VEHICLE-INDUCED FLOOR VIBRATIONS IN A MULTI-STORY FACTORY BUILDING

Transcription

1 VEHICLE-INDUCED FLOOR VIBRATIONS IN A MULTI-STORY FACTORY BUILDING By Tso-Chien Pan 1, Akira Mita 2, Members and Jing Li 3 ABSTRACT: A multi-story factory building with elevated access allows loading and unloading the raw materials and finished products right in front of each factory unit. This enhances the land productivity of land-scarce Singapore. However, container trucks traveling within the building may cause vibration of a production floor where high-precision equipment is sited. In this study, a dynamic vehicle model is established to simulate a 40-ft container truck. The road roughness is represented by a power spectral density function according to ISO 8606 (1995). The random response of a typical production floor is analyzed by the fully coupled vehicle-structure interaction method as well as the decoupled moving dynamic nodal loading method. Compared with the acceleration and velocity acceptance criteria, the random response results show that the vertical response of production floor to the container truck traveling at 15, 30, and 40 km/h over road classes B and C is generally acceptable. However, the maximum vertical vibration may exceed the more stringent criteria for some extremely high-precision equipment. Key Words: structural dynamics, floor vibration, vehicle dynamics, vehicle loading, moving load, and vibration acceptance 1 Professor and Director, Protective Technology Research Center, School of Civil & Structural Engineering, Nanyang Technological University, Singapore cpan@ntu.edu.sg, Tel: , Fax: Assoc Professor, Graduate School of Science and Technology, Keio University, Hiyoshi, Kohoku-ku, Yokohama , Japan. mita@sd.keio.ac.jp, Tel & Fax: Research Scholar, School of Civil & Structural Engineering, Nanyang Technological University, Singapore

2 INTRODUCTION With the rapid industrial development in the land-scarce Singapore, there is a pressing need for creative measures to enhance land productivity, which is measured by the total net value-added per square meter of land used in production. Generally speaking, industries that operate in a multi-story environment are better able to achieve higher land productivity levels than those do not. The structural configuration of a typical stack-up multi-story factory has vehicular ramp access to every floor of a factory unit (Figure 1). This allows loading and unloading the raw materials and finished products right in front of the factory unit. However, trucks traveling over a road within the multi-story factory building will generate a series of moving dynamic loading because of the road roughness. It is therefore important to be able to determine the dynamic performance of the factory production area subjected to these moving dynamic loading. The dynamic performance will determine whether certain high technology industries could be housed within such a multi-story factory building with elevated access. The investigation of dynamic behavior of beam-structures under moving loads has been a topic of interest for well over a century, especially in recent years. The dynamic problems induced by heavy vehicles and their interaction with a bridge have interested many engineers. Research on the dynamic response of bridges subjected to moving vehicle loads dates back to the work of Jeffcott (1929). In early studies, a moving vehicle traveling along a bridge has been modeled as a moving load, neglecting the effect of inertia. Such an assumption remains good for a wide range of problems encountered in bridge engineering, where the inertia of the vehicle is small compared with that of the bridge. For cases where the inertia of the vehicle cannot be neglected, a moving-mass model has to be used instead. Recently, more sophisticated models that consider various dynamic characteristics of the moving vehicle have been used (Henchi and Fafard, 1997; Esmailzadeh and Ghorashi, 1997; 2

3 Green, and Cebon 1997; Yang and Fonder, 1996; Yang and Lin, 1995; Chompooming and Yener, 1995). For the multi-story construction of factory buildings with vehicles moving within the structure, the dynamic performance of factory production area has seldom been studied (Pan and Li, 1999). In studying the dynamic response of a vehicle-structure system, two sets of equations of motion can be written, one for the vehicle and the other for the structure. It is the interaction forces existing at the contact points between the two subsystems that make the two sets of equations coupled. One feature of this contact problem is that the contact points move from time to time. Another feature is that the road surface in contact is rough. These two features make the problem more complicated to deal with. The purpose of this study is to look into the effects of vibration resulting from container trucks traveling at specified speeds within a multi-story factory building with elevated access. In particular, the maximum vibration response levels of the production floor within a typical factory unit will be estimated for the specified traveling speeds of the container trucks. Two methods will be used in this study. One is the decoupled dynamic nodal loading method (DNL) (Pan and Li, 1999). The other is the fully coupled dynamic finite element (DFE) method for vehicle-structure system (Pan and Li, 1999). Both methods could consider the detailed behavior of vehicle systems. The excitation force of a vehicle system results from the road roughness. With the dynamic nodal loading (DNL) method, the dynamic analysis of vehicle systems is carried out without considering the dynamic deflection of the supporting structure. This method therefore ignores the interaction between the vehicle and the structure, but has the advantage of not solving the coupled vehiclestructure equations. When the stiffness of the vehicle is much less than that of the structure, this simplified method is expected to yield good engineering precision. In this study, the vibration response results obtained from these two methods for dynamic analysis of a large 3

4 building system with elevated access will be compared. Furthermore, several vibration acceptance criteria in terms of acceleration and velocity are used to compare with the response levels. The results could therefore give guidelines for considering whether to house high technology industries in such a multi-story factory building with elevated access. ROAD ROUGHNESS ANALYSIS Even the best of roads exhibits random spatial unevenness about a mean level and could be the source of random vibration to a structure, e.g. when a truck is moving inside the structure. The dynamic response of such a structure depends on the nature of road surface unevenness, truck motion, road-truck contact and the dynamic characteristics of the truck and the structure. To carry out a random vibration analysis of the structure, it is necessary to construct first a stochastic model of the road profile. Depending on the truck motion and the nature of wheel-road contact, the road unevenness can be transformed into time-dependent random excitations at each contact point. It is then necessary to construct the mathematical model of a moving truck. The response of the truck-road system can then be represented by a set of differential equations with random forcing function. The random reaction force on the structure can be determined through the theory of random vibration. Road roughness The road profile can be represented by a power spectral density (PSD) function. To determine the power spectral density function, or PSD, it is necessary to measure the surface profile with respect to a reference plane. Generally, for a random vibration analysis of vehicles moving on a road, it is necessary to fit an analytical expression to the measured PSD. A set of spectra which indicates the boundaries of eight classes of roads, defined according to 4

5 the ISO 8606 code (ISO, 1995), can be represented by the following analytical descriptions which have been proposed to fit the measured PSD: G(n) = G(n )( n Ω ) G( Ω) = G( Ω0 )( ) n 0 Ω0 (1) where n and Ω are the spatial and angular spatial frequencies, and G (n) and G( Ω ) are the one-sided and one dimensional power spectral density functions in terms of n and Ω. Note that n 0 = 0.1 cycle/m is the reference spatial frequency; Ω 0 = 1rad/m is the reference angular spatial frequency; and G(n 0 ) and ( Ω ) are the roughness coefficients which G 0 represent the height of these spectra. The values of G(n 0 ) defined at the reference frequency n 0 = 0.1 cycle/m are listed in Table 1 for road classes A to H. The PSD functions defining the eight classes of roads A to H according to equation (1) are shown in Figure 2. Paved roads are generally considered to be among road classes A to D. Road class A corresponds to a very good road, which typically indicates a newly paved highway. An unpaved road where a truck would hardly be able to travel at a speed of 40 km/h corresponds to road class E or F. Spectral analysis of the road roughness As a truck traverses a road, the wheels follow the profile and transmit a timedependent vertical displacement to the truck at each contact point, while the truck transmits the random reaction forces to the contact points. The temporal nature of the transmitted excitations depends on the speed of the truck. When trucks moving with a constant speed V, the road profile is linearly transformed from the space domain to the time domain. Since the road profile is modeled as a homogeneous, Gaussian random process in the space domain, it is transformed to a stationary, Gaussian random process in the time domain. Let z (t) represent the vertical displacement transmitted at time t to a moving truck at the contact point. 5

6 Then, for a road whose vertical spatial profile is represented by ẑ (s) at distance s, the vehicle speed V is related to distance as V = ds. If the two-sided temporal spectral density function dt of z(t) is represented by S (ω) in which ω is the angular frequency and the two-sided spatial spectral density function of z$( s ) is represented by S (Ω) in which Ω represents the angular spatial frequency or the wave number, the relationship between S(ω) and S( Ω ) can be shown as S ( ω ) = 1 V S( Ω ) (2) The two-sided PSD of vertical acceleration &&() zt and velocity zt &( ), S ( ω ) and S ( ω) & z z&, could be represented by G ẑ (n), the one-side PSD of z$( s ) defined in equation (1), as follows: S ( ω ) = (2πf ) & z 4 1 G 4πV ẑ (n) S ( ω) = (2πf ) z& 2 1 G 4πV ẑ (n) (3) Changing from the continuous PSD to discrete PSD, the discrete series of PSD of &&() zt, Sz&& ( k), can be obtained from * S ( k) = F ( k) F ( k) (4) && z && z && z * where Fz&& ( k) is the conjugate of Fz&& ( k) which is the DFT of time series &&() z t. The phase of Fz&& ( k) could be obtained from random series. The time series of &&() z t could then be generated from the inverse discrete Fourier transformation (IDFT) of F k z&& ( ), & z (r) = N 1 k= 0 F i(2πkr / N) & z (k)e r = 0,1, 2,...,(N 1) (5) This discrete time series of acceleration will be used in the dynamics analysis of the truck. The spatial profile of the road roughness, ẑ (s), could be also derived from (n) G ẑ, the oneside PSD of z$( s ) defined in equation (1), through the inverse discrete Fourier transformation. 6

7 As an example, the spatial histories of road surface roughness corresponding to the boundaries of road classes A, B, C and D are shown in Figure 3. DYNAMIC REACTION FORCE OF VEHICLES Dynamic characteristics of the vehicle For the vehicle system, the dynamic reaction force on the road, which resulted from the road roughness, is of major concern. The vehicle system could be modeled as a massstiffness-damping system according to the wheel axles. With respect to an observer on the moving vehicle, the displacement of the vehicle ( z v ) and the road roughness ( z g ) (Figure 4) are functions only of time, and the equations of motion of the vehicle are m & z + cz& + kz = cz& + kz (6) v v v g g Using the relative co-ordinates of the vehicle z v and the road roughness z g, the motion equations of the vehicle take the following form in matrix notations: T where z = { z z z } and z = { z z } T g g1 g2 z g3 m & z + cz& + kz = mz & g (7). In equation (6) or (7), m, c and k are the mass, damping and stiffness matrices, respectively; and & z& g is the ground acceleration derived from road PSD; and z i represents the motion at the i-th axle of the container truck, while z gi represents the ground motion under the i-th axle. The typical truck model is a 40-foot container truck (tractor-trailer assembly). The dimensions and axle loads of the truck are shown in Figure 5. For dynamic response analysis purpose, the container truck can be modeled approximately by a three degrees-of-freedom (DOFs) system as depicted in Figure 4. The spring constants are determined based upon the models of spring stiffness in serial for a single-tire axle and a double-tire axle. Axles 1 and 2 are single-tire and double-tire systems, respectively, while axle 3 consists of two double-tire systems. The spring constants used in 7

8 the models are K s = 14,700 kn/cm for suspensions and K t = 11,760 kn/cm for tires. The damping constant c 1 is chosen so that the critical damping ratio of the tractor is equal to 0.1. Similarly, the damping constant c 2 and c 3 are so chosen as to make the critical damping ratio of the tailor equal to The dynamic properties of the 3-DOF truck-trailer assembly can be characterized in terms of the predominant frequencies of the axle vibrations as shown in Figure 6. Figure 6 shows that while axle 1 exhibits an independent motion of about 2.5 Hz, axles 2 and 3 are in fact coupled motions of around 2.0 Hz and 2.4 Hz. Random reaction forces of the moving truck From the displacement time histories generated for a class of road surface roughness, Figure 3, the acceleration time histories & z& g can be obtained as input to the equations of motion for the container truck, equation (7). The resulting motion of the container truck gives rise to the time-varying reaction forces acting on the road surface through the axles as follows: ftotal = f static + f dynamic (8) f = c z& z& ) + k( z z ) = cz& + kz dynamic ( v g v g The reaction forces, excluding the static axle load, through axles of the container truck traveling at 15, 30 and 40 km/h are plotted in Figure 7, respectively. The PSD function used in the example is from road class B. With the dynamic nodal loading method (DNL) (Pan and Li, 1999), the reaction forces of truck axles could be directly input to a structure as forcing time series. Therefore, it is a decoupled approach for vehicle-structure interaction problem. With the dynamic finite element (DFE) method (Pan and Li, 1999), the coupled vehicle-structure system is considered, where the trucks are moving parts of the entire system. The dynamic interaction 8

9 forces, including road roughness, between trucks and the structure are considered automatically. VERTICAL FLOOR RESPONSE TO A TRAVELING CONTAINER TRUCK Structural model Figure 8 shows the typical floor plan of a company in a standard unit of the multistory factory building with elevated accesses (Figure 1). Figure 9 shows the cross-sectional view of a typical unit. The finite element model used in the following dynamic response analyses is constructed based on the typical floor plan. The mezzanine floor, covering only partially above the factory floor area, is ignored in the model. In addition to the typical floor area (52 m 76 m), the structural model also includes one-half of the 15 m wide aerial driveway. The plan dimension of the structural model is thus 52 m 83.5 m, as shown in the perspective view of the overall 3-D finite element model in Figure 10. Symmetric boundary conditions are imposed on nodal points along three of the four edges of the model. The lines of symmetry are located along the center line of the aerial driveway and along the long edges of 83.5 m. The first row of plates along the y-axis represents the aerial driveway, and the entrance to the company is located between the first two columns on the left-hand side. Moving dynamic load Including the static axle loading, the moving dynamic load generated by the container truck traveling at 15, 30, and 40 km/h are shown in Figure 7. In the figure, the largest loading results from axle 3 (rear axle) and the smallest loading results from axle 1 (front axle). The reaction force at axle 3 (rear axle) of the container truck reaches an absolute maximum of about 37 tonne, inclusive of the static axle load. 9

10 The moving dynamic loads are applied in turn at the nodal points along the centre lines of the aerial driveway, the front access road, the side access road, and the rear access road. At a typical nodal point (n), the time varying load can be approximately obtained by multiplying the time varying series of loading with a triangular shape function between nodal points (n-1) and (n+1). The triangular shape function starts with a zero value at nodal point (n-1), reaches a maximum value of 1.0 at nodal point (n), and ends with a zero value at nodal point (n+1). Vertical floor response to a moving container truck In the dynamic response analysis, it is assumed that the container truck may travel on the aerial driveway at speeds of 15, 30, or 40 km/h. It is also assumed that within the company compound, the container truck would only travel at a slower speed of 15 km/h on the internal access roads, i.e. the front, the side, and the rear access roads. Based on these assumptions, the DFE method and the DNL method have been used separately to analyze the transient dynamic response of a typical floor. For the response calculations, a constant damping ratio of 0.03 is used for all natural vibration modes considered in the modal superposition procedure and a Rayleigh damping with coefficient α = and β = are used in the Newmark average acceleration direct integration procedure with s time step. The dynamic response to the container truck traveling on the aerial driveway at 40 km/h is computed at the center point of the production floor for road class C. The computed acceleration response time histories of at the center node are shown in Figure 11 in the units of m/s 2. The acceleration response to the traveling speed of 40 km/h with road class B reaches a maximum value of mm/s 2 (i.e. about 0.04 gal) and the RMS value of velocity response reaches 3.43 µm/s for the non-interaction cases, and gal of 10

11 acceleration and 0.96 µm/s of RMS velocity for the interaction cases. The responses are much smaller when the interaction effects are considered via the DFE method. At the center point of the production floor, the velocity and acceleration responses to the container truck traveling at 15 km/h on road class C within the factory compound on the front, the side, and the rear access roads are also computed. The various acceleration response time histories of the center node are shown in Figures 12 to 14 in the units of m/s 2. Among the three cases considered, the maximum response occurs when the truck is moving on the rear access road. For road roughness class C, the maximum acceleration response reaches an absolute maximum value of 1.93 gal (non-interaction case) or 0.54 gal (interaction case) (Figure 14), while the RMS value of vertical velocity response reaches an maximum value of 108 µm/s (non-interaction case) or µm/s (interaction case). The RMS values of velocity response and the maximum values of acceleration response of the four cases considered are summarized in Table 2. As an upper bound approximation, the worst case scenario is assumed to be the case when there are multiple container trucks operating simultaneously on the aerial road as well as on the front, the side and the rear access roads. Figure 15 is acceleration response at the center point of the production floor when four trucks move simultaneously on the four roads. The maximum acceleration responses are 0.48 gal (road class B) and 0.97 gal (road class C), and the RMS velocity responses are 45.3 µm/s (road class B) and 88.7 µm/s (road class C). The absolute upper bound maximum acceleration and velocity values can be obtained by adding absolutely the maximum response value produced by each container truck. The upper bound values of multiple vehicles and the absolute maximum values of all cases are listed in Table 3. 11

12 VIBRATION CRITERIA FOR VARIOUS INDUSTRIES, Last printed 12/10/2002 1:03 PM High technology equipment such as that used for the production of advanced integrated circuits, for precision metrology, and for microbiological or optical research, requires environments with extremely limited vibrations. However, ground motions, personnel activities, and the extensive support machinery typically present in high technology facilities may produce unacceptably severe vibrations, unless mitigation of these vibrations is taken into account in the facility design. Acceptable magnitudes of vibration cannot be specified rigidly and are dependent upon specific circumstances. Instead, tentative guidelines are often used in practice for the design of various building structures in order to limit their vibration severity. The vibration criteria are generally based upon human acceptance of vibration levels. In cases where sensitive equipment or delicate operations impose vibration criteria, which are more stringent than those for human comfort, the more stringent criteria should be applied. The acceptance criteria of vibration level for a specific industry are governed by the vibration acceptance criteria for the types of high-precision equipment used in the specific industry. The vibration acceptance criteria are therefore equipment-oriented rather than industry-oriented. The acceptance criteria for vibration-sensitive equipment are usually specified by its manufacturer in terms of the vibration levels at the base of equipment for various frequency ranges. However, it should be noted that, even for similar vibrationsensitive equipment, such as electron microscopes or steppers, the vibration acceptance criteria specified by the various equipment manufacturers may vary substantially. Acceleration criteria The most popular high precision, vibration sensitive equipment currently used in the semiconductor, computer, chemicals and electronic industries is probably the electron 12

13 microscopes and steppers. Typical criteria for vibration tolerance of an electron microscope, for example, are 0.05 gal and 0.07 gal for horizontal and vertical motions, respectively. In this case, the criteria are specified to control the amplitude over all vibration frequencies. Frequently used in the semiconductor, wafer and computer industries, steppers are extremely sensitive to vibrations. The major manufacturers of steppers include Nikon and Canon. However, the vibration acceptance criteria specified by the equipment manufacturers may vary substantially. For example, the vibration acceptance criteria for steppers made by four different manufacturers are shown in Figure 16. Although the manufacturers usually provide the various equipment-specific vibration acceptance criteria, experiences have shown that keeping the vibration level below 0.3 gal on the floor is usually satisfactory for most precision equipment with an isolation system properly installed at the base. Velocity criteria Ungar et al (1990) developed a practically useful facility vibration criteria via reviewing numerous specifications provided by equipment manufactures as well as carrying out measurements on a number of equipment items of various types. They found that specifications, which were based on frequency dependent tests, might conveniently be bounded by curves of constant velocity. A general criterion curve of RMS velocity is shown in Figure 17. A constant vibration velocity value applies between 8 and 80 Hz. Below 8 Hz, two alternatives are indicated which depend on the fundamental natural frequency of sensitive equipment: (1) for equipment items that do not incorporate pneumatically isolated systems, the velocity criterion increases by a factor of 2 from 8 Hz to 4 Hz and does not extend below 4 Hz; and (2) for equipment with pneumatically isolated systems, the velocity criterion remains constant and extends down to 1 Hz. Below and above the frequency range indicated in Figure 17, no 13

14 generally applicable data were available, but much greater vibration velocities than indicated by the curve may be permissible at these frequencies. The velocity value that applies between 8 and 80 Hz may be used conveniently to designate a given criterion curve. The velocity criterion values have been found suitable for facilities housing various classes of sensitive equipment, together with some values suggested by ISO standards. Observations For the typical floor analyzed in this study, vibrations generated by a 40-ft container truck traveling at the specified speeds over the assumed road surface roughness, the simulation results suggest that the results of non-interaction cases are much larger than those of interaction cases. Under the single vehicle case, the maximum vertical vibration level happened when the vehicle operated at the rear access. For non-interaction model, the maximum acceleration values are 1.93 gal for road class B and 1.78 gal for road class C, while the RMS velocity values are µm/s for road class B and µm/s for road class C. For interaction model, the maximum acceleration values are 0.54 gal for road class B and 0.95 gal for road class C, while the RMS velocity values are µm/s for road class B and µm/s for road class C. These maximum values are much smaller compared with those from the non-interaction cases. Under multiple vehicles acting, for the non-interaction model, the maximum acceleration values are 2.36 gal for road class B and 2.24 gal for road class C, while the RMS velocity values are µm/s for road class B and µm/s for road class C. For the interaction model, the maximum acceleration values are 0.48 gal for road class B and 0.97 gal for road class C, while the RMS velocity values are 45.3 µm/s for road class B and 88.7 µm/s 14

15 for road class C. From the results, one could see that the results of interaction model are around one half of those of non-interaction model. In this study, the results of interaction model with road class B will be used to compare with the vibration acceptance criteria. From Table 3 for single vehicle, the maximum vertical vibration level of 0.54 gal at the center of the production floor meets the vibration acceptance criteria specified by stepper manufacturers A and C (Figure 16). The same observation applies to the worst case scenario of 0.72 gal when multiple container trucks operating simultaneously. However, these levels of acceleration response (0.54 gal and 0.72 gal) exceed the vibration acceptance criteria of 0.1 gal specified for steppers made by manufacturer B for the frequency range between 1 Hz and 100 Hz. In other words, the maximum level of vertical vibrations at the centre of the production floor generally meets most of the vibration acceptance criteria but may exceed, though within a manageable margin, the more stringent criteria for some very high precision equipment, e.g. the steppers made by manufacturer B. The simulation results also suggest that, the maximum vertical vibration level of 49.4 µm/s (Table 3) at the center of the production floor meets the vibration acceptance criteria level 5 for class I equipment (Figure 17). The same observation applies to the worst case scenario of 49.5 µm/s (Table 3) due to the effects of multiple container trucks operating simultaneously. However, these levels of RMS velocity response (50 µm/s) exceed the vibration acceptance criteria of 25 µm/s specified as level 5 for class I equipment for the frequency range between 8 Hz and 80 Hz (Figure 17). In other words, the maximum level of vertical vibrations at the center of the production floor generally meets most of the vibration acceptance criteria but may exceed the more stringent criteria for some very high precision equipment, e.g. level 6 to 9 for class II to V equipment. 15

16 CONCLUSIONS The simulation results show that the response produced by the interaction model is generally much smaller than that produced by the non-interaction model. This is because the non-interaction model produces more impact influence than the interaction model. From the response results for one vehicle operating separately on the four access roads, it could be found that the vehicle vibration influence is very localized. Only when the vehicle moves near the production floor in the rear access, there is a high response value. Compared with the various vibration acceptance criteria, it is shown that for road class B, the vibration level of production areas in a multi-story building with elevated access can be acceptable for certain high technology manufacturing. However, it may exceed the more stringent criteria for some very high precision equipment, e.g. the steppers made by manufacturer B or level 6 to 9 for class II to V equipment. Generally speaking, the multi-story factory buildings with elevated access are large complex structural systems, for which the parallel processing methodology (Pan and Li, 1999) would be an ideal way to efficiently simulate the response of a small area embedded within the large complex structural system. This will be further explored in future studies. 16

17 APPENDIX. REFERENCES Chompooming, K. and Yener, M., (1995), The Influence of Roadway Surface Irregularities and Vehicle Deceleration on Bridge Dynamics Using the Method of Lines, Journal of Sound and Vibration, Vol. 183(4), pp Esmailzadeh, E. and Ghorashi, M., (1997), Vibration Analysis of a Timoshenko Beam Subjected to a Traveling Mass, Journal of Sound and Vibration, Vol. 199 (4), pp Green, M. F. and Cebon, D., (1997), Dynamic Interaction Between Heavy Vehicles and Highway Bridges, Computers & Structures, Vol. 62, pp Henchi, K. and Fafard, M., (1997), Dynamic Behavior of Multi-span Beams Under Moving Loads, Journal of Sound and Vibration, Vol. 199 (1), pp Jeffcott, H. H. (1929), On the Vibration of Beams Under the Action of Moving Loads, Phil. Meg., 7(8), 66. ISO 8606, (1995), Mechanical Vibration Road Surface Profiles Reporting of Measured Data, British Standard, BS 7853, Pan, T. C., and Li, J. (1999), Dynamic FE Method for Transient Response of Vehicle- Structure Coupling System, Asia-Pacific Vibration Conference 99 (A-PVC 99), Dec. 1999, Singapore, Vol. I, pp Ungar, E. E., Sturz, D. H. and Amick, C. H., (1990), Vibration Control Design of High Technology Facilities, Sound Vibration, Vol. 24, No. 7, pp Yang, F. and Fonder, G. A., (1996), An Iterative Solution Method for Dynamic Response of Bridge-Vehicles Systems, Earthquake Engineering and Structural Dynamics, Vol. 25, pp

18 Yang, Y. B. and Lin, B. H., (1995), Vehicle-Bridge Interaction Analysis By Dynamic Condensation Method, Journal of Structural Engineering, Vol. 121, No. 11, pp

19 Table 1. Definition of Road Classes Degree of roughness G(n 0 ) (10-6 m 3 ) where n 0 = 0.1 cycle/m Road Class Lower limit Geometric mean Upper limit A B C D 512 1,024 2,048 E 2,048 4,096 8,192 F 8,192 16,384 32,768 G 32,768 65, ,072 H 131, , ,288 19

20 Table 2. RMS values of velocity response and maximum values of acceleration response at the center of production area Access Roughness Non-interaction Interaction Road Class model model aerial B MAX Acc. (gal) driveway RMS Vel. (µm/s) (40 km/h) C MAX Acc. (gal) RMS Vel. (µm/s) B MAX Acc. (gal) front access RMS Vel. (µm/s) (15 km/h) C MAX Acc. (gal) RMS Vel. (µm/s) B MAX Acc. (gal) side access RMS Vel. (µm/s) (15 km/h) C MAX Acc. (gal) RMS Vel. (µm/s) B MAX Acc. (gal) rear access RMS Vel. (µm/s) (15 km/h) C MAX Acc. (gal) RMS Vel. (µm/s)

21 Table 3. Upper bound value of velocity and acceleration responses RMS velocity (µm/s) MAX acceleration (gal) Class B Class C Class B Class C Single vehicle (non-interaction model) Single vehicle (interaction model) Absolute Maximum (Non-interaction model) Absolute Maximum (Interaction model) Multiple vehicles (Interaction model)

22 Figure 1. Multi-story Factories Served by Two Vehicular Ramps and Driveways 22

23 Figure 2. PSD of Road Classes A to H Displacement (cm) Road Class A Road Class C Road Class B Road Class D Length (m) Figure 3. Displacement Time Histories of Road Classes A, B, C and D 23

24 V z c 1 g k 1 c 2 z 1 M k 2 c z 3 2 k 3 z 3 z v o ( s ) u structure Figure 4. Road Roughness and Moving Vehicle Model 40 Container t m t t 5.39 t Container Trailer chassis Truck tractor Total m t 4.25 t 5.96 t t Figure 5. Dimensions and Axle Loads of a 40-ft Container Truck 24

25 Figure 6. Dynamic Characteristics of Tractor-Trailer Assembly 25

26 Figure 7. Axle Reaction Forces (Road Class B) 26

27 Front side access, Last printed 12/10/2002 1:03 PM Rear access road Side access road 15 m wide aerial driveway Figure 8. Plan of a Typical Company on 2nd Story COMPANY D COMPANY C COMPANY B MEZZANINE FLOOR COMPANY A Figure 9. Cross-Sectional View of a Typical Unit 27

28 y z x Figure 10. Perspective View of 3-D Finite Element Model 28

29 5.E-04 3.E-04 DNL DFE Acc. (m/s/s) 1.E-04-1.E E-04-5.E-04 Time (s) Figure 11. Acceleration Response at the Center of Production Floor to Moving Dynamic Load (Aerial Driveway, 40 km/h, Road Class C) 4.E-03 3.E-03 2.E-03 DNL DFE Acc. (m/s/s) 1.E-03 0.E+00-1.E-03-2.E-03-3.E-03-4.E Time (s) Figure 12. Acceleration Response at the Center of Production Floor to Moving Dynamic Load (Front Access Road, 15 km/h, Road Class C) 29

30 3.E-03 2.E-03 DNL DFE Acc. (m/s/s) 1.E-03 0.E+00-1.E-03-2.E-03-3.E Time (s) Figure 13. Acceleration Response at the Center of Production Floor to Moving Dynamic Load (Side Access Road, 15 km/h, Road Class C) 2.E-02 1.E-02 FEM DNL DFE Acc. (m/s/s) 0.E+00-1.E-02-2.E time (s) Figure 14. Acceleration Response at the Center of Production Floor to Moving Dynamic Load (Rear Access Road, 15 km/h, Road Class C) 30

31 1.E-02 road class C 5.E-03 Acc. (m/s/s) 0.E+00-5.E-03-1.E Time (s) Figure 15. Acceleration Response of Multi-Vehicle Traveling with DFE Method 31

32 Figure 16. Vibration Acceptance Criteria (0-Peak Acceleration) for Steppers Figure 17. Vibration Acceptance Criteria (RMS Velocity) for High-Tech Equipment 32