests of a multi-story scale model building structure subjected to seismic excitation and controlled by a semi active fluid damper control system. The semi active dampers were installed in the lateral bracing of the structure and the mechanical properties of the dampers were modified according to control algorithms which utilized the measured response of the structure. A simplified time delay compensation method was developed to account for delays within the control system. The results of shaking table tests are presented and interpreted and analytical predictions are shown to compare reasonably well with the experimental results. These tests included an undamped system, passive damping, and semi-active damping. Both the purely passive damper system and the semi-active system significantly reduced seismic response.

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Case Study

48. Arrowhead Regional Medical Center

This article describes every aspect of the design and construction of the Arrowhead Regional Medical Center, including the use of base isolators and viscous dampers to insure continuous operation even after a major seismic event. The article even includes many of the financial aspects of this huge project.

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White Paper

47. Development and Testing of an Electronically Controlled Shock and Vibration Damper Having an Electrorheological Fluid Medium

An electrorheological (ER) fluid has been developed comprised of zeolite particles suspended in silicone oil. Testing of this fluid in a damper of 1,000 lbs. nominal output force rating has demonstrated the ability to control damper output with internal pressures above 500 psi and control power requirements of less than one watt. The damper control valve is a simple ER duct, with no moving parts, requiring only that a voltage potential exists across the duct’s cross section to activate the ER material, and thus cause the material to exhibit plastic behavior. All tests were successful, with no degradation of the damper or ER material occurring over large numbers of activation cycles or with time.

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Case Study

46. Design of Steel Pyramid Using Fluid Viscous Dampers with Moment Frame

The Eleven story 450,000 ft2 pyramid shaped office building described in this article was one of the first new buildings in the United States to use Seismic Dampers. This National Headquarters for a financial institution is located in West Sacramento, CA. The basic lateral force resisting system of the building consists of steel moment frames. In addition, approximately 15% of critical damping was provided using Fluid Viscous Dampers (FVD) in order to reduce displacement and acceleration. The steel moment frames were designed to remain well below the yield strength, and the story drift ratio was limited to 0.005 to protect the welded moment connections for the Design Basis Earthquake (DBE). Earthquake performance, cost effectiveness, and architectural requirements were the primary concerns in designing this building.

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White Paper

45. Electrorheological Damper with Annular Ducts for Seismic Protection Applications

This paper presents the design, analysis, testing and modeling of an electrorheological (ER) fluid damper developed for vibration and seismic protection of civil structures. The damper consists of a main cylinder and a piston rod that pushes an ER fluid through a stationary annular duct. The basic equations that describe the fluid flow across an annular duct are derived. Experimental results on the damper response with and without the presence of electric field are presented. A combination of a simple phenomenological model and a neural network is proposed as a practical tool to approximate the nonlinear and velocity dependent damper response.

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White Paper

44. Fluid Viscous Damping as an Alternative to Base Isolation

Base isolation of large structures has proven to be an effective way to attenuate seismic excitation. However it can be costly, and can also involve major building modification. It is now possible to attain a comparable degree of earthquake mitigation with fluid viscous dampers located throughout a structure, without having to isolate the building. This paper describes several techniques for doing this, provides analytical back-up and describes several applications of this technology.

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Case Study

43. Pre-Qualification Testing of Viscous Dampers for the Golden Gate Bridge Seismic Rehabilitation Project

This report presents the results of the testing of a viscous damping device provided to the Earthquake Engineering Research Center (EERC) of the University of California at Berkeley for pre-qualification testing as part of the seismic rehabilitation of the Golden Gate Bridge. In all, four different viscous dampers from four different manufacturers were tested in the prequalification program. This report presents the test results for the damper denoted Damper C. The test results for the other three dampers, Dampers A, B, and D, are presented in separate reports. Conclusions were that Damper C performed consistently and well throughout the entire testing/pre-qualification program. This report also includes a complete specification for production dampers for this project.

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White Paper

40. Energy Dissipation Devices in Bridges Using Hydraulic Dampers

Specially designed energy dissipation systems are well known for improving seismic performance of structures by absorbing earthquake induced energy. In this paper, the use of linear and nonlinear hydraulic dampers is investigated in a bridge application. A two-span, skewed, cast-in-place prestressed concrete bridge with an outrigger bent is examined. The bridge is located in a highly seismic area of Southern California. It is observed that dampers alleviate the torsional movement and reduce the transverse and longitudinal movements of the superstructure.

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White Paper

39. Seismic Evaluation and Retrofitting of U.S. Long-Span Suspension Bridges

This paper is a first attempt to raise issues about the seismic evaluation and retrofitting of longspan suspension bridges in the United States. The issues discussed in this paper deal seismic hazards and risks; performance and design criteria; ground motions; geotechnical engineering, substructure mathematical modeling, and soil structure interaction (SSI); actual conditions of structural components; superstructure mathematical modeling; ambient vibration testing; analysis of superstructure; suspension bridge component vulnerabilities; instrumentation and monitoring; laboratory testing; retrofitting; and the effects of limited funding and time constraints.

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White Paper

36. Viscous Damping for Base Isolated Structures

Seismic Base Isolation can use elastomeric pads, sliding plates or inverted pendulums. Each method can include an energy dissipation means, but only as some kind of hysteretic damping. Hysteretic damping has limitations in terms of energy absorption and may tend to excite higher modes in some cases. It’s possible to avoid these problems with viscous dampers. Viscous damping adds energy dissipation through loads that are 90o out of phase with bending and shear loads so even with damping levels as high as 40% of critical adverse side effects tend to be minimal. This paper presents basic theory of viscous damping and also describes a sample project. Viscous dampers being built for the new San Bernardino Medical Center reduce both deflections and loads by 50% compared with high damping elastomer base isolation bearings by themselves.

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Case Study

35. Seismic Rehabilitation of a Historic Non-Ductile Soft Story Concrete Structure Using Fluid Viscous Dampers

Hotel Woodland is one of the first structures in North America to be seismically retrofitted using viscous dampers. This four story 1927 vintage Historical Landmark reinforced concrete building is located in Woodland, California. It was essential to improve the earthquake response performance of the building and minimize cost while maintaining the historical appearance of the building. This paper presents the processes and decisions regarding retrofit criteria and design procedure for earthquake demand, building response performance, historical interests, and economic considerations.

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White Paper

34. Fear of Trembling

This article describes the effects of both Kobe earthquake and the Northridge earthquake in detail, including technical and economic details. It also discusses building codes and practices and what is being done around the world to decrease the risk of severe seismic damage.

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White Paper

32. Application of Fluid Viscous Dampers to Earthquake Design

This article summarizes the extensive viscous dampers investigation performed by NCEER at State University of New York, Buffalo Campus. This included computer modeling of both the dampers and complete isolated systems, along with shake table testing and correlation of results. The article also describes a very large damper projects; dampers + base isolation for a set of five hospital buildings near San Bernardino, CA.

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White Paper

31. Study of Seismic Isolation Systems for Computer Floors

This report describes the development and testing of a computer floor seismic isolation systems which uses existing devices developed for the seismic isolation of buildings and shock isolation of military equipment. A computer floor system with raised floor and a generic slender equipment cabinet was constructed. It was isolated by spherically shaped sliding bearings and was highly damped either by utilizing high friction in the bearings or by installing fluid viscous dampers. The spherically shaped bearings provided the simplest means of achieving long period in the isolation system under low gravity load. The isolation system prevented rocking of the cabinet on top of the isolated floor and substantially reduced its acceleration response in comparison to that of a conventional computer floor. An analytical study was also conducted in order to extend the results to a range of parameters which could not be tested.

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White Paper

30. Experimental and Analytical Study of a System Consisting of Sliding Bearings and Fluid Restoring Force/Damping Devices

This report describes an experimental study of the behavior of a bridge seismic sliding isolation system consisting of flat sliding bearings and fluid restoring force/damping devices. Earthquake simulator tests were performed on a model bridge structure both with isolators and without. The experimental results demonstrate a marked increase of the capacity of the isolated bridge to withstand earthquake forces. Analytical techniques are used to predict the dynamic response of the system and the obtained results are in very good agreement with the experimental results.

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White Paper

29. Experimental and Analytical Investigation of Seismic Response of Structures with Supplemental Fluid Viscous Dampers

This 206 page report presents the results of an extensive study on fluid viscous dampers. A series of component tests with various dynamic inputs was performed to determine the mechanical characteristics and frequency dependencies of the dampers. In addition, temperature dependencies were evaluated by varying the ambient temperature of the damper during component testing. Based on these component tests, a mathematical model was developed to describe the macroscopic behavior of the damper. Earthquake simulation tests were then performed on one story and three story steel structures both with and without dampers. The addition of supplemental dampers significantly reduced the response of the structure for both interstory drift and shear forces. The experimental responses correlated well with analytical predictions.

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White Paper

27. University at Buffalo – Taisei Corporation Research Project on Bridge Seismic Isolation Systems

This paper describes the first part of a project to produce a class of passive sliding seismic isolation systems for bridges. This includes experimental verification of the systems by large scale shake table testing, analytical techniques for interpretation of the experimental results, and design procedures for sliding bridge isolation systems. A quarter length scale bridge model was tested on a shake table. Restoring force was provided by various means. First, spherically shaped sliding bearings (known as FPS bearings) were used to provide restoring and frictional forces within a compact unit. Next, flat sliding bearings were combined with various devices placed between the deck and the pier to provide restoring force and additional energy dissipation capacity. These devices were in the form of: a) arc-shaped rubber elements between a moving central rod and a cylindrical housing, b) wire rope springs, c) fluid spring-damper devices and d) fluid viscous dampers.

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Technical Brief

25. Test Methodology and Procedures for Fluid Viscous Dampers Used in Structures to Dissipate Seismic Energy

Taylor Devices, Inc. has manufactured damping devices since 1955. Until 1990 most applications were military, using dampers to attenuate weapons effects. Until recently, information on these applications and the associated damper designs has not been public due to security restrictions. Most of these restrictions have now been relaxed and much of this damping technology is now available to the structural engineering community. Taylor Devices can now provide compact fluid viscous dampers in the 100 kip to 2,000 kip output range that greatly reduces earthquake response of structures. This paper describes how the military has been testing shock mitigation dampers for many years and how this type of testing can apply to the large dampers required for seismic protection of structures.

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White Paper

23. Semi-Active Fluid Viscous Dampers for Seismic Response Control

The addition of passive damping to a structure greatly increases its earthquake resistance. It is possible to get further increase through an active or semi-active control system for the dampers. Semi-active damping is preferred due to low external power requirements and fail-safe operation. This paper describes the history of the successful use of semi-active fluidic control devices in military applications and how this technology has been adapted to earthquake hazard mitigation. Testing of a semi-active continuously adjustable damping device through fluid orificing is described. Mathematical models of the behavior of the device are also presented.

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White Paper

21. Seismic Response of Structures with Supplemental Damping

This paper presents a review of supplemental damping devices used for the control of the seismic response of structures. The mechanical properties of these devices are discussed and considerations in the design of energy absorbing systems are presented. Conventional structures passively resist earthquakes through a combination of strength, deformability and energy absorption. They have very little damping, so elastic energy absorption is small. Strong earthquakes deform these structures well beyond their elastic limit through localized plastic hinging, which results in increased flexibility and energy dissipation. Most of the earthquake energy is absorbed by the structure through localized damage of the lateral force resisting system. This is somewhat of a paradox in that the effects of earthquakes (i.e. structural damage) are counteracted by allowing structural damage. Structural performance can be greatly improved if a large portion of the input energy can be absorbed, not by the structure itself, but by some type of supplemental device. This paper describes a number of ways to do this, including friction devices, yielding metal systems, elastomeric viscoelastic dampers and fluid viscous dampers.

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