馆藏文物直线导轨‒恒力弹簧复合隔震体系振动台试验研究

Shaking Table Test of Composite Seismic Isolation System with Linear Guides and Constant Springs for the Cultural Collection

摘要

针对博物馆中展柜、文物的防震保护，本研究设计并研发一种直线导轨‒恒力弹簧3维复合隔震装置。以某一博物馆的展柜和文物为原型，创建两个等比例的展柜文物模型：一个展柜文物模型安装有直线导轨‒恒力弹簧3维复合隔震装置；另一套系统未安装此装置。通过三向地震动加载，测试展柜文物隔震体系的动力响应，并对比分析隔震装置的加速度响应、减震率及水平位移响应，验证其隔震效果。试验结果表明：直线导轨水平隔震装置的隔震率和相对位移随地震烈度的增加而增大，隔震装置的水平隔震率在65%以上，水平行程始终在设计有效行程容许范围内；竖向隔震装置可发挥竖向隔震作用，竖向隔震率在30%以上；在不同场地类别和不同强度的地震动下，相比非隔震展柜内文物发生倾覆，隔震展柜文物基本保持相对静止。因此，直线导轨‒恒力弹簧3维复合隔震系统具有良好的隔震效果，能满足文物展陈3维隔震的需求。研究成果可为地震频发地区的博物馆文物保护提供有力的技术支持，降低地震对文物的潜在风险，保护珍贵的文化遗产。此外，本研究还详细说明试验工况的加载过程、测点仪器的布置及试验现象，为后续研究提供了重要的参考。

Abstract

Objective This study addresses the issue of immature vertical and three-dimensional seismic isolation technologies both domestically and internationally. A composite seismic isolation device that integrates linear guides and constant-force springs is designed and developed. This device, intended for the seismic isolation of artifacts in museum display cases, aims to mitigate potential earthquake-induced damage to artifacts. Methods Firstly, two models of museum display cabinets and cultural relics, both at the same scale, were created based on those of a specific museum. One of the cultural relic models within the display cabinet was outfitted with a composite seismic isolation device incorporating linear guides and constant-force springs. The linear guide rail seismic isolation device was positioned at the bottom of the display cabinet, while the vertical constant-force spring seismic isolation device was placed at the base of the cultural relics. In contrast, the other system lacks a seismic isolation device. Secondly, two sets of cultural relic display cabinet systems were tested on a shaking table. The dynamic characteristics of both the seismic isolation-equipped display cabinets and the non-seismic isolation display cabinets were examined using white noise with an amplitude of 0.1g. Then, seismic waves of varying intensities and from different locations were applied. The acceleration response of the shaking table, the surface of the seismic isolation device, the top surface of the display cabinet, and the displacement response of the linear guide's horizontal seismic isolation device were measured. Finally, the acceleration at the top of the isolated display cabinet was compared to that of the non-isolated display cabinet. The horizontal and vertical isolation rates were calculated, and the displacement response of the vibration isolator was analyzed. Results and Discussions The effectiveness of the isolation device in reducing seismic acceleration was clearly observed by comparing the top acceleration of isolated display cabinets with non-isolated ones. When comparing typical acceleration responses, under the EI‒Centro wave (0.4g) effect, the peak acceleration response in the X direction at the top of the non-isolated display cabinet was 1.68g, and in the Y direction was 1.89g. In contrast, on the isolated device platform, the peak acceleration response in the X direction was only 0.35g, and in the Y direction was only 0.36g. These results indicated that the isolation device effectively mitigated seismic acceleration. Through calculations, it was evident that the isolation efficiency of the linear guide's horizontal isolation device increased with the magnitude of seismic activity, ranging from 65% to 90%. This demonstrated the device's capability to effectively isolate vibrations in all horizontal directions. The isolation efficiency of the constant-force spring vertical isolation device ranged from 30% to 40%. The lower isolation efficiency in the vertical direction compared to the horizontal direction can have been attributed to different reference accelerations: Vertical isolation efficiency employed the Z-axis acceleration of the platform as a reference, while horizontal isolation efficiency used the acceleration of the non-isolated display cabinet as a reference. In terms of absolute acceleration values, the acceleration of the vertical isolation device was similar to that of the non-isolated horizontal display cabinet, indicating that this vertical isolation device effectively isolated vibrations in the vertical direction. The relative displacement of the horizontal isolation device on the linear guide increased with the intensity of the earthquake. At a seismic intensity of 0.1g, the relative displacement ranged from 5.9 to 24.9 mm in the X direction and from 5.4 to 21.1 mm in the Y direction. For a seismic intensity of 0.1g, the relative displacement was minimal for the Wenchuan wave in both the X and Y directions and maximal for the artificial wave in both the X and Y directions. Under a seismic intensity of 0.2g, the relative displacement ranged from 12.4 to 66.4 mm in the X direction and from 12.3 to 62.9 mm in the Y direction. For a seismic intensity of 0.2g, the relative displacement was minimal for the Wenchuan wave in both the X and Y directions, maximal for the artificial wave in the X direction, and maximal for the EI‒Centro wave in the Y direction. Under a seismic intensity of 0.3g, the relative displacement in the X direction ranged from 20.6 to 108.0 mm, and in the Y direction from 18.9 to 118.0 mm. The relative displacement was minimal for the Wenchuan wave in both the X and Y directions, maximal for the artificial wave in the X direction, and maximal for the EI‒Centro wave in the Y direction. Under a seismic intensity of 0.4g, the range of relative displacements in the X direction was between 31.4 and 140.0 mm, while in the Y direction, it spanned from 33.8 to 146.0 mm. For a seismic intensity of 0.4g, the relative displacement was minimal for the Wenchuan wave in both the X and Y directions, maximal for the artificial wave in the X direction, and maximal for the EI‒Centro wave in the Y direction. In all scenarios, the displacement of the isolation device did not exceed the designed effective stroke of 200 mm, indicating the reasonableness of the effective stroke design for the isolation device. Conclusions The conclusion indicates that the three-dimensional composite isolation system, which comprises a linear guide and a constant force spring, demonstrates a favorable isolation effect. This system has the potential to enhance the seismic safety of cultural relics during earthquake events. It exhibits strong innovation and practical applicability, fulfilling the three-dimensional isolation requirements of cultural relic display systems.

Graphical abstract

关键词

馆藏文物 / 3维隔震 / 直线导轨 / 恒力弹簧 / 振动台试验

Key words

collection of cultural relics / three-dimensional seismic isolation / linear guide rail / constant force spring / vibration table test

随着科技的迅猛发展和文化遗产的重要性日益凸显，博物馆展柜文物的保护成为备受关注的议题。地震是一种常见的自然灾害，其对文物的破坏潜在而严重^[1‒4]。因此，研发有效的隔震系统装置，最大程度地降低地震对文物的损害成为当务之急。

隔震技术在机械、土木、航空等多个领域应用广泛，为隔震技术的发展提供了强大的推力。为更好地保护文物，国内外学者将建筑隔震^[5]技术应用到博物馆文物保护^[6‒8]，并开展了一系列研究。隔震装置通常放置于展柜或文物底部，起到隔震的效果，有助于改善文物在地震条件下的振动特性，从而提高文物的抗震性能。

近年来，国内外文物水平隔震装置的研究已经取得了一定进展^[9]。Venanzi^[10‒11]等研究了基座主动控制对博物馆文物抗震保护的作用，结果表明，其可有效地抵消地震激励，避免文物损伤。De等^[12]提出一种质量阻尼器以控制刚性块的摇摆运动，研究表明，质量阻尼器会降低块体倾覆的概率。周乾^[13‒14]、Zou^[15]、蒋巧玲^[16]和赵守江^[17]等分别研制出滚珠式、平行连杆单摆式、滑动式、双向滚轮式及曲线轨道式水平隔震装置，并通过振动台试验验证了其隔震效果，且能有效减少文物在地震中的位移和加速度响应，提高其抗震性能。王亚等^[18]提出固定刚度支座和变刚度支座滑动型文物隔震支座，并通过数值模拟对其进行研究，结果表明，两种支座均可实现文物水平方向的防震。纪金豹^[19]、张毅^[20]和Alberti^[21]等提出直线导轨式文物展柜水平隔震装置、模块式金属隔震支座和双向基层隔离装置，并通过振动台试验验证了隔震装置的可行性。Ning等^[22]提出一种由硅胶阻尼器和连接元件组成的隔震装置，并通过振动台试验和数值模拟分析，结果表明，该装置可有效提高展柜和文物本身的抗震性能。尤军峰等^[23]提出一种基于固体发动机珠承结构，采用滚珠、滑盘、回位弹簧和阻尼器的文物隔震装置，并进行动力学仿真与试验，结果表明，该装置性能可满足文物隔震要求。邓淞文等^[24]将3类惯容系统应用于文物陈列柜，建立动力学模型，证明这类装置具有一定的减震效果。Sorace等^[25]将基础隔离地板应用于博物馆的文物防震中，有效降低了文物的地震响应。

竖向地震分量的影响也不容忽视^[26]，对竖向隔震装置和3维隔震装置的研究也在不断进行。朱泽瑾^[27]提出一种基于永磁悬浮的文物竖向隔震方法，通过振动台试验和数值模拟，验证了其本构关系及减震效果。王维等^[28]对碟形弹簧竖向隔震装置恢复力模型进行研究，通过往复荷载下的力学性能试验，对其有效性进行了验证。邹爽^[29]和常伟哲^[30]等提出了由水平隔震装置和竖向隔震装置两部分组成的新型3维减隔震装置，通过理论分析及试验验证了其可有效降低结构的水平和竖向地震响应。

国内外针对水平向隔震装置研发较为成熟，但竖向与3维隔震尚无成熟技术。本研究借鉴国内外相关研究成果，开发由直线导轨水平向隔震与恒力弹簧竖向隔震系统组成的3维隔震系统装置，直线导轨隔震装置与竖向恒力弹簧隔震装置分别放置在展柜底部和文物底部，用于博物馆展柜中的文物隔震，以减少地震对文物的潜在破坏。本文详细介绍该隔震装置的结构和工作原理，并通过振动台试验验证其隔震效果，为未来实际应用提供可靠的依据。

1 直线导轨‒恒力弹簧3维复合隔震系统

1.1 隔震装置

直线导轨‒恒力弹簧3维复合文物隔震系统，由水平向直线导轨隔震装置与竖向恒力弹簧隔震装置组成，分别如图1、2所示。水平向直线导轨隔震装置放置在展柜底部，竖向恒力弹簧隔震装置放置在文物底部。直线导轨水平隔震装置的组成部件包括底板、中间板、顶板、弹簧和导轨，其平面尺寸为1 000 mm×1 000 mm，高为100 mm。底板采用厚度为10 mm的钢板制成，中间板则使用角钢材料，用于稳固支撑导轨轨道，顶板设有螺栓孔以便于安装和固定。在弹簧方面，选用预伸长量为200 mm、最大伸长量为400 mm、自由长度为300 mm的拉簧。对于直线导轨，选用低摩擦滑块和轨道的组合，轨道的总长度为400 mm，且上下正交各设有两条，每条轨道的竖向承载力在200～500 kg之间。原理为：遭遇地震时，装置底板、中间板、顶板发生相对水平滑动。在水平运动过程中，弹簧提供水平刚度和恢复力，导轨之间的摩擦力提供阻尼。此设计使结构避开地震波特征周期，产生隔震效果。水平直线导轨双向正交布置可实现水平双向隔震。恒力弹簧竖向隔震装置的组成部件包括底板、连接板、顶板、竖向杆、恒力弹簧、刚度调节弹簧和水平杆，其平面尺寸为500 mm×500 mm，高为400 mm。制作各部件所用的材料为普通碳钢、不锈钢和铝合金。原理为：恒力弹簧与连接板相连并固定于外部导轨侧面，连接板与可以竖向伸缩的内部导轨相连。在内部导轨伸缩的过程中带动导向杆运动，同时带动刚度调节弹簧水平伸缩。隔震器顶板和隔震器底板通过可竖向伸缩的外部导轨相连。隔震器顶板上放置被隔震物体，在遭遇地震时，隔震装置的竖向刚度由刚度调节弹簧提供，上部文物重力由恒力弹簧平衡。恒力弹簧提供与被隔震对象大致相同的恒定竖向力，竖向恢复力由并联的螺旋弹簧提供。这样隔震装置就能有效地降低自振频率，从而避开地震波特征周期，产生隔震效果。

1.2 参数取值

合理的参数取值可实现良好的隔震效果。直线导轨水平隔震装置的参数取值：水平直线布置弹簧实现隔震装置的水平运动，通过降低水平刚度并提供合适的阻尼实现水平基础隔震。一般隔震装置设置自振频率为0.2～0.5 Hz、阻尼比为10%～20%，可取得良好的隔震效果。当已知隔震对象的质量时，可计算出对应的圆频率\omega为：

\omega =\sqrt[]{\frac{k}{m}}（1）

式中，k为水平弹簧刚度，m为隔震对象的总质量。

计算得到弹簧刚度^[31]。采用拉簧，隔震装置上部的总质量为250 kg，自振频率取0.3 Hz，则弹簧的总刚度为：

k={(\mathrm{2}\mathrm{\pi }\times \mathrm{0.3})}^{\mathrm{2}}\times \mathrm{250}=\mathrm{887}（2）

恒力弹簧竖向隔震装置的参数取值：利用恒力弹簧平衡上部结构重力，刚度调节弹簧调整隔震装置自振频率。刚度调节弹簧取值同水平弹簧。恒力弹簧的拉力应与上部结构的重力相近。被隔震文物和配重总质量为20 kg，恒力弹簧数量为4，每个恒力弹簧的拉力为6 kg。

2 振动台试验

为测试直线导轨‒恒力弹簧3维复合隔震装置的隔震效果，将2组文物展柜体系放置在振动台上进行试验，振动台试验布置如图3所示。两组体系的区别在于是否放置隔震装置。隔震文物展柜体系布置：直线导轨水平隔震装置布置在展柜底部，展柜浮放于水平隔震装置上，恒力弹簧竖向隔震装置布置在文物底部，文物浮放于恒力弹簧竖向隔震装置上。非隔震展柜浮放在振动台上，文物浮放于展柜台面上。展柜四周的上下部为钢板、中部为玻璃。展柜的尺寸为2 200 mm×800 mm×800 mm（长×宽×高），质量为220 kg。文物模型为某陶瓷文物仿制品，包含配重总质量为20 kg，尺寸为120 mm×120 mm（底部半径×重心高度）。本次试验在北京工业大学工程结构实验中心的地震模拟振动台系统上进行，其性能指标为：台面尺寸为2.5 m×2.5 m，台面重量为5.3 t，试件最大重量为10.0 t，最大位移为水平向行程±125 mm，最大加速度为±2.0g（满载）、±2.5g（空载），频率范围为0.1～50.0 Hz。满足此次试验自振频率和振动能级的要求。

2.1 测试仪器与测点布置

为检测展柜文物隔震体系的自振特性和动力响应，对振动台台面、隔震装置台面、展柜顶面的加速度响应和直线导轨水平隔震装置的位移响应进行测量。加速度传感器均布置X和Y两个方向。加速度采用ICP型加速度传感器、位移信号采用拉线式位移计进行量测。试验的加速度位移测点布置如图4所示。测点仪器与测点布置如表1所示。

2.2 试验工况

试验先加载幅值为0.1g的白噪声以测试隔震展柜文物和非隔震展柜的动力特性，然后加载不同强度和不同场地的地震波，研究隔震装置的隔震效果。振动台试验工况详情如表2所示。试验选用3条天然地震波、1条人工地震波和白噪声；通过X、Y、Z 3向施加于振动台，加速度峰值调幅为0.1g、0.2g、0.3g、0.4g，X∶Y∶Z=1.00∶1.00∶0.85，按原型加载不进行频率压缩。

2.3 试验现象

将振动台试验各工况试验现象进行分类整理，如表3所示，典型照片如图5所示。试验现象说明如下：1）所有工况加载过程中，隔震展柜以及隔震展柜内的浮放花瓶均与隔震装置相对静止，不同工况下隔震装置有不同程度的运动；非隔震展柜会有一定程度的颠簸，非隔震展柜内的浮放花瓶有摇晃、倾覆现象；2）在加速度峰值0.2g及以上地震动作用下，非隔震展柜内的浮放花瓶会发生摇晃和倾覆。在人工波0.3g工况下，花瓶倾覆后发生破碎现象；3）隔震装置具有良好的隔震性能，在0.4g地震波幅值下，隔震装置运动范围未超过容许量程，文物也未发生摇晃和倾覆。

3 试验分析

3.1 隔震率和加速度响应

隔震率定义与试验结果说明如下。

水平隔震率为：

a=\frac{a_{\mathrm{1}}-a_{\mathrm{2}}}{a_{\mathrm{1}}}\times \mathrm{100}\mathrm{\%}（3）

式中：a_{\mathrm{1}}为非隔震展柜顶部加速度响应峰值，对应A04加速度传感器；a_{\mathrm{2}}为隔震展柜顶部加速度响应峰值，对应A03加速度传感器。

竖向隔震率为：

a=\frac{a_{\mathrm{3}}-a_{\mathrm{4}}}{a_{\mathrm{3}}}\times \mathrm{100}\mathrm{\%}（4）

式中：a_{\mathrm{3}}为振动台台面加速度响应峰值，对应A01Z1加速度传感器；a_{\mathrm{4}}为竖向隔震装置台面的加速度响应峰值，对应A01Z2加速度传感器。

各工况的加速度响应峰值与隔震率如表4所示。

通过对比隔震展柜顶部加速度与非隔震展柜顶部加速度两组数据，可清晰地看到隔震装置在减小地震加速度方面的效果。选取典型加速度响应对比如图6所示，在EI‒Centro波（加速度峰值0.4g）作用下，非隔震展柜顶部的X向加速度峰值响应为1.68g，Y向加速度峰值响应为1.89g，而隔震装置顶面的X向加速度峰值响应仅为0.35g，Y向加速度峰值响应仅为0.36g，表明隔震装置有效地降低了地震加速度。

分析可知，直线导轨水平隔震装置的隔震率随地震作用的增大而增大，隔震率基本在65%～90%之间，说明此隔震装置水平各方向能发挥良好的隔震作用。恒力弹簧竖向隔震装置的隔震率为30%～40%。竖向隔震率不如水平向的原因可能为：参考加速度不同，竖向隔震率选用台面Z向加速度为参考，水平隔震率选用非隔震展柜加速度为参考。从绝对加速度值来看，竖向隔震装置加速度与水平隔震展柜加速度相近。说明此竖向隔震装置在竖向能发挥良好的隔震作用。

3.2 隔震器位移响应

试验各工况下直线导轨水平隔震装置位移响应峰值如表5所示。

由表5可以看出，直线导轨水平隔震装置相对位移随地震烈度的增加而增大，在0.1g地震作用下，隔震装置X向相对位移为5.9～24.9 mm，Y向相对位移为5.4～21.1 mm；在0.1g地震作用下，汶川波X、Y向相对位移最小，人工波X、Y向相对位移最大；在0.2g地震作用下，X向相对位移为12.4～66.4 mm，Y向相对位移为12.3～62.9 mm；在0.2g地震作用下，汶川波X、Y向相对位移最小，人工波X向相对位移最大，EI‒Centro波Y向相对位移最大；在0.3g地震作用下，X向相对位移为20.6～108.0 mm，Y向相对位移为18.9～118.0 mm；在0.3g地震作用下，汶川波X、Y向相对位移最小，人工波X向相对位移最大，EI‒Centro波Y向相对位移最大；在0.4g地震作用下，X向相对位移为31.4～140.0 mm，Y向相对位移为33.8～146.0 mm，在0.4g地震作用下，汶川波X、Y向相对位移最小，人工波X向相对位移最大，EI‒Centro波Y向相对位移最大。在所有工况中，隔震装置均未超过设计有效行程（200 mm），说明隔震装置的有效行程设计是合理的。

4 结论

1）直线导轨水平隔震装置的隔震率随地震烈度的增加而增大。隔震率基本在65%～90%之间，说明此隔震装置水平各方向能发挥良好的隔震作用。直线导轨水平隔震装置相对位移随地震烈度的增加而增大，0.4g地震作用下相对位移为146 mm，在其设计有效行程容许范围内（200 mm）。

2）恒力弹簧竖向隔震装置的隔震率为30%～40%。竖向隔震装置水平加速度与隔震展柜的水平加速度相近。此竖向隔震装置在竖向能发挥良好的隔震作用。

3）直线导轨‒恒力弹簧3维复合隔震系统具有良好的隔震效果，在遭遇地震作用时可以提高文物的地震安全性，具有较强的新颖性、实用性，能满足文物展陈系统3维隔震需求。

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基金资助

国家重点研发计划项目(2019YFC1521000)

国家自然科学基金项目(51978015)