Foundation Damping Research Articles

Dynamic Stiffness and Damping of a Shallow Foundation from Forced Vibration of a Field Test Structure

Foundation impedance ordinates are identified from forced vibration tests conducted on a large-scale model test structure in Garner Valley, California. The structure is a steel moment frame with removable cross-bracing, a reinforced concrete roof, and a nonembedded square slab resting on Holocene silty sands. Low-amplitude vibration is applied across the frequency range of 5–15 Hz with a uniaxial shaker mounted on the roof slab. We describe procedures for calculating frequency-dependent foundation stiffness and damping for horizontal translational and rotational vibration modes. We apply the procedures to test data obtained with the structure in its braced and unbraced configurations. Experimental stiffness ordinates exhibit negligible frequency dependence in translation but significant reductions with frequency in rotation. Damping increases strongly with frequency, is stronger in translation than in rocking, and demonstrates contributions from both radiation and hysteretic sources. The impedance ordinates are generally consistent with numerical models for a surface foundation on a half-space, providing that soil moduli are modestly increased from free-field values to account for structural weight, and hysteretic soil damping is considered.

Moving two-axle high frequency harmonic loads on axially loaded pavement systems

The dynamic displacement response of axially loaded pavement models was investigated comprehensively when the system was subjected to two-axle moving harmonic loads whose frequencies were higher than the natural frequency of the system. The axially loaded beam on an elastic foundation was employed as a simplified pavement model under axial compression. The foundation was assumed to have damping of a linear hysteretic nature. Formulations were developed in the transformed field domains of time and moving space, and the steady-state responses to moving harmonic loads were obtained using a Fourier transform. The effects of various parameters, such as the load distance, load phase, axial compression, foundation damping, load velocity, and load frequency, on the displacement amplitude distribution and maximum displacement were investigated. The analysis results showed that the displacement responses were much affected by the load distance and load phase between two moving loads. For relatively low load velocities, the critical axial compression was dependent on the load distance and load phase, but for relatively high load velocities, it was not affected by them. There were two critical values of the load velocities and load frequencies. The second critical velocity and the first critical frequency were independent of the load distance and load phase; however, the first critical velocity and the second critical frequency were affected by them.

Expert System Approach for Soil Structure Interaction and Land Use

The application of expert systems has emerged as a cost efficient tool in civil engineering over the past decades. Use of these tools for decision making in land use will be outlined in this paper. In this study, soil-structure interaction (SSI) is discussed by using expert systems, namely, neural network (NN) approaches. This method provides a new point of view for evaluations of SSI and land use. Data from 58 local sites in California, namely, earthquake, structure, and soil property data, are used. In the expert system approach, two NN architectures are used: the back propagation NN architecture and the general regression NN (GRNN) architecture. There are 21 parameters considered as input and 4 output parameters. The four output parameters chosen are soil-to-structure rigidity ratio, period lengthening, foundation damping, and whether SSI effects can be neglected or not. The results show that the GRNN approaches are more useful and powerful for evaluation of SSI and land use.

Study of vibrating foundations considering soil-pile-structure interaction for practical applications

An investigation of soil-pile-structure interaction is carried out, based on a large reciprocating compressor installed on an elevated concrete foundation (table top structure). A practical method is described for the dynamic analysis, and compared with a 3D finite element (FE) model. Two commercial software packages are used for dynamic analysis considering the soil-pile-structure interaction (SPSI). Stiffness and damping of the pile foundation are generated from a computer program, and then input into the FE model. To examine the SPSI thoroughly, three cases for the soil, piles and superstructure are considered and compared. In the first case, the interaction is fully taken into account, that is, both the superstructure and soil-pile system are flexible. In the second case, the superstructure is flexible but fixed to a rigid base, with no deformation in the base (no SSI). In the third case, the dynamic soil-pile interaction is taken into account, but the table top structure is assumed to be rigid. From the comparison beteen the results of these three cases some conclusions are made, which could be helpful for engineering practice.

Unbalance Response of a Super-Critical Rotor Supported by Foil Bearings—Comparison with Test Results©

This article compares theoretical and experimental results on the unbalance response of a super-critical rotor supported by two kinds of gas foil bearings. Analysis of the super-critical rotor is performed with viscoelastic foil bearings (VEFB) and conventional bump foil bearings and compared with early published experimental data. The vibration orbits obtained by theoretical investigation on the viscoelastic foil bearings (VEFB) and the conventional bump foil bearings are compared with the experimental vibration orbits of the super-critical rotor supported by both foil bearings. A numerical analysis program can calculate the static and dynamic characteristics of the elastically supported gas foil bearing using the measured stiffness and damping of the elastic foundation. After the stiffness and damping of both foil bearings are calculated using the perturbation method, vibration orbits of the flexible rotor modeled by the finite element method are calculated. Vibration orbits calculated by numerical analysis agree well with experimental data when the vibration amplitude is small and the rotating speed is below the bending critical speed. The numerical results also show that the enhanced structural damping of the elastic foundation reduces vibration near the bending critical speed.

Dynamic Response of Kirchhoff Plate on a Viscoelastic Foundation to Harmonic Circular Loads

In this paper Fourier transform is used to derive the analytical solution of a Kirchhoff plate on a viscoelastic foundation subjected to harmonic circular loads. The solution is first given as a convolution of the Green’s function of the plate. Poles of the integrand in the integral representation of the solution are identified for different cases of the foundation damping and the load frequency. The theorem of residue is then utilized to evaluate the generalized integral of the frequency response function. A closed-form solution is obtained in terms of the Bessel and Hankel functions corresponding to the frequency response function of the plate under a harmonic circular load. The result is partially verified by comparing the static solution of a point source obtained in this paper to a well-known result. This analytical representation permits one to construct fast algorithms for parameter identification in pavement nondestructive test.

Evaluating foundation mass, damping and stiffness by the least‐squares method

AbstractThis paper discusses how to use the three‐dimensional (3D) time‐domain finite‐element method incorporating the least‐squares method to calculate the equivalent foundation mass, damping and stiffness matrices. Numerical simulations indicate that the accuracy of these equivalent matrices is acceptable when the applied harmonic force of 1+sine is used. Moreover, the accuracy of the least‐squares method using the 1+sine force is not sensitive to the first time step for inclusion of data. Since the finite‐element method can model problems flexibly, the equivalent mass, damping and stiffness matrices of very complicated soil profiles and foundations can be established without difficulty using this least‐squares method. Copyright © 2003 John Wiley & Sons, Ltd.

Time-frequency analysis of thin slabs subjected to dynamic ring loads

Fourier transform is used to obtain the analytical solution of a slab on a viscoelastic foundation subjected to impulse and harmonic ring loads. The solution is given as a convolution of the Green's function of the plate. Poles of the integrand are identified for different cases with respect to load frequency and foundation damping. Both impulse response function and frequency response function (FRF) are obtained. Theorem of residue is utilized to evaluate the FRF analytically. A closed-form solution in terms of Bessel and Hankel function is obtained, which enables one to construct algorithms for parameter identification of the inverse problem involved in pavement nondestructive test. The result is partly verified by comparing the static solution of a point load derived from this paper to a well-known result.

Seismic Soil-Structure Interaction in Buildings. II: Empirical Findings

System identification analyses are used to evaluate soil-structure interaction effects for 77 strong motion data sets at 57 building sites that encompass a wide range of structural and geotechnical conditions. Kinematic interaction effects on the “input” motion at the bases of structures are found to be relatively modest in many cases, whereas inertial interaction effects on the structural response to these motions can be significant. To quantify inertial interaction effects, fixed- and flexible-base modal vibration parameters are used to evaluate first-mode period lengthening ratios T˜/T and foundation damping factors ζ˜0. The response of some structures is dominated by inertial interaction (e.g., T˜/T ≈ 4, ζ˜0 ≈ 30%), whereas others undergo negligible soil-structure interaction (e.g., T˜/T ≈ 1, ζ˜0 ≈ 0). Simplified analytical formulations described in the companion paper by Stewart et al. are used to predict inertial interaction effects. The predictions are found to be reasonably accurate relative to empirical results, with some limitations for deeply embedded and long-period structures. A collective examination of the empirical and predicted results reveals a pronounced influence of structure-to-soil stiffness ratio on inertial interaction, as well as secondary influences from structure aspect ratio and foundation embedment, type, shape, and flexibility.

Dynamic response of pile groups with different configurations

A general methodology is outlined for a complete seismic soil—pile-foundation—structure interaction analysis. A Beam-on-Dynamic-Winkler-Foundation (BDWF) simplified model and a Green's-function-based rigorous method are utilized in determining the dynamic response of single piles and pile groups. The simplified model is validated through comparisons with the rigorous method. A comprehensive parameter study is then performed on the effect of pile group configuration on the dynamic impedances of pile foundations. Insight is gained into the nature of dynamic pile—soil—pile interaction. The results presented herein may be used in practice as a guide in obtaining the dynamic stiffness and damping of foundations with a large number of piles.

The Point-Load Solution and Simulation of a Flexible Spinning Disk Using Various Disk-to-Baseplate Air-Flow Models

In magnetic and/or optical recording on flexible media, an elastic disk rotates at a constant angular velocity in close proximity to a stationary baseplate. Such a configuration can be used to stabilize the transverse motion of the flexible disk, whose natural frequencies and critical speeds would otherwise be too low for stability of the flexible-disk-to-head interface. In this investigation, the air-flow between the disk and the baseplate is accounted for by two foundation parameters, stiffness and damping, for each Fourier mode. The effect of using this new model and three other models on the point-load solution and on the simulation of the disk-to-head interface is investigated. Steady-state solutions are obtained by using an exponential Fourier series expansion in the circumferential direction and a finite difference approximation radially. The simulation solution also accounts for the effect of disk-to-head contact in an approximate manner. It is further shown that the use of a Fejer sum for the Fou...

Boundary element reservoir model for seismic analysis of gravity dams

AbstractThe boundary element method has been successfully applied in the past to the analysis of hydrodynamic forces in two‐ and three‐dimensional finite water reservoirs subjected to seismic ground motions. In extending the method to an infinite reservoir, the loss of energy due to pressure waves moving away towards infinity must be taken into account. In addition, for both finite and infinite reservoirs, energy is lost owing to partial absorption of the waves incident on a flexible bottom consisting of alluvial deposits. This paper presents the results of more recent research on the application of the boundary element method to the analysis of 2D reservoir vibration. Two different formulations are used: a constant boundary element formulation and a linear boundary element formulation. Special boundary conditions to treat infinite radiation and foundation damping have been incorporated in both formulations. Numerical results have been obtained for each of the two alternative formulations and compared against each other as well as with classical solutions and results obtained by other researchers.

Dynamic stiffness and damping of foundations by simple methods : Dobry, R; Gazetas, G Proc Symposium on Vibration Problems in Geotechnical Engineering, Detroit, 22 October 1985P75–107. Publ New York: ASCE, 1985

Dynamic stiffness and damping of foundations by simple methods : Dobry, R; Gazetas, G Proc Symposium on Vibration Problems in Geotechnical Engineering, Detroit, 22 October 1985P75–107. Publ New York: ASCE, 1985

Experimental study of soil-structure interaction at an accelerograph station

AbstractForced harmonic vibration tests, using eccentric mass shakers, were conducted at the Jenkinsville, South Carolina, accelerograph station to determine the effect of soil-structure interaction on the motions recorded during four small magnitude earthquakes. The station consisted of a 4′ × 4′ × 2′ concrete pad that was embedded in a stiff clayey to medium sandy silt with a shear-wave velocity estimated at 500 fps. A five-foot-high wooden hut was attached to the pad and provided shelter to the SMA-1 accelerograph, which was bolted directly to the pad. The real parts of complex foundation impedance functions, which were obtained by solving the equations of motion for the vibration tests, were generally similar to the theoretical impedance functions for an embedded rectangular foundation. However, the imaginary parts, which are a measure of the foundation damping, were closer to the theoretical prediction for a surface foundation. The tests also showed that the soil-pad-hut system had two strongly coupled translational and rocking modes of vibration in the frequency range of 1 to 60 Hz. The first mode occurred at approximately 11 Hz (N40°W direction) and 17 Hz (N50°E direction) and involved mostly the response of the hut, while the second mode occurred at approximately 50 Hz in both directions and involved mostly the response of the concrete pad. Approximate transfer functions between the motions recorded at the station during the earthquakes and the free-field motions were computed from the experimental data. These functions showed significant amplification in the frequency band 20 to 50 Hz with a maximum amplification of 3 occurring at 50 Hz. Some measurable amplification also was observed at the fundamental natural frequencies in both directions. Calculations based on the transfer functions indicated that the average response spectra of the recorded earthquake motions were amplified by an average of about 30 per cent for frequencies greater than 15 Hz. These results suggest that careful attention must be given to the design of accelerograph stations if they are to record true ground motions over a wide frequency range.

System dynamics of large rotating machinery and its foundation

System dynamics of a single‐speed centrifugal induced draft fan on an isolated pile foundation was investigated to determine the adequacy of foundation design and fan balance. The investigation involved dynamic soils and pile evaluation to establish stiffness and damping of foundation supporting medium. A dynamic computer analysis of complete fan, concrete foundation, soil‐pile system was conducted to establish resonant frequencies and system sensitivity to rotating unbalance. Dynamic impact testing using the transfer function technique was performed to determine system natural frequencies and damping for comparison with analytical results. Vibration levels during fan startup and steady‐state operation were monitored to determine system resonances, sensitivity, and residual unbalance. Resonant frequencies associated with foundation motion were observed in the 5‐ to 7‐Hz and 10‐ to 12‐Hz regions; and in the the 21‐ to 25‐Hz region for the fan rotor. The fan operating speed is 14.7 Hz which is outside the r...

The airborne path in shipboard noise control

Reverberant noise in living and working spaces other than the machinery room is typically controlled by structure‐borne paths. However, as machinery vibration isolation and foundation damping techniques are perfected, airborne flanking paths discussed in this paper become increasingly important. In contrast to representative masonry walls, the finite extent of shipboard partitioning and bulkheads is an essential factor in determining transmission loss (TL). Consequently, structural damping is beneficial not only near coincidence, but also at higher frequencies. A second distinguishing feature of much shipboard partitioning is frame stiffening. This extends the beneficial effect of damping to frequencies below coincidence. Stiffening frames cause marked TL degradation below the TL of the underlying uniform plate, in spite of the latter's smaller mass. In conclusion, the concept that mass per unit area is the single most important factor in determining TL is not relevant to the shipboard situation.

Dynamic Interactions Between Long, High Speed Trains of Air Cushion Vehicles and Their Guideways

Trains of high speed air cushion vehicles traversing simple spans are modeled as uniform pressure segments traveling at arbitrary speeds over identical Bernoulli-Euler beams. Series solutions are found for the transient span and vehicle responses where the trains overlap several spans at a time. Elastic foundation, span tension, and span damping effects are included. Conclusions reached after studying some realistic numerical examples for constant-speed trains on elevated spans are: (a) for trains which are longer than one span length, the dynamic deflection factors (maximum ratios of dynamic to static deflection at midspan) approach 2.0 at speeds between 300 and 600 mph, and occur as the end of the train approaches, midspan; (b) these dynamic deflections may be reduced by the addition of damping, by a reduction of span length, by the addition of span tension, and by an increase in span stiffness; (c) the high vertical accelerations of the vehicles, which may approach 2 g’s at speeds of 300 mph, show the need for advanced suspension systems to insure passenger safety and comfort.

Dynamic Response of Beam on Viscoelastic Subgrade

Initial elasticity and restricted viscous flow of a subgrade greatly influence the dynamic response of a Bernoulli-Euler beam supported by such a subgrade. The beam is of infinite length and is subject to a moving concentrated load. The standard linear viscoelastic solid represents the Winkler-type viscoelastic foundation. It is shown that the effect of the foundation damping is most pronounced over a certain limited velocity range of the concentrated load. Unbounded critical-velocity resonance does not occur. The influence of initial elasticity is exhibited by a comparison with the response of a beam supported by a foundation of Kelvin models. Analytical expressions as well as graphs are presented for the beam deflections and the bending moments.