Dynamic Response of the Inertial Platform of the Laser ELI-NP Magurele-Bucharest Facility

Abstract

Previous studies on the vibrational behavior of the inertial platform installed at ELI-NP, in Magurele-Bucharest have reported eigenfrequencies in the domain in which excitations can occur from earthquakes which manifests itself periodically in this geographical area. The paper aimed to study the vibrational response that may occur, due to human activities or natural phenomena (earthquakes), at the inertial platform of the Laser + Gamma building within the ELI-NP complex. The large mass of the platform, 54,000 tons in full condition, must ensure that the experiments are carried out without being disturbed by unwanted vibrations. The laser and gamma beam must be very precisely positioned and the shocks and vibration from the external environment must be damped or absorbed. To realize this, the behavior of the inertial concrete platform at external excitations was studied based on a model with finite elements. The response to the forced vibrations of the platform and the possible behavior in case of an earthquake were obtained.

1. Introduction

Within the ELI-NP (Extreme Light Infrastructure–Nuclear Physics) project, one of the important elements for the proper functioning of this facility is the inertial platform. It has the role of hosting all the equipment necessary for research and, for normal service of the equipment, extremely sensitive and precise, it must ensure adequate anti-vibration isolation, in front of human (anthropogenic) and natural factors (earthquakes). It will host an advanced 10 MeV Gamma ray source. The mentioned project was financed by the European Commission for a high-intensity laser system (up to 1024 W/cm²). To this is added a high brightness Gamma Beam system. Two main objectives are foreseen in this project: a very high-intensity laser system (10–30 PW) and a very bright γ beam (19 MeV). The project in its entirety is presented in WhiteBook [1] and in Technical Design Reports [2]. This paper aimed to study the behavior of the platform in the presence of the forced vibrations.

The gamma source expected to be installed in the ELI-NP project can ensure the success of major experiments in the field of nuclear resonance fluorescence (NRF) [3,4,5] (Figure 1 and Figure 2). The small size of the beam and the ability to position it very precisely can lead to spectacular results for this type of experience. The extremely precise positioning system cannot achieve its performance if the place where it is installed is not very rigorously isolated in front of the vibrations that come from human activities and from natural phenomena (earthquakes). As a result, designers must pay special attention to the construction of the inertial platform on which the equipment will be positioned. This platform has an extremely high weight which helps to inertial isolate the research equipment. It represents a unique engineering achievement both due to its size but also due to its exceptional insulation performance.

The platform must meet special requirements for the proper operation of the equipment. First, insulation must be provided for the vibrations coming from outside the building to the platform. These are anthropogenic vibrations due to the current activities of humans. To achieve this insulation, spring batteries provided with viscous dampers are used. The large number of such batteries also ensures an approximately uniform distribution of the weight of the platform together with the equipment on the ground. Then the protection of the equipment in case of natural phenomena, i.e., earthquakes, must be ensured. These are rare phenomena, but the damage they can cause can be very serious. It is important to achieve this isolation, if it takes into account the price of the equipment that will be positioned on the platform. Thirdly, the isolation of the equipment in front of the vibrations given by other equipment operating on the platform must be ensured. This can be done relatively easily by carefully designing the fixing systems to the floor of the inertial platform. Research has been carried out to isolate large inertial masses since the last century [5,6]. At present, following the experience gained, the support of large masses is made with metal springs and associated shock absorbers or rubber elements, which have the advantage of providing the necessary damping [7]. Projects of this size are rarely encountered in practice. Taking into account the very high costs of the project and the high performances that must be ensured, a modeling as precise as possible must be used to choose the optimal solution achieved with the lowest costs.

One way to model the inertial platform is to consider a rigid six degrees of freedom. The study of such a system has been carried out in numerous papers, summarized in Ref. [8]. Various methods have been used to address such a problem, for example, genetic sorting algorithms [9]. More sophisticated models of vibration isolation of a rigid elastic suspension are presented by other authors [10]. Active vibration isolation systems were presented in Ref. [11]. The methods are presented for a classic Stewart platform. Such systems are high performance and robust.

The sources of vibration that can act on the platform in a current way are generally due to human activity and are generally complex primarily to the various activities that take place daily. It is mainly due to public or industrial transport activities, activities that take place continuously inside a city. The standard methods for analyzing these vibrations acting on an inertial platform are described in Ref. [12]. An analytical study model of this system and results on the reduction of transmitted vibrations are presented in Ref. [13].

Regarding the natural sources of vibration, it is considered the earthquake, which, for the area where the platform is installed, is a phenomenon that exists at a relatively low level over a period of about 40 years but which then manifests itself dramatically within this periodicity. So, the protection of the equipment that exists on the platform in case of strong earthquakes, occurring periodically historically despite their rarity, must be taken into account. The vibrations generated by an earthquake are characterized by the fact that they are of low frequency. The effect of these natural excitations on an inertial platform was studied in Ref. [14]. The paper also proposed a solution that allows the simultaneous isolation of horizontal and vertical vibrations. A method of reducing the effect of vibration on the platform was presented in Ref. [15], where an innovative vibration reduction system was proposed. For the particular case of nuclear physics, isolation solutions were presented in Refs. [16,17,18,19].

In the paper, based on a finite element model of the massive concrete platform, its eigenvalues and behavior to excitations (that may come from anthropogenic sources or from natural sources/earthquakes) were determined. Following this analysis performed on the structural configuration of the fully equipped platform, useful conclusions can be obtained for the designer.

Usually the study of the dynamic behavior of an inertial platform, supported by springs, is made on a rigid model with six degrees of freedom. In reality, such a platform is made of concrete, has a significant weight and, on the scale of the whole assembly, it also has an elastic deformation. In the paper, a modeling was carried out with the finite element method in order to be able to take into account the elasticity of the platform. It was found that the natural frequencies due to the elasticity of the concrete are of the same order of magnitude as the natural frequencies of the platform considered as rigid, so obviously the elasticity could influence the vibration behavior of the platform and cannot be neglected.

2. Materials and Methods

Within the research facility, a variety of equipment necessary for research activities, precision equipment, which impose specific operating conditions, is used. All this equipment was placed on an inertial platform, of very high mass (equipped with all the equipment the platform can reach 54,000 tons). This inertial platform must provide support for all equipment and also insulate it from shocks and vibrations from surrounding anthropogenic activities. Another event that must be considered is the possibility of an earthquake. This inertial platform is a massive concrete construction [20,21,22,23], placed on a number of approximately 1000 spring-loaded batteries together with viscous shock absorbers. The purpose of the springs is to evenly transmit the weight of the platform on the floor of the assembly and to ensure the anti-vibration insulation. These spring batteries can be placed under load (i.e., activated) or can be taken out of use depending on the loads on the platform and the vibration behavior of the whole assembly. The whole platform is built out of two concrete blocks stiffened between them. On this ensemble are fixed massive concrete blocks that represent the walls of the construction and other massive blocks with the role of roof (Figure 3 and Figure 4). It is obvious that the main role of this platform is to ensure the isolation from the anthropic activities around the facility and the protection against a possible earthquake. Although the platform represents a very large mass, having the rigidity of the concrete used, its elasticity is manifested due to its large drilled dimensions and also large masses that load the platform by their weight. The spring battery system consists of springs and elastic dampers that have known mechanical properties.

Ref. [8] presented the rigid model of the platform suspended on the elastic springs. In the case of the present study, a FEM model [24,25,26,27] of the inertial platform was adopted in order to take into account the deformations due to the elasticity of the concrete. The way in which anthropogenic vibrations will be transmitted from the floor of the building to the inertial platform was analyzed. The platform’s eigenmodes of vibration were calculated to obtain the spectrum of its eigenfrequencies to be monitored during system operation (Figure 5). There is also the problem of the behavior of the platform in case of vibrations caused by an earthquake.

Using the FEM model, it is possible to write the motion equations of the elastic concrete platform supported by the springs [28]:

$$\left[M\right]\left\{\ddot{X}\right\}+\left[C\right]\left\{\dot{X}\right\}+\left[K\right]\left\{X\right\}=\left\{F(t)\right\},$$

(1)

$\left[M\right]$ is the inertial matrix, $\left[C\right]$ the damping matrix, and $\left[K\right]$ the stiffness matrix. The solution vector is $\left\{X\right\}$, containing the generalized displacements as time functions, and $\left\{\dot{X}\right\}$ and $\left\{\ddot{X}\right\}$ are the generalized velocities and accelerations.

The equation of the free undamped vibration is:

$$\left[M\right]\left\{\ddot{X}\right\}+\left[K\right]\left\{X\right\}=0.$$

(2)

and offers the eigenfrequencies of the system using the equation:

$$\det \left(\left[K\right]-{\omega }^2\left[M\right]\right)=0.$$

(3)

For the platform, the first eigenvalues are presented in

Table 1. The eigenvalues of the elastic suspended platform.

No. of Mode	Frequency (Hz)	No. of Mode	Frequency (Hz)
1	1.655	16	4.162
2	1.692	17	4.215
3	1.781	18	4.582
4	2.856	19	4.857
5	3.045	20	4.987
6	3.258	21	5.121
7	3.381	22	5.245
8	3.403	23	5.443
9	3.412	24	5.614
10	3.458	25	5.773
11	3.603	26	6.051
12	3.668	27	6.312
13	3.699	28	6.372
14	3.933	29	6.517
15	4.067	30	6.805

and eigenmodes in

Table 2. The first 12 eigenmodes.

Mode 1	Mode 2	Mode 3
Mode 4	Mode 5	Mode 6
Mode 7	Mode 8	Mode 9
Mode 10	Mode 11	Mode 12

.

The matrix:

$$\left[\Phi \right]=\left[\begin{array}{cccc}{\Phi }_1& {\Phi }_2& \dots & {\Phi }_n\end{array}\right].$$

(4)

represents the modal matrix.

The canonical form of the motion equations are:

$$\left[M_r\right]\left\{\ddot{q}\right\}+\left[C_r\right]\left\{\dot{q}\right\}+\left[K_r\right]\left\{q\right\}=\left\{F_r(t)\right\}.$$

(5)

where the inertia matrix $\left[M_r\right]$ and the stiffness matrix $\left[K_r\right]$ are diagonal matrices with the diagonal elements:

$$M_{ii}={\left[{\Phi }_i\right]}^T\left[M\right]\left[{\Phi }_i\right];K_{ii}={\left[{\Phi }_i\right]}^T\left[K\right]\left[{\Phi }_i\right];i=\overline{1,n}.$$

(6)

For the usual engineering applications, the damping matrix can be considered proportional to the system mass and/or stiffness matrix:

$$\left[C\right]=\alpha \left[M\right]+\beta \left[K\right].$$

(7)

In the conditions of Equation (7), we obtain the diagonal damping matrix:

$$\left[C_r\right]={\left[\Phi \right]}^T\left[C\right]\left[\Phi \right]=\alpha {\left[\Phi \right]}^T\left[M\right]\left[\Phi \right]+\beta {\left[\Phi \right]}^T\left[K\right]\left[\Phi \right]=\alpha \left[M_r\right]+\beta \left[K_r\right].$$

(8)

The Equation (5) can be written under the form:

$$M_i{q}_i+C_i{q}_i+K_i{q}_i=f_i,i=\overline{1,n}.$$

(9)

Dividing by $M_i$ it results in:

$${\ddot{q}}_i+2\varsigma {\dot{q}}_i+{\omega }_i^2{q}_i=f_i,i=\overline{1,n}.$$

(10)

where:

$${\varsigma }_i=\frac{C_i}{2\sqrt{M_i{K}_i}},i=\overline{1,n}.$$

(11)

represents the modal damping ratio and:

$${\omega }_i^2=\sqrt{\frac{K_i}{M_i}},i=\overline{1,n}.$$

(12)

the undamped natural frequency. Equation (10) was used in the Finite Element Model to obtain the dynamic response of the structure.

The FE model was created using Hypermesh as preprocessing software, running analysis with OPTISTRUCT, and post processing with Hyperview. The total number of FE entities used: total nodes = 88,988, total elements: 88,823. The type of elements used for discretization structure was SHELL with 4 corner nodes, and any node has 6 DOF (three translations and three rotations).

3. Results

The eigenfrequencies and eigenmodes of the platform are presented in Table 1 and Table 2. Only the first 12 eigenvalues are presented.

$$\left(\left[K\right]-{\omega }^2\left[M\right]\right)\left\{U\right\}=0.$$

(13)

In the following it is studied how a harmonic excitation with unit amplitude applied to the ground will influence the transmission of the vibration to some important points of the platform [29,30,31]. For the studied platform the modal damping factors are presented in Appendix A. These points were chosen on the basis of the platform and are presented in Figure 6. It excites all the points on the base of the platform with a harmonic oscillation, with the same phase of amplitude that can be considered unitary. At such an excitation that could come, for example, from an earthquake, the magnitude of the amplitude of the harmonic oscillation of the different points of the platform is followed [32,33]. This study was carried out in a range starting from zero and going up to 7 Hz, by varying the excitation frequency, at each step, by 0.1 Hz and graphically representing the amplitude of the oscillation at the chosen points. A graph of transmissibility was thus obtained, depending on the excitation frequency of the platform (Figure 7 and Figure 8). The study was conducted at low frequencies, firstly due to the fact that the excitation frequencies in case of an earthquake are low frequencies, as it is possible to see in the analysis of the acceleration spectrum recorded in case of an earthquake and, secondly, due to the fact that at higher frequencies, it was found that the transmissibility of the system decreased.

Figure 9 shows the transmissibility graphs determined at some of the points indicated in Figure 6 in the case of applying a harmonic excitation according to the OX direction. Transmissibility is defined as the ratio between the amplitude of the harmonic oscillation transmitted at the considered points and the amplitude of the harmonic excitation of the base on which the platform rests. It is observed that this transmissibility was manifested similarly for all points considered on the platform. For excitation after the OX direction, it is maximum around the fundamental oscillation frequency. With the maximum being around this frequency, the interest of designers should be focused around this frequency. Figure 10 shows the fundamental eigenmode and next to it, the displacement response of the system in case of applying a harmonic excitation, along the OX axis, with a frequency equal to the fundamental natural frequency.

The same conclusions can be drawn in the case of applying a harmonic excitation along the OY axis. Figure 11 shows the transmissibility graphs. Similarly as in the case of the study of motion in the OX direction, for excitation in the OY direction the maximum is around the fundamental eigenfrequency. Figure 12 shows the fundamental eigenmode and next to it, the displacement response of the system in case of applying a harmonic excitation, along the OY axis, with a frequency equal to the fundamental frequency.

At an excitation of the base in the Y (horizontal) direction with unit amplitude, it can be seen that the maximum amplitude of approx. 1.2 mm was obtained in the set of boards near the low-frequency modes—mode 1 (1.66 Hz), mode 2 (1.69 Hz), and mode 3 (1.781 Hz).

In the following, the behavior of the ceilings at unitary excitations of the ground in vertical direction is studied. This needs to be done because the ceilings are made of concrete blocks, 0.6 m thick, but unlike the base platform, which is placed on about 1000 resource batteries that standardize the loading on the base, the ceilings have a large opening, over ten meters, without being supported on these very large openings. In addition, the thickness of the concrete layer at the ceilings is less than the thickness of the main, base plate, which is about 1.6 m. It is expected, therefore, that the surface of the ceiling will suffer large displacements, at a unitary excitation of the base, obviously much larger displacements than the points of the base platform. Two points were chosen (Figure 13), which are supposed to be the maximum displacement points for the ceiling. The centers of the ceilings of two rooms were chosen and their displacements were followed when the base was excited with a harmonic unitary excitation, in the frequency range from 0 to 7 Hz. The transmissibility of vibration in this case is represented in Figure 14. The coordinates of point 1 are (30.23 m; 73.73 m) and of the point 2 are (86.01 m; 73.63 m). The transmissibility in this case is defined as the ratio between the amplitude of the vibration in points 1 and 2 and the amplitude of the harmonic vibration of the base. Figure 14 shows that at both points the transmissibility was very high. In the center of the ceiling with a larger opening (point 1) it is normal to have a higher transmissibility than in the center of the ceiling of room 2. In both cases, the transmissibility was very high, which indicates that in the event of an earthquake the ceilings are the most threatened elements of destruction. Additional supports to support these ceilings could significantly reduce this transmissibility and risk.

To extract data from frequency response analysis, a frequency increment of 0.05 Hz was considered in order to determine with more accuracy the output data (transmissibility—report between displacement output data and displacement input data on a direction axis considered). The frequency range domain considered for interpretation output results is 0–7 Hz.

The field of displacements around points 1 and 2, in the case of an excitation with a frequency equal to the fundamental frequency is shown in Figure 15.

Figure 16 and Figure 17 show the transmissibility to an excitation in the horizontal plane, along the OX axis and, respectively, the OY axis. In both cases, the transmissibility values were relatively similar.

Let us further analyze what can happen if the platform is subjected to an excitation with an evolution of the accelerations shown in Figure 18. This distribution of accelerations was obtained experimentally, following the earthquake of 4 March 1977 (Figure 18). An FFT analysis obtained the acceleration graph versus frequency (Figure 19).

Figure 20 and Figure 21 present the model of the platform subjected to excitations similar to 4 March 1977 earthquake, and the displacement of the platform. In the time (Figure 22) between 15.2 and 15.85 s, the platform was thrown from −12.5 mm to +11.5 mm. During this time, it is observed that the biggest shock of the earthquake occurred in the vertical direction.

4. Discussion and Conclusions

For the analysis of the dynamic response of the inertial concrete platform, an FEM model was considered in which the effect of the elasticity of the concrete platform was studied. The previous studies, stated in the first part of the paper, in which a rigid model of the platform suspended on elastic springs, with six degrees of freedom, were considered, were thus improved. The effort required is obviously much increased but is justified by the results obtained. The elasticity of the concrete platform cannot be neglected, the eigenfrequencies due to the elasticity being in the same range as the eigenfrequencies computed for the rigid body model.

The platform, placed on a number of about 1000 spring batteries, provided with shock absorbers, proved to be able to ensure a satisfactory insulation in case of anthropogenic activities. Some problems can be reported regarding the very high transmissibility of the ceilings, which requires the attention of the designers in the analysis of these constructive elements to decrease the opening of these ceilings.

The transmission of vibrations from one piece of equipment to another is well studied and can be easily carried out in the design stage. In the event of earthquakes, however, equipment safety issues may arise. Thus, it was found that the transmissibility of vibrations to the platform was of the same order of magnitude for the three directions of movement of the platform. As such, it is possible for the platform to reach the side walls, which are located at a distance of 150 mm from the platform, in the initial position.

An in-depth study of the behavior of the huge platform in the event of an earthquake, the vibration damping measures that can be taken in this case, and the analysis of the safety of each piece of equipment are necessary to conduct in the future. The analysis showed that there were a large number of natural frequencies below 5 Hz. This is a negative aspect of the earthquake’s behavior. Based on the analysis it can be considered that anthropogenic activities will not significantly influence the behavior of the system, if the frequencies generated by these activities are analyzed. However, in case of a catastrophic event (earthquake), the movement of the platform can be amplified, which can lead to the destruction of the system. The ELI-NP project has a decoupling system in case of earthquakes but it is necessary to study an additional system for isolating the entire mass.