Cabinet and Shelter Vibration Isolation: Numerical and Experimental Investigation

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1 Cabinet and Shelter Vibration Isolation: Numerial and Experimental Investigation G. Di Massa, S. Pagano, S. Strano Abstrat Passive isolation systems are often adopted to redue vibrating energy ating on a sensitive equipment due to external soures as mahinery, road/rail traffi, earthquakes, et. The paper desribes a theoretial and experimental investigation onduted on a steel light struture, simulating a abinet or a shelter ontaining sensitive equipment. It is isolated from the ground seismi aeleration by means of four isolators eah onsisting of a ball transfer unit (BTU) and a wire rope spring (WRS). This kind of isolator has hystereti non-linear behaviour with damping aused by the dry frition due to the wires relative motion; the non-linear stiffness and damping is funtion of the wire rope onfiguration and on its diameter and length. Some experimental tests have been performed to haraterize the isolator and to obtain an analytial desription of its dynami behaviour; then the steel light struture, supported by four WRS-BTU isolators, has been tested on a shake-table to evaluate the isolation effiieny. The experimental results have been ompared with the theoretial ones obtained with a numerial model in whih the isolator hystereti behaviour has been modelled with the Bou-Wen theory. The validated model has been then used to simulate the abinet dynami response due to reorded seismi ground motion. Index Terms Seismi Isolators, Bou-Wen, Nonlinear Dynamis, Wire Rope, Vibration Isolation. Seismi passive isolation requires the use of devies with high vertial stiffness, in order to avoid large omplianes due to the weight of the struture, and low horizontal stiffness to shift the natural period away from the period range having the most of earthquake energy. All base isolation systems have ertain ommon features suh as re-entring apability and energy absorbing apaity; they an be divided into three main types: elastomeri, rolling and sliding devies. The most ommon isolators are the elastomeri steelreinfored ones that are made up of elastomeri layers alternated with steel sheets, whose number and size are hosen to obtain a high vertial stiffness and a low horizontal stiffness. Rolling isolators are instead onstituted by two parallel rigid plates with interposed rolling bodies. As an example, Fig. 1 shows a rolling devie with three steel balls rolling on a plate; the balls sustain a disk on whih is onneted the struture to be isolated. The isolator is equipped with three pre-stressed helial steel springs able to re-entre the disk and other three helial springs to re-entre the balls agespaer; the horizontal stiffness depends on the diretion and amplitude of the disk displaement as shown in the polar diagram reported in Fig. 2a. As three (or more than three) isolators onstitute the isolation system, it is possible to properly orient them to obtain a quite rounded stiffness polar diagram (Fig. 2. T I. INTRODUCTION ough and durable abinets and shelters are used for housing eletro-mehanial and eletroni high-teh items (as devies for teleommuniations, ontrol systems, power equipment, et.) having a vital role of work in many industries and often plaed in very harsh operating environments. They assure protetion against weathering, spread of fire, noise, et. Some shelters have to support antennas and satellite dishes for signal emission and/or reeption. Sometimes, both internal and external devies must be proteted against vibrations and they must operate even during a seismi event. Fig. 1. Rolling seismi isolator with helial springs (DII, Naples, Italy). G. Di Massa is with the Dipartimento di Ingegneria Industriale, Università degli Studi di Napoli Federio II, ITALY, ( giandomenio.dimassa@unina.it). S. Pagano is with the Dipartimento di Ingegneria Industriale, Università degli Studi di Napoli Federio II, ITALY, ( pagano@unina.it). S. Strano is with the Dipartimento di Ingegneria Industriale, Università degli Studi di Napoli Federio II, ITALY, (orresponding author, phone: ; salvatore.strano@unina.it). Fig. 2. Horizontal stiffness polar diagram: single isolator; four isolators.

2 Several types of rolling supports are now available. For example, two linear reirulating ball guides orthogonally arranged (Fig. 3), to allow movement along any horizontal diretions, onstitute the THK support. Fig. 4 reports the rolling devie proposed by M. Ismail et al. [1], made up of a stiff rolling body plaed between the superstruture and substruture, respetively. The sliding isolators mainly onsist of a teflon disk, supporting the struture, that slides on a stainless steel plate. Sliding and rolling supports an be realized with sloped or spherial surfaes so that a relative horizontal displaement, between superstruture and substruture, generates a gravitational restoring fore and a dissipative fore due to frition [2]. Both devies are generally haraterized by a frition oeffiient equal to about 3%. has a longer servie life sine they are not very sensitive to temperature hanges and resists aggressive environments aused by the presene of ozone, oil, grease and salt spray; they dissipate energy due to frition between the wires. It is haraterized by a hystereti non-linear behaviour depending on the onfiguration, the diameter and the length of the seleted wire rope. The desribed isolator an be onsidered as an extension of the mono-diretional devie introdued by Demetriades et al. [6], onstituted by a ombination of a wire rope spring and a loked astored wheel. This paper reports a theoretial and experimental investigation on the seismi isolation of a light mass struture, as a abinet, adopting WRS-BTU isolators. Fig. 3. THK rolling devie (from: Fig. 5. Rolling devie with sloped surfae; Sliding devie with spherial surfaes (frition pendulum system, FPS). Fig. 4. Ismail et al. rolling isolator. Fig. 5a shows the sheme of sloped rolling-type isolation devies. The roller an also be onstituted by ylinders plaed between two V-shaped sloping surfaes [3]. In [4] an approximate expression is derived for prediting the peak aeleration response of a struture isolated by the rollingtype isolators, as there is a lower-bound PGA for triggering a sloped rolling mehanism. Fig. 5b represents the sheme of the single frition pendulum system (FPS) that is a sliding devie with spherial surfaes. The struture natural frequeny is seleted simply by hoosing the radius of urvature of the onave surfae. The present paper desribes the dynami behaviour of a rolling isolator that an be used to isolate light strutures or sensitive equipments housed in abinets or shelters. The isolator [5] is very simple and heap; it onsists (Fig. 6) of two plates between whih it is plaed a ball transfer unit (BTU) that has the task of supporting the abinet weight allowing horizontal relative displaements with low frition. The restoring fore is provided by some ropes onneting the two plates, making up a wire rope spring (WRS). This kind of spring, with respet to most ommon rubber ones, CABLE Fig. 6. WRS-BTU isolator. BTU ELASTOMERIC PAD The experimental haraterization of the isolator has been performed adopting the BPI testing mahine [7], available at the DII laboratory, whih allows to impose a horizontal periodi shear fore to the devie with a onstant vertial ompression (Fig. 7). The mobile platform of the mahine (Fig. 8) has been then adopted as a vibrating shake-table on whih the isolated abinet has been tested. In [8] the results of some experimental investigations are

3 reported; in partiular, starting from the hystereti yles, deduted by shear tests, the equivalent stiffness and damping have been derived. Then, the results of an experimental modal analysis, arried out on the isolated abinet has been presented to highlight the isolation performanes. Some linear and nonlinear analytial models have been tested to desribe the isolator restoring fore [9]. In the following, the analytial results obtained with a nonlinear model, based on a modified Bou-Wen model, are reported and ompared with the experimental ones. The validated model has also been used to simulate the abinet dynami response due to seismi exitations, some results are reported in setion IV. unertainties and the unknown isolator reation fore. This ontrol riterion allows to design a ontrol ation that results minimally invasive on the stability harateristis and allows to obtain good traking results without the inreasing of the feedbak ontrol gain. The test rig is instrumented to detet the following measurements: table position y by means of magnetostritive position sensor (FS = 0.4 m - estimated unertainty = ± 1.2E-4 m); atuation fore by means of strain gauge load ell (FS = N - estimated unertainty = ± 500 N); vertial load pressing on the speimen under test by means of strain gauge load ell (FS = 1E6 N - estimated unertainty = ± 230 N); platform and abinet aelerations by means of two piezoeletri aelerometers. Sine the BPI has been designed to haraterize more rigid isolators, the sensitivity of the load ell and the frition fores of the platform linear guides do not allow to make aurate investigation for the isolator desribed in the present paper. For this reason, a suitable devie has been realized (Figs. 9 and 10). It is made up of a slide horizontally onneted to the BPI platform by means of a load ell and vertially supported by four BTUs; two ouples of rolling bearing laterally guide the slide. Fig. 7. BPI testing mahine. Fig. 8. BPI adopted as shake-table. II. WRS-BTU ISOLATOR CHARACTERIZATION The isolator is onstituted by 8 ables; eah one has a length of 90 mm and a the diameter of 5 mm. Some haraterization tests have been performed using the BPI testing mahine; the isolator upper plate has been horizontally loked and has been loaded with a vertial onstant fore; the lower plate has been fixed on the platform, exited with a harmoni motion. The ontroller of the hydrauli atuator, employed to move the platform, must ensure the traking of the target displaement in presene of the unknown restoring fore of the isolation devies. For this reason, a ontrol based on a mixed approah has been adopted; it is onstituted by a model inversion based ontrol, oupled with a feedbak ontribution [7]. To this aim, a non-linear model for the hydrauli atuation system has been derived and adopted for the feedforward synthesis through the inverse dynamis resolution. As a onsequene, feedbak ontrol has the funtion to ompensate for the traking error due to model Fig. 9. Devie for the haraterization of isolator stiffness. The load ell is haraterized by FS = 1335 N; estimated unertainty is equal to ± 0.13 N. When the platform moves, the following fores at on the slide (Fig. 10: isolator restoring fore, F; inertia fore of the slide mass and of the isolator bodies onneted to the slide (lower plate and isolator BTU), m s x ; frition fores of four BTUs supporting the slide: 4F f ; horizontal onstraint fore (measured by load ell), F LC. Therefore, the expression for the restoring fore F is: F F m x 4F (1) LC s f The inertia fore, m s x, is obtained from the measurement of the slide horizontal aeleration and the knowledge of the

4 mass m s. The frition fore, exerted by the four supporting BTUs, is: F f =f s N, being N the vertial load and f s the frition oeffiient. Fig. 11 shows the results of some tests arried out by imposing sinusoidal deformation law with an equal amplitude A (0.03m) and three different values of frequeny f (0.1, 0.5; 1 Hz). In eah ase, the yle has been obtained with and without the ontat between the BTU and the bearing surfae to put in evidene the BTU rolling resistane due to a vertial load of 1220N, smaller than the maximum allowed, equal to 1400N. The deteted yles show that: without ontat between BTU and bearing surfae, the yle area inreases with the foring frequeny; the wire rope spring is therefore haraterized even by a visous damping; the ontat between BTU and bearing surfae leads to a further inrement of the yle area; the devie has a hardening behaviour more marked at low frequenies and for greater deformation of the ables. Fig. 12 shows other tests onduted without BTU ontat, for three different frequeny values and with the same amplitude of 0.02m; the behaviour is similar to the one shown in Fig. 11. The experimental yles have been used to define analytially the isolator restoring fore that mainly depends on the instantaneous ropes deformation, on the deformation veloity and on the history of the ropes deformation [9]. The isolator reation F has been modelled as the sum of the following two omponents: F(t) = F (t) +F r (t) (2) where, F represents the wire ropes ation and Fr fr N sgn( x ) is the BTU rolling frition fore. x F LC LOAD CELL WRS-BTU ISOLATOR BTU BPI PLATFORM F f m x s VERTICAL N SLIDE x x, x, x F SLIDE SLIDE Fig. 10. Devie for the haraterization of isolator stiffness: sheme; fores ating on the slide. ACCELEROMETER f F F Fig. 11. Fore-displaement yles for different frequenies, with amplitude of 30mm.

5 Fig. 12. Fore-displaement yles for different frequenies in no BTU ontat ondition. In the following, the analytial expressions of the above omponents are reported in order to obtain a model that an be used to desribe the isolator dynami behaviour. The F omponent has been modelled as the sum of four independent terms: for different kinds of exitations. F F F F F (3) el h nl v where: Fe kex( t), is the elasti omponent, proportional to the displaement x(t); F h is the hystereti 3 omponent; Fnl knl x( t), is a non-linear omponent proportional to the ube of the displaement, and Fv σv x, is the visous damping omponent. The hystereti omponent has been derived from a simplified version of the Bou-Wen model presented in [10]: Fh kww( t) w x 1 sgn( x ) w( t) where ρ and k w are positive parameters that hange the shape of the yle. By appropriately hoosing these two last parameters, it is possible to aommodate the response of the model to the real hysteresis loops; the use of system identifiation tehniques is a pratial way to perform this task [11]. The identifiation proedure has been onduted adopting the least mean squared method between experimental and theoretial data. In Table I the identified parameter are reported. Model parameter TABLE I WRS-BTU FORCE MODEL PARAMETERS k e k nl σ v f r ρ k w Value (4) Fig. 13. Comparison between theoretial and experimental yle for f=0.1 Hz and without BTU ontat. Amplitude: 0.02m; 0.03m.. Unit N/m N/m 3 Ns/m - 1/m N The omparisons between the numerial and experimental results are shown in Figs. 13 and 14; the figures highlight that the numerial model results are satisfatory. The main differenes are due to the asymmetries of the experimental yles aused by the unavoidable asymmetries of the isolator. The model results are in good aordane with the experimental ones even in the ase of BTU ontat as shown in Fig. 14b. Therefore, the isolator model an be used to evaluate the isolation effetiveness of strutures isolated with these devies, for different strutures inertial harateristis and/or Fig. 14. Comparison between theoretial and experimental yle for f=0.5 Hz, A= 0.03m. without BTU ontat; with BTU ontat. In the following setions the model is adopted to predit the dynami behaviour of a light steel struture exited by a harmoni ground motion; the theoretial results are ompared with the experimental ones. Afterwards, the same model is adopted to predit the dynami response of strutures subjeted to seismi exitation.

6 III. CABINET FREQUENCY ANALYSIS WRS-BTU isolators have been adopted to isolate a laboratory abinet (Figs. 15 and 16) onstituted of a rigid steel frame (0.60 x 0.70 x 1.20 m) on whih may be fixed additional masses to modify the inertial properties. The tests have been onduted with the abinet overall mass of 165 kg plaed on the moving platform of the BPI, driven by a position-ontrolled hydrauli atuator [12]. The ontroller of the platform hydrauli atuator, even when the BPI testing mahine works as a shaking-table, assures a good traking of the target displaement. Also in this BPI utilization, the fores ating on the platform are unknown. In this ase, the abinet transmits fores to the platform, depending on its dynamis, whih, in turn, are related to the platform movement and to the isolator harateristis. The ratio (a /a g ) of the aeleration synhronous omponents, versus the foring frequeny (Fig. 17), shows a peak in the neighbourhood of 1 Hz; this frequeny may be onsidered as a resonant frequeny. The system is then isolated for foring frequenies greater than about 1.5 Hz. This threshold value depends on the motion amplitude as shown by the two urves obtained for two different platform motion amplitude (5 and 10 mm). Fig. 17. Aeleration ratio vs. foring frequeny. It must be noted that for linear systems the aeleration ratio, if defined as a /a g (i.e. output/input), is equivalent to the orrespondent displaement ratio d / d g, also known as displaement transmissibility : 2 2 T a / a ( d / d ) d / d (5) g g g Fig. 15. Cabinet on the shake-table. Fig. 16. Cabinet isolators and additional masses. The additional masses have been arranged in the lower part of the abinet to avoid the abinet overturning. In order to haraterize the isolated abinet in the frequeny domain, the input motion to the platform of the shaking table has been hosen of harmoni type. The tests have been onduted for two different values of the amplitude and foring frequeny in the Hz range. By means of two aelerometers, platform and abinet aeleration have been deteted and the two time histories have been ompared. As the platform movement is not perfetly harmoni, for eah test, a frequeny analysis of the two time histories (platform and abinet aelerations) has been performed. The amplitudes of the omponents, synhronous with that imposed to the platform, have been ompared. being the exiting irular frequeny. For this reason, the experimental aeleration ratio has a qualitative shape (Fig. 17) that resembles the linear displaement transmissibility of vibrating linear systems, haraterized by a peak amplitude in orrespondene of the resonant frequeny and very low values for high frequenies. The aeleration signals have been ompared with those ones oming from the numerial integration of the motion equations in whih the isolator behaviour is modelled as indiated in the previous paragraph. The motion equations are based on the assumption that the abinet entre of the masses oinides with isolators stiffness entre; under this hypothesis, the abinet an be onsidered as a single degree of freedom system. Fig. 18. Cabinet sketh.

7 The abinet motion equation is: m x 4F 0 (6) being (Fig. 18): - x(t), abinet displaement; - F, the restoring fore exerted by eah isolator; - m, the mass of the abinet. Indiating with x g (t) the ground (platform) displaement, the relative displaement between abinet and ground is: d x xg (7) The simulations regard the dynami behaviour of the abinet fored to vibrate by a harmoni ground aeleration: x g ag sin( t) (8) where a g is the platform horizontal aeleration amplitude. The orresponding platform displaement has the following form: ag xg sin( t) 2 (9) m d 4 F m xg (10) The numerial simulations have been performed imposing to the platform a harmoni displaement law haraterized by amplitude and foring frequeny in aordane with those ones assigned for the experimental investigation. In Fig. 19 a omparison between the numerial and experimental results is reported for three different values of the foring frequeny and equal platform amplitude displaement (0.01m). For eah foring frequeny, the omparisons between theoretial and experimental abinet aeleration show a good agreement; the differenes an be even attributed to a slight yaw rotation of the abinet deteted by the aelerometer and to the unavoidable dissymmetry of the isolators. The numerial ode an be onsidered validated and so it has been adopted to desribe the dynami system behaviour. As an example in the same Fig. 19 the platform absolute displaements (d p ) versus the abinet ones (d ) and the trend of the restoring fore (F) versus the relative displaement (d), are reported. In aordane with Fig. 17, the first diagrams type (d p vs. d ), show that for a given platform displaement amplitude (0.01m), the abinet motion is amplified at about 1 Hz while it is isolated for higher frequenies (3 Hz). Therefore the abinet equation, in term of relative motion, is: Fig. 19. Comparison between experimental and theoretial aeleration; platform displaements (d p ) versus the abinet displaements (d ); restoring fore (F) versus the relative displaement (d).

8 The F-d diagrams are haraterized by yles whose areas represent the energy dissipation due to the presene of hysteresis, visous damping and frition. It an be noted that the areas inrease with the foring frequeny showing an evident visous ontribute. Moreover, due to the presene of frition, the equilibrium position is not univoal as highlighted in the F-d diagrams, where the final equilibrium position does not oinide with the initial one. For the foring frequeny equal to 3 Hz the relative motion appears rather large, while the absolute abinet displaement is signifiantly lower than the platform one. This ondition of isolation is so haraterized by large restoring fore, large energy dissipation and small absolute abinet motion amplitude. The displaement transmissibility (d /d g ) has been dedued adopting the simulation ode. For an assigned ground harmoni displaement amplitude (d g ) and irular frequeny (), the abinet time history has been evaluated. The ratio between the amplitude of their fundamental harmoni omponents amplitude has been plotted versus the foring frequeny f (Fig. 20). The urve has a qualitative trend similar to the experimental ones reported in Fig.17. The aeleration transmissibility is defined, similarly to linear systems, as: 2 T d / d (8) a g (In linear vibrating systems, this quantity is divided for the squared natural irular frequeny and therefore it is a dimensionless ratio). The orrespondent diagram shows that the abinet aeleration rapidly grows with foring frequeny, until the resonant frequeny (1 Hz); then, the aeleration ontinues to grow although with a lower slope (Fig. 21). In seismi appliations, both displaement and aeleration transmissibility have partiular importane; it is neessary to ontain the maximum displaement value to avoid exessive stresses in the onnetions of the struture with the neighboring plants (pipes, wires, et.) and to not exeed the maximum isolator deformation; besides, it is neessary to limit struture aeleration to ontain inertia fores. The damping of the isolation system ontains the maximum abinet aeleration reahed in resonane ondition. A trade-off between displaement and aeleration amplitudes an be obtained in the frequeny range 1-2 Hz. Fig. 21. Aeleration/displaement ratio (d g =10 mm) IV. CABINET SEISMIC RESPONSE The good agreement between theoretial and experimental results, highlighted in the previous setion, in ase of harmoni ground aeleration, allows the proposed model to be used even to simulate different base exitations and in partiular seismi ones. The reported results have been obtained onsidering as ground exitation the horizontal time history aeleration of the Irpinia earthquake (Italy, 1980) [13]. Simulations have been repeated by saling the aelerogram in order to take into aount the hardening harateristi of the insulator. Figs. 22, 23 and 24 report the simulation results for the following sale fator (SF): 0.50; 1.0; 1.5. Fig. 22. Comparison between ground and abinet aeleration with SF=0.5; aelerograms (aeleration ratio = 1.9); restoring fore vs. relative displaements. Fig. 20. Displaement transmissibility (d g = 10 mm)

9 restoring fore vs. relative displaement has the typial shape of the hardening isolators haraterized by an evident inrease of the fore in the final part of the stroke. Fig. 23. Comparison between ground and abinet aeleration with SF=1; aelerograms (aeleration ratio = 1.5); restoring fore vs. relative displaements. Fig. 24. Comparison between ground and abinet aeleration with SF=1.5; aelerograms (aeleration ratio = 1.4); restoring fore vs. relative displaements. Examining diagram it an be observed that: a /a g (intended in this ase as the ratio between ground and abinet peak aeleration) derease with SF; it varies from 1.9 to 1.4 for SF=0.5 and SF=1.5, respetively; passive seismi protetion dereases with ground aeleration; abinet peak displaements is lower than the maximum allowed displaement (about 50mm); V. CONCLUSION In this paper, a numerial method useful to simulate and predit the dynami behaviour of abinets or shelters, equipped with WRS-BTU devies, is presented. A survey to assess the effiieny of the isolation system has been onduted. The proposed isolator is heap and easy to realize by oupling a BTU with WRS springs; both the omponents are easily obtainable from industrial prodution and are already haraterized by the manufaturers. In the design stage, a suitable horizontal stiffness an be easily obtained to set the desired system natural frequeny. Moreover, the two omponents must not neessarily be integrated in a single unit. The proposed numerial model has been validated and then has been used to simulate the abinet dynami response due to a seismi ground motion. The effetiveness of the isolation devie has been evaluated omparing the ground aeleration diagram with the orresponding abinet one. REFERENCES [1] M. Ismail, J. Rodellar, F. Ikhouane, An innovative isolation bearing for motion-sensitive equipment, Journal of Sound and Vibration, vol. 326, no. 3 5, pp , Ot [2] A. Mokha, M. Constantinou, A. Reinhorn, V. Zayas, Experimental Study of Frition Pendulum Isolation System, J. Strut. Eng., vol. 117, no. 4, pp , [3] S.J. Wang, C.H. Yu & J.Y. Hsiao, Development of Sloped Rolling- Type Isolation Devies for Seismi Protetion of Important Equipment and Failities, 15th World Conferene in Earthquake Engineering, Lisboa, [4] M.H. Tsaia, S.Y. Wub, K.C. Chang, G.C. Leed, Shaking table tests of a saled bridge model with rolling-type seismi isolation bearings, Engineering Strutures, vol. 29, no. 5, pp , May [5] G. Di Massa, S. Pagano, E. Roa, S. Strano, Sensitive equipments on WRS-BTU isolators, Meania, vol. 48, no. 7, pp , [6] G.F. Demetriades, M.C. Constantinou, A.M. Reinhorn, Study for wire rope systems for seismi protetion of equipment in buildings, Engineering Strutures, vol. 15, no. 5, pp , September [7] S. Pagano, M. Russo, S. Strano, M. Terzo, Seismi isolator test rig ontrol using high-fidelity non-linear dynami system modeling, Meania, vol. 49, no. 1, pp , [8] R. Branati, G. Di Massa, S. Pagano, E. Roa, S. Strano, Experimental investigation of the performanes of a WRS-BTU seismi isolator, World Congress on Engineering, London, U.K., 3-5 July, [9] G. Di Massa, S. Pagano, S. Strano, F. Timpone, A omparison between linear and nonlinear modelling of a wire rope seismi isolator, International Review on Modelling and Simulations, vol. 6, no. 4, pp , Aug [10] M. Ismail, F. Ikhouane, J. Rodellar, The Hysteresis Bou-Wen Model, a Survey, Arh. Comput. Methods Eng, vol. 16, no.2, pp , [11] I.I. Lazaro, A. Alvarez, J. Anzurez, The Identifiation Problem Applied to Periodi Systems Using Hartley Series, Engineering Letters, vol. 21, no.1, pp , Feb [12] S. Strano, M. Terzo, A first order model based ontrol of a hydrauli seismi isolator test rig, Engineering Letters, vol. 21, no. 2, pp , [13] N. Ambraseys, P. Smit, R. Sigbjornsson, P. Suhadol, B. Margaris, Internet-Site for European Strong-Motion Data, European Commission, Researh-Diretorate General, Environment and Climate Program ESD_Loal/frameset.htm [24 July 2013].