1 Introduction

As a carrier of cultural heritage, museums play an important role in cultural inheritance, education and popularization, social guidance and international exchange, such as the Capital Museum shown in Fig. 1. At the same time, cultural relics are an important symbol of our culture and one of the rich and diverse cultural heritages in the world, such as the Golden Winged Bird of a cultural relic in the collection of Yunnan Provincial Museum shown in Fig. 2. However, China is an earthquake-prone country, located in the Eurasian seismic zone and the Pacific seismic zone between the two major seismic zones, many collections of cultural relics were damaged or completely destroyed by the effects of the earthquake. For example, the 8.0-magnitude earthquake that occurred in Wenchuan, Sichuan Province in 2008, the 7.1-magnitude earthquake that occurred in Yushu County, Qinghai Province in 2010, and the 7.0-magnitude earthquake that occurred in Lushan County, Ya'an, Sichuan Province in 2013, all caused different degrees of damages to a large number of cultural relics and cultural relics protection units [1, 2].

Fig. 1
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Capital Museum

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Fig. 2
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Collection of cultural relics

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Since earthquakes cause large economic and cultural losses, and it is difficult to recover after a disaster, strengthening the protection and research of cultural relics is an important prerequisite for good earthquake prevention and mitigation work. The ‘‘Specification for Seismic Protection of Museum Collection’’ (WW/T0069-2015) stipulates that the seismic design of museum cultural relics should have multiple lines of defense. The seismic protection of museum cultural relics includes the seismic protection of museum structures, the seismic protection of cultural relics showcases and the seismic protection of cultural relics themselves, among which the research on the seismic protection of museum structures, as well as the research on showcases, which is an important link in the transmission of seismic waves from structures of museums to the middle of cultural relics, need to attract sufficient attention [3]. In recent years, people's awareness of cultural relics protection has been increasing, and at the same time, with the rapid development of shock absorption technology and seismic isolation technology, research scholars at home and abroad have carried out a large number of studies on the seismic protection of museum structures and cultural relics showcases.

For the research on seismic protection of museum structures, the new Shantou Museum [4] adopted 137 laminated rubber pads placed at the bottom of the beams on the 2nd floor, and the seismic response of the isolated structure can be reduced to 1/10–1/4 of the base fixed structure in strong earthquakes. Shanxi Museum [5] of 2nd-4th floors of the main museum were set with 92 ZN-400 liquid viscous dampers, which effectively consumed the seismic energy transferred to the structure. The new Yunnan Provincial Museum [6] adopted base isolation, and 166 rubber isolation bearings were installed in the seismic isolation layer. Xu Yuxiang, Liu Yang and Liao Shujiang et al. [7,8,9,10] conducted seismic shaking table tests on a 1/30 scale model of the non-isolated and isolated structures of the new Yunnan Provincial Museum to compare and analyze the superstructure response. Yan Xingxiang and Wang Ya et al. [11,12,13] established three-dimensional finite element models of the base isolated and base fixed structures of the new Yunnan Provincial Museum to comparatively analyze the floor response spectra at different intensities. The new Chengdu Museum [14] adopted more than 300 stacked rubber isolation bearings at the bottom of the structure. Ge Jiaqi et al. [15] studied the design indexes of tensile performance of rubber seismic isolation bearing, through vertical tensile test and shear tensile test of rubber seismic isolation bearing, in conjunction with the project of the new Chengdu Museum. Liu Xingang et al. [16] established finite element models of non-isolated and isolated structures of the Chengdu Museum, compared and analyzed the vibration patterns and torsion effects of the two model structural systems. Japan's POLA Museum of Art [17] adopted the laminated natural rubber seismic isolation bearings as seismic isolation elements in the design, while the frequency-modulated mass dampers and viscous dampers with a track were installed in the main parts of the building, to ensure the safety of people’s lives and art collections that under the action of strong earthquakes.

For the research on seismic protection of cultural relics showcases, Shen Ping [18] established finite element models of the simplified viscous fluid damping showcase, tuned mass damping showcase and rubber isolation bearing showcase, and calculated the seismic reduction rate of the three showcase models. Liu Tong and Wen Zhu et al. [19, 20] proposed a sliding friction pendulum isolation device for cultural relics and conducted shaking table tests. Zhou Qian et al. [21] proposed a rolling-type horizontal isolation device for cultural relics showcases, and conducted comparative tests on the isolated and non-isolated showcase models through a shaking table to study the shock absorption effect of floating cultural relics in the collection. Zou Xiaoguang et al. [22] produced a scaled-down model of an actual showcase and proposed a sliding seismic isolation support for cultural relics, forming a sliding cultural relics isolation support showcase system. Song Ruiqing et al. [23] proposed a vertical variable stiffness isolation bearing for cultural relics consisting of a vertical spring group and a four-link mechanism and analyzed the effects of the initial angle of the link, spring stiffness, and spring preload length on the bearing force and stiffness through theoretical derivation. Wu Shicheng et al. [24, 25] proposed a three-way arched rubber isolation bearing for cultural relics and derived the fitting formula for the vertical compression stiffness of the bearing. Ji Jinbao et al. [26] proposed a linear guide-type horizontal isolation device for cultural relics showcases with a damping rate of more than 60%. Zhang Yi et al. [27] proposed a modular metal seismic isolation support for cultural relics showcases, while the slip and overturning calculations of cultural relics were carried out. Calio et al. [28] proposed a base isolation device for the protection of statues and vessels. Berto et al. [29] proposed a friction pendulum isolation device to isolate the small floating objects, and the tests were conducted with unidirectional and bi-directional seismic input respectively, which the importance of conducting experimental tests with 2D seismic input or 3D seismic input was confirmed. Sorace et al. [30] proposed a biconcave curved slider isolation device with a significant seismic isolation effect. Ceravolo et al. [31] investigated the strategy to control the sway response of art objects and structures based on rigid body dynamics and proposed a semi-active control measure.

For the double shockproof of museum structures and cultural relics showcases, Nie Yansen [32] input the floor wave time-history of the non-isolated and isolated structures of a museum into the finite element model of a showcase equipped with sliding isolation bearings, analyzed the optimal bearing spring stiffness, and proposed variable stiffness isolation bearings. Wang Ya et al. [33] extracted the acceleration time-history response curves at the building elevation of the non-isolated and isolated structure of a museum in Sichuan, and acted on two new slide-type isolation bearing models of cultural relics with fixed stiffness and variable stiffness to analyze the displacement and acceleration response at the showcase countertop, and deduced the design methods of the two types of bearings. Kong Derui et al. [34] analyzed the performance of a 4-story reinforced concrete frame museum of the basic fixed structure and base isolated structure, and at the same time carried out shaking table tests on the showcase with rubber and sliding sleeve combination isolation bearings and non-isolated cultural relics showcase to study their seismic isolation performance.

In summary, most of the existing museums have only taken seismic isolation measures for museum structures, or only taken seismic isolation measures for cultural relics showcases, and there are relatively few researches on double shockproof for museum structures and cultural relics showcases. The innovation of this paper lies in the seismic isolation devices or energy dissipation and damping devices are simultaneously installed in certain specific locations of the museum structure and cultural relics showcases, to extend the natural periods of the structure or consume the seismic energy input to the structure, reduce the seismic response of the structure, to achieve the purpose of disaster prevention and mitigation, and to ensure the safety of human life and precious cultural relics.

Therefore, in this paper the double shockproof of the museum structure and the cultural relics showcase in the museum are studied, the base fixed structure, base isolated structure and viscous fluid damper structure models of the museum are established respectively with the finite element software SAP2000, and the modal analysis and time-history analysis are carried out to study the response of the superstructure of the three models. At the same time, the finite element models of the fixed cultural relics showcase, isolated cultural relics showcase and viscous fluid damper cultural relics showcase are established, and seismic waves and the floor waves of museum structures are input to study the displacement and acceleration response of the countertop of the cultural relics showcase for comparative analysis. To find seismic design ideas which suitable for museum structures and cultural relics showcases, and to provide feasible solutions and references for seismic design of cultural relics in museums.

2 Establishment of museum model

2.1 Model overview

A museum is a 5-story reinforced concrete frame structure, with a width of 30 m along the X direction and 30 m along the Y direction, and the heights of the floors are all 3.6 m. According to the ‘‘Code for Seismic Design of Buildings’’ (GB50011-2010) [35], the seismic fortification intensity level is 8 degrees, the design base seismic acceleration is 0.2 g, the design seismic grouping is the second group, the site category is Class II, the characteristic period of the site is 0.4 s, and the coefficient of seismic effects under fortified earthquakes is \(\alpha_{\max } = 0.45\). The size of the frame column is 600 × 600 mm, the size of the frame beam is 600 × 300 mm, the thickness of the slab is 240 mm, the strength class of the concrete beam is C40, and the strength class of the concrete column is C40. According to the ‘‘Code for Design of Concrete Structures’’ (GB50010-2010) [36], the longitudinal stress reinforcement adopts HRB400, the hoop reinforcement adopts HRB335, the thickness of the protective layer of the concrete of the beam is 60 mm, and the thickness of the protective layer of the concrete of the column is 40 mm. In addition to the self-weight of the structure, the constant load includes the floor surface load of 3 kN/m2 and the line load of the outer ring beam of 10 kN/m2, and the live load is the floor surface load of 2 kN/m2. The layout plan of the standard floor of the structure is shown in Fig. 3, and the three-dimensional model of the structure is shown in Fig. 4.

Fig. 3
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Layout plan of the standard floor of the structure

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Fig. 4
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Three-dimensional model of the structure

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The finite element models of the base fixed structure, base isolated structure and viscous fluid damper structure of the museum are established by the software SAP2000, where the frames are modeled with line units and the floor slabs are modeled with surface units.

2.2 Selection of base isolation bearings

Seismic isolation bearings are installed in the base fixed structure of the museum, and the seismic isolation bearings are arranged according to the total horizontal yield force, which is 2% of the base vertical reaction force under the standard value of gravity load. Corner columns, center columns, and side columns all use lead-core rubber seismic isolation bearings LRB500, with a total of 49 bearings, the bearing parameters are shown in Table 1, the 3D view of lead-core rubber bearing is shown in Fig. 5 and the arrangement of bearings is shown in Fig. 6. The Rubber Isolator connecting units in SAP2000 are used to simulate isolation bearings, the direction U1 of the connection unit is set as a linear attribute, U2 and U3 are set as nonlinear attributes. Where the directions U1, U2 and U3 of the seismic isolation bearing correspond to the Z, X and Y directions of the structure respectively.

Table 1 Parameters of lead-core rubber bearings
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Fig. 5
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3D view of lead-core rubber bearing

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Fig. 6
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Arrangement of lead-core rubber bearings

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2.3 Arrangement of viscous fluid dampers

The viscous fluid dampers with the same parameters and numbers are arranged at each layer in the base fixed structure of the museum to form a viscous fluid damper structure[37]. The parameters of viscous fluid dampers are shown in Table 2, the 3D view of viscous fluid damper is shown in Fig. 7 and the layout is shown in Fig. 8. The Damper-Exponential connecting units in SAP2000 are used to simulate viscous fluid dampers. As a result, the models of the base fixed structure, base isolated structure and viscous fluid damper structure of the museum can be obtained, as shown in Fig. 9.

Table 2 Parameters of viscous fluid dampers
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Fig. 7
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3D view of viscous fluid damper

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Fig. 8
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Layout of viscous fluid dampers

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Fig. 9
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SAP2000 model of the museum

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2.4 Modal analysis

Modal analysis is performed with SAP2000 for the models of the museum of the basic fixed structure, base isolated structure and viscous fluid damper structure. In order to verify the accuracy of the SAP2000 finite element model, PKPM was also used to conduct the modal analysis of three models, and the natural periods of the first six orders of each structure calculated by the two software were compared, as shown in Table 3. As can be seen from Table 3, the difference in the natural periods of the first six orders of the three models in PKPM and SAP2000 is within -4%, which indicates that the finite element model established by SAP2000 is accurate and can well respond to the self-vibration characteristics of the structure.

Table 3 Comparison of natural periods between PKPM and SAP2000 models
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In SAP2000, it can be known that the 1st order vibration mode of the three structures is Y-direction translation, the 2nd order vibration mode is X-direction translation, the 3rd order vibration mode is Z-direction torsion, and the mass participation factors of museum structures are shown in Table 4. It is analyzed that the fundamental periods of the base fixed structure and base isolated structure are 0.583246 s and 1.913014 s respectively, the fundamental period of the base isolated structure is 3.3 times of the base fixed structure, and compared with the base fixed structure, the natural periods of the first three orders of the base isolated structure are significantly increased. Therefore, setting the seismic isolation bearing can effectively prolong the fundamental period of the structure, avoiding the general excellence period of the building site, realizing the purpose of seismic isolation, and reducing the damage of the structure under seismic action. The fundamental period of the viscous fluid damper structure is 0.583246 s, which is unchanged compared with the base fixed structure, this is because the viscous fluid damper only increases the damping of the structure, does not increase the structural stiffness, and does not significantly change the structure's natural period [38].

Table 4 Mass participation factors of museum structures
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2.5 Selection of seismic waves

According to the ‘‘Code for Seismic Design of Buildings’’ (GB50011-2010), the selection of actual strong earthquake records and artificially simulated acceleration time-history curves should be chosen under the type of the building site and design seismic grouping, in which the number of actual strong earthquake records should not be less than 2/3 of the total number of records. In this paper, seven seismic waves are chosen which are five natural waves and two artificial waves, earthquakes are analyzed using elastic–plastic time-history analysis by considering an earthquake of 8 degrees of fortification, and the maximum acceleration peak is tuned to 200 cm/s2, seismic waves of the main direction are input along the X-direction. The five natural waves are selected from the Pacific Earthquake Engineering Research Center, which are RSN9, RSN17, RSN40, RSN54 and RSN122, and the information on natural seismic waves is shown in Table 5. The artificial waves RG1 and RG2 are generated according to the standard response spectrum using the software GM Tool, the calculation of seven seismic waves information is shown in Table 6, and the comparison between the acceleration time-history curves response spectrum and standard response spectrum is shown in Fig. 10.

Table 5 Information of natural seismic waves
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Table 6 Calculation for seismic wave information
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Fig. 10
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Comparison of acceleration reaction spectra

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According to the code, the bottom shear of the structure calculated for each time-history should not be less than 65% of the results of the vibration mode decomposition reaction spectrum calculation, and the average of the bottom shear of the structure calculated for multiple time courses should not be less than 80% of the results of the vibration mode decomposition reaction spectrum calculation [39]. The results of the verified seismic waves are shown in Table 7, and it can be seen that all seven seismic waves satisfy the code requirements.

Table 7 Results of verified seismic waves
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3 Seismic response analysis of the museum

3.1 Comparative analysis of inter-story shear force

Inter-story shear force refers to the shear force generated by the difference in displacement between floors when the building is subjected to lateral forces. By calculating the inter-story shear force, the bearing capacity of the structure can be determined to ensure that the building will not collapse when subjected to lateral forces. At the same time, it helps to detect potential structural problems in time and to determine whether the building meets safety standards.

The inter-story shear forces of the base fixed structure, base isolated structure and viscous fluid damper structure of the museum under the action of seven seismic waves respectively, are shown in Fig. 11. From the figure, it can be seen that the inter-story shear forces of the base fixed structure are much larger than that of the base isolated structure and viscous fluid damper structure, which indicates that the base fixed structure itself does not have strong seismic performance. The magnitude of the reduction of the inter-story shear force is also different under different seismic wave actions. The average values of inter-story shear force reductions in floors 1–5 under the action of seismic waves RSN9, RSN17, RSN40, RSN54, RSN122, RG1, and RG2 are 69.72%, 72.69%, 68.96%, 63.87%, 70.13%, 71.59%, and 71.59% for the base isolated structure respectively. The average values of inter-story shear force reductions in floors 1–5 under the action of seismic waves RSN9, RSN17, RSN40, RSN54, RSN122, RG1, and RG2 are 81.97%, 85.29%, 80.50%, 86.52%, 79.04%, 87.92% and 87.74% for the viscous fluid damper structure respectively. The data show that the base isolated structure and viscous fluid damper structure can effectively reduce the inter-story shear force, thus improving the safety and reliability of the structure, and the viscous fluid damper structure has a better effect.

Fig. 11
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Inter-story shear force of each structure under seismic wave action in the X-direction

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3.2 Comparative analysis of inter-story drift

The inter-story drifts of the base fixed structure, base isolated structure, and viscous fluid damper structure of the museum under the action of seven seismic waves respectively, are shown in Fig. 12. It can be seen that relative to the base fixed structure, the inter-story drifts of the base isolated structure and viscous fluid damper structure are significantly reduced, but the inter-story drifts of the bottom layer of the base isolated structure are relatively larger, which is because the seismic isolation layer has absorbed a large amount of ground vibration energy, and the deformation of the structural system is more concentrated in the seismic isolation layer, which reduces the influence of the superstructure by seismic action.

Fig. 12
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Inter-story drift of each structure under seismic wave action in the X-direction

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The reduction in the drift of inter-story is more significant as the floor height increases. Compared with the base fixed structure, the inter-story drifts of the top floor of the base isolated structure are reduced by 68.65%, 70.28%, 67.82%, 63.41%, 63.38%, 70.77% and 71.51% under seismic waves RSN9, RSN17, RSN40, RSN54, RSN122, RG1, and RG2 respectively. The inter-story drifts of the top floor of the viscous fluid damper structure are reduced by 94.57%, 94.89%, 96.02%, 95.11%, 95.03%, 94.83%, and 95.58% under seismic waves RSN9, RSN17, RSN40, RSN54, RSN122, RG1 and RG2 respectively. According to Fig. 12 and the data, the viscous fluid damper structure is more effective in controlling the inter-story displacement.

3.3 Comparative analysis of floor acceleration response

The floor acceleration response of the base fixed structure, base isolated structure and viscous fluid damper structure of the museum under the action of seven seismic waves are shown in Fig. 13. It can be seen that the acceleration response of the base fixed structure is drastic, and the reduction of the floor acceleration response of the base isolation structure and viscous fluid damper structure is more considerable compared with that of the base fixed structure. The acceleration response of the bottom floor of the base isolated structure is relatively large and then decreases, that is because the isolation layer can dissipate the seismic energy transmitted to the building.

Fig. 13
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Acceleration response of each structural floor under seismic wave action in the X-direction

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Meanwhile, it can be seen from Fig. 13 that the maximum values of the floor acceleration response of the three structures under the action of different seismic waves generally appear on the 5th floor. The 5-story acceleration response of the base isolated structure under seismic waves RSN9, RSN17, RSN40, RSN54, RSN122, RG1 and RG2 is 60.38%, 40.58%, 45.09%, 47.90%, 58.62%, 56.76% and 51.03% of the base fixed structure respectively. The 5-story acceleration response of the viscous fluid damper structure under seismic waves RSN9, RSN17, RSN40, RSN54, RSN122, RG1 and RG2, is 46.12%, 31.36%, 42.59%, 34.46%, 46.32%, 62.63% and 49.37% of the base fixed structure respectively. The data indicate that the viscous fluid damper structure can better reduce the structure's vibration of itself.

In summary, the installation of seismic isolation bearings and viscous fluid dampers in the structure can reduce the inter-story shear force, inter-story displacement and floor acceleration response of structures, to realize the seismic isolation and shock absorption, of which the viscous fluid dampers have a more significant absorption effect of the seismic.

4 Establishment of cultural relics showcase model

4.1 Model overview

This paper is based on the four-sided freestanding cultural relics showcase commonly used in museums, SAP2000 finite element software is used to carry out simplified modeling, the stiffness and self-weight of the upper glass and lower steel plate of the showcase are distributed to the load-bearing beam and column members, the frames are adopted as line units, and the panels are adopted as surface units.

The material of cultural relics showcase is made of steel Q235, the modulus of elasticity is 206 kN/mm2, the Poisson's ratio is 0.3, the length, width and height of the showcase are 700 mm, 700 mm and 1500 mm, the thickness of the top surface and countertop panel is 1 cm, the beam and column members are made of solid square steel with the length and width of 4 cm, the quality of the showcase is 222.626 kg, and the showcase of the cultural relics exhibits studied in this paper has a lighter mass and does not consider the effect of the quality of cultural relics. The constant load of the showcase includes a face load of 1500 kg/m2 and a line load of 500 kg/m2, and the live load is a face load of 500 kg/m2.

SAP2000 finite element software is used to establish the models of the fixed cultural relics showcase, isolated cultural relics showcase and viscous fluid damper cultural relics showcase respectively. After modal analysis, the first three orders of natural periods of the fixed cultural relics showcase are 0.0642 s, 0.0642 s and 0.057725 s.

4.2 Design of seismic isolation parameters

According to the characteristics of the cultural relics showcase, lead-core rubber seismic isolation bearings are installed at the bottom of the four columns of the fixed cultural relics showcase, with the height of the bearings of 60 mm, the Rubber Isolator connecting units in SAP2000 are used to simulate seismic isolation bearings, and only the effect of the horizontal stiffness of the isolation bearings is considered. The total horizontal stiffness of the isolated system is determined by estimating the design circular frequency of the isolated system for the cultural relics showcase and assigning them to each seismic isolation bearing. The design circular frequency of the isolated system and the total horizontal stiffness of the seismic isolation device are calculated according to Eqs. (1) and (2) respectively [40, 41]:

$$\omega_{n} = 2\pi /T$$
(1)
$$K = \omega_{n}^{2} M$$
(2)

where \(K\) is the total horizontal stiffness of the seismic isolation device (N/m); \(\omega_{n}\) is the design circular frequency of the isolated system; \(M\) is the mass of the cultural relics showcase.

Considering the seismic isolation effect when the fundamental natural period of the isolated cultural relics showcase is 2.5 s, the horizontal stiffness of the corresponding seismic isolation device should be less than:

$$K < \omega_{n}^{2} M = 1406.23$$
(3)

Based on the form of a four-sided freestanding cultural relics showcase, four seismic isolation bearings are installed at the bottom of four columns, and the horizontal stiffness of each bearing should be less than:

$$K_{1} < K/4 = 1406.23/4 = 351.56\,\,\left( {{N \mathord{\left/ {\vphantom {N m}} \right. \kern-0pt} m}} \right)$$
(4)

The seismic isolation bearings are machined according to this parameter, and the horizontal stiffness of each bearing is taken as 350 N/m.

4.3 Arrangement of fluid viscous dampers

Two viscous fluid dampers are set in the fixed cultural relics showcase to form a viscous fluid damper cultural relics showcase. The Damper-Exponential connecting units in SAP2000 are used to simulate the viscous fluid dampers, with a damping coefficient of 10 \({\text{kN}} \cdot {\text{m/s}}\) and a damping index of 0.2[18, 37]. In summary, the actual model of the four-sided freestanding cultural relics showcase, as well as the finite element models of the fixed cultural relics showcase, isolated cultural relics showcase and viscous fluid damper cultural relics showcase are shown in Fig. 14.

Fig. 14
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Models of cultural relics showcases

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5 Seismic response analysis of cultural relics showcase

5.1 Extraction of floor waves

The cultural relics showcases are placed on the 4th floor of the museum, since the models adopt the rigid floor slab assumption without considering the effect of floor elasticity, the acceleration time-history curves at the building elevation of 10.8 m are extracted as the floor waves, and the floor waves of the three museum structures under the action of seven seismic waves respectively are shown in Fig. 15

Fig. 15
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Acceleration time-history curves at 10.8 m elevation of each structural building under seismic wave action in the X-direction

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Considering three kinds of cultural relics showcases are placed in three kinds of museum structures, seismic waves, and the floor waves of the three kinds of museum structures are input into the fixed cultural relics showcase, isolated cultural relics showcase and viscous fluid damper cultural relics showcase along the X-direction respectively, to carry out the seismic response analysis, and to study the acceleration and displacement response of the countertop of three kinds of cultural relics showcases.

5.2 Indicators for evaluation of shock absorption and seismic isolation

According to the shock absorption and seismic isolation effect of the shock absorption system and seismic isolation system of cultural relics showcases, the indicators for the evaluation of shock absorption and seismic isolation for cultural relics showcases are proposed.

For the viscous fluid damper cultural relics showcase, the shock absorption rate is calculated according to Eq. (5), and for the isolated cultural relics showcase, the seismic isolation rate is calculated according to Eq. (6):

$${\text{Shock absorption rate }} = \frac{{A_{1} - A_{2} }}{{A_{1} }}$$
(5)
$${\text{Seismic isolation rate }} = \frac{{A - A_{3} }}{A}$$
(6)

In the formula, \(A\) is the peak horizontal seismic acceleration at the placement of the cultural relics showcase (m/s2); \(A_{1}\) is the peak horizontal seismic acceleration of the countertop of the fixed cultural relics showcase (m/s2);\(A_{2}\) is the peak horizontal seismic acceleration of the countertop of the viscous fluid damper cultural relics showcase (m/s2); \(A_{3}\) is the peak horizontal seismic acceleration of the countertop of the isolated cultural relics showcase (m/s2).

5.3 Analysis of seismic isolation effect of isolated cultural relics showcase

The isolated cultural relics showcase is subjected to seismic waves and three kinds of museum structures' floor waves respectively, the peak absolute acceleration of the showcase countertop, isolation effect, and horizontal displacement of the isolation bearing are shown in Table 8. From the table, it can be seen that the acceleration amplitude difference between the floor waves and seismic waves is large, so the seismic waves are input to the cultural relics showcase directly for time-history analysis is unreasonable, and the floor waves should be used as the input excitation, so the results under the action of seismic waves are not used as a reference.

Table 8 Peak acceleration of showcase countertop, isolation effect and isolation bearing displacements under seismic and floor waves in the X-direction
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From the data in Table 8, it can be seen that under the action of floor waves of the base fixed structure, base isolated structure and viscous fluid damper structure of the museum, isolated cultural relics showcase can all reduce the acceleration of showcase countertop to a certain extent, the seismic isolation effect of floor waves under the action of different seismic waves is different, and the average seismic isolation rate is 39.39%, 54.82% and 77.41% respectively. Compared with the base fixed structure of the museum, under the action of floor waves of the base isolated structure and the viscous fluid damper structure of the museum, the isolated cultural relics showcase reduces the acceleration of the showcase countertop while the displacement of the seismic isolation bearing is also effectively controlled. However, the isolated cultural relics showcase is set up in the viscous fluid damper structure of the museum with the best seismic isolation effect.

5.4 Analysis of seismic isolation effect of viscous fluid damper cultural relics showcase

The viscous fluid damper cultural relics showcase is subjected to seismic waves and three kinds of museum structures' floor waves respectively, the peak relative acceleration of the showcase countertop, shock absorption effect, and displacement response are shown in Table 9. Due to the large difference between the acceleration amplitude of floor waves and seismic waves, the results under the action of seismic waves are not used as a reference.

Table 9 Peak acceleration, shock absorption effect and displacement response of showcase countertop under seismic and floor waves in the X-direction
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From the data in Table 9, it can be seen that under the action of floor waves of the base fixed structure, base isolated structure and viscous fluid damper structure of the museum, viscous fluid damper cultural relics showcase can all reduce the acceleration and displacement response of the showcase countertop, and the shock absorption effect of floor waves under the action of different seismic waves is different, with an average shock absorption rate of 62.14%, 75.55%, and 80.89% respectively. At the same time, under the action of floor waves of the viscous fluid damper structure of the museum, the viscous fluid damper cultural relics showcase can better control the displacement of the showcase. In conclusion, the viscous fluid damper cultural relics showcase is set up in the viscous fluid damper structure of the museum with the most obvious effect of shock absorption.

6 Conclusion

In this paper, the finite element models of the base fixed structure, base isolated structure and viscous fluid damper structure of the museum are established, modal analysis and time-history analysis are carried out to compare the seismic performance of the three kinds of museum structures, at the same time, the fixed cultural relics showcase, isolated cultural relics showcase and viscous fluid damper cultural relics showcase are established, and the seismic response analysis is carried out by inputting seismic waves and floor waves, and the following conclusions are obtained :

  1. (1)

    Compared with the base fixed structure of the museum, both the base isolated structure and viscous fluid damper structure of the museum can significantly reduce the inter-story shear force, inter-story drift and floor acceleration response of the structure, effectively consume the seismic energy input to the structure, reduce the seismic response, and achieve the purpose of seismic isolation and shock absorption, thus reducing the structural damage and improving the safety and reliability of the structure. After comparative analysis, the viscous fluid damper structure of the museum has the best effect on shock absorption.

  2. (2)

    When conducting seismic response research on cultural relics showcases, due to the large difference between the acceleration amplitude of seismic waves and floor waves, therefore, the direct input of seismic waves into the cultural relics showcase for time-history analysis is not of reference value, and the floor waves should be used as the input excitation.

  3. (3)

    Under the action of floor waves of the basic fixed structure, base isolated structure and viscous fluid damper structure of the museum, isolated cultural relics showcase all can reduce the acceleration response of the showcase, to achieve the purpose of seismic isolation. However, under the action of floor waves of the viscous fluid damper structure, the seismic isolation effect of the isolated cultural relics showcase is more pronounced, and at the same time, it can better control the displacement of isolation bearings.

  4. (4)

    Under the action of floor waves of the basic fixed structure, base isolated structure and viscous fluid damper structure of the museum, viscous fluid damper cultural relics showcase can reduce the acceleration and displacement response of the showcase countertop to a certain extent, to realize the effect of shock absorption. However, under the action of floor waves of the viscous fluid damper structure of the museum, the viscous fluid damper cultural relics showcase has the best effect on shock absorption, and can better control the displacement response of the showcase.

  5. (5)

    In summary, for this study, the isolated cultural relics showcase and viscous fluid damper cultural relics showcase are placed in the viscous fluid damper structure of the museum, which can achieve double shockproof of cultural relics and reduce the damage to cultural relics under earthquakes.

  6. (6)

    In addition, the finite element model is built with some necessary and reasonable assumptions and simplifications, which are usually made to facilitate model solving and the improvement of computational efficiency. When solving the calculations, some error factors will inevitably be introduced, so the results of the analysis have certain limitations and there is a need for further research.