爆破震动下框架结构动力响应的现场实测与数值模拟研究
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摘要
近年来,我国城市化速度逐步加快,城市建设规模越来越大。爆破技术在城乡建设中的应用也变得越来越广泛了。爆破施工给周边环境和人们的正常生活带来了很多不利影响,从而受到更多关注。过去,我们常以质点峰值振速为安全判据,但是这种评价体系由于其片面性己经越来越不能满足当前工程爆破震动安全的要求了,从而有必要更深入的研究。
本文以爆破地震波的特征及相关因素为切入口,对深圳市留仙洞场平工程爆破震动测试结果分析:一方面分析了本场地爆破地震波的传播特点;另一方面通过回归分析求得爆破地震波衰减的经验公式,并得出适合本工程采用的不同区段的安全用药量,从而为进一步有效控制爆破地震动造成的危害提供参考。
为了能比较直观地反映建筑物对爆破地震动的响应,本文运用ANSYS有限元分析软件建立多层框架结构的三维计算模型,对其进行结构动力响应时程分析。首先,通过现场实测得到爆破地震波,以调整后的地面波为结构震动输入,采用时程分析法得到的结果与实测结构响应两方面来说明结构的震动响应特点。然后分别计算了天然震波和爆破地震波作用下顶层水平位移的时程曲线、水平位移沿楼高的分布曲线以及顶层加速度的时程曲线。进一步指出与天然地震相比,爆破震动对框架结构的破坏力较小,但对人来说震感强烈。由此,最后本文还进引入烦恼率模型来探讨爆破震动环境下人体舒适度问题,并提出建议考虑加速度限值,以控制爆破对人体的不适影响。
Along with the explosive technique in the city and countryside construction's gradual application, the harm of the demolition vibration has been extensive attention more and more. In the past, we regard the particle peak value as the security criterion. But this kind of appraisal system is unilateral, more and more could not satisfy the current project demolition vibration security the request. Therefore, this article will begin from the demolition earthquake wave's parameter. Comprehensive discussion demolition earthquake wave each related parameter to building dynamic action characteristic.
In view of the fact that demolition earthquake wave is particularity. Firstly this article introduced the demolition earthquake wave characteristic and the correlation factor. Then kept the immortal hole field even project demolition vibration test in view of Shenzhen to demolish the earthquake wave the characteristic to carry on the elaboration. And we can obtain the empirical formula through the regression analysis the coefficient.
This article utilizes the finite element analysis software establishment multistory building structure the three dimensional computation model. Carries on the structure dynamic analysis to it, and used the time interval analytic method to carry on the earthquake to respond the analysis. Has calculated the natural seismic wave and under separately the demolition earthquake wave action the top layer horizontal curve, horizontal departure along building high distribution curve as well as top layer acceleration time interval curve. The computed result indicated that uses the ANSYS software establishment three-dimensional model, can good carry on the structure the vibration response analysis, and to the demolition designers to provide the reference. Hence, this paper also introduced annoyance rate to evaluate human comfort under the environment of the blasting vibration, considering the acceleration threshold to control the blasting effect of discomfort.
本文以爆破地震波的特征及相关因素为切入口,对深圳市留仙洞场平工程爆破震动测试结果分析:一方面分析了本场地爆破地震波的传播特点;另一方面通过回归分析求得爆破地震波衰减的经验公式,并得出适合本工程采用的不同区段的安全用药量,从而为进一步有效控制爆破地震动造成的危害提供参考。
为了能比较直观地反映建筑物对爆破地震动的响应,本文运用ANSYS有限元分析软件建立多层框架结构的三维计算模型,对其进行结构动力响应时程分析。首先,通过现场实测得到爆破地震波,以调整后的地面波为结构震动输入,采用时程分析法得到的结果与实测结构响应两方面来说明结构的震动响应特点。然后分别计算了天然震波和爆破地震波作用下顶层水平位移的时程曲线、水平位移沿楼高的分布曲线以及顶层加速度的时程曲线。进一步指出与天然地震相比,爆破震动对框架结构的破坏力较小,但对人来说震感强烈。由此,最后本文还进引入烦恼率模型来探讨爆破震动环境下人体舒适度问题,并提出建议考虑加速度限值,以控制爆破对人体的不适影响。
Along with the explosive technique in the city and countryside construction's gradual application, the harm of the demolition vibration has been extensive attention more and more. In the past, we regard the particle peak value as the security criterion. But this kind of appraisal system is unilateral, more and more could not satisfy the current project demolition vibration security the request. Therefore, this article will begin from the demolition earthquake wave's parameter. Comprehensive discussion demolition earthquake wave each related parameter to building dynamic action characteristic.
In view of the fact that demolition earthquake wave is particularity. Firstly this article introduced the demolition earthquake wave characteristic and the correlation factor. Then kept the immortal hole field even project demolition vibration test in view of Shenzhen to demolish the earthquake wave the characteristic to carry on the elaboration. And we can obtain the empirical formula through the regression analysis the coefficient.
This article utilizes the finite element analysis software establishment multistory building structure the three dimensional computation model. Carries on the structure dynamic analysis to it, and used the time interval analytic method to carry on the earthquake to respond the analysis. Has calculated the natural seismic wave and under separately the demolition earthquake wave action the top layer horizontal curve, horizontal departure along building high distribution curve as well as top layer acceleration time interval curve. The computed result indicated that uses the ANSYS software establishment three-dimensional model, can good carry on the structure the vibration response analysis, and to the demolition designers to provide the reference. Hence, this paper also introduced annoyance rate to evaluate human comfort under the environment of the blasting vibration, considering the acceleration threshold to control the blasting effect of discomfort.
引文
1李锋,魏晓林,郑炳旭.城市复杂环境下石方控制爆破安全.爆破, 2003, 20(2):37~43
2杨军,孙振.爆破振动对周围环境的影响.四川建筑, 2004, 24(3):103~105
3言志信,王永和,江平,王后裕.爆破地震测试及建筑结构安全标准研究. 2003, 22(1): 1907~1911
4 R. M. Wheeler. How Millisecond Delay Periods May Enhance or Deduce Blast Vibration Effects. Mining Engineering, 1988, 40(10):969~973
5 H. D. Charles. Monitoring and Control of Blast Effect. Mining Engineering Handbook,1990,746~760
6 C. L. Jimeno, A. A. Balkema. Drilling and Blasting of Rocks. Printed In Netherlands, 1995
7 A. J. Hendron, L. L. Oriard. Specification for Controlled Blasting And Civil Engineering Projects, Proceedings of North American Rapid Excavation And Tunneling Conference, AIME, 1972
8 C. H. Dowding. Blast Vibration Monitoring and Control. Practice Periodical on Structural Design and Construction, 2006, 12, 11(1):8~12
9 R. Holmberg, P. A. Persson. Design of Tunnel Perimeter Blasthole Patterns to Prevent Rock Damage, Proceedings Tunnelling, 1979
10 J. F. Devine. Effect of Charge Weight on Vibration Levels from Quarry Blasting. U. S. Bureau of Mine RI 6774. 1966
11 A. Gosh, J. K. Deamen. A Simple New Blast Vibration Predictor Based On Wave Propog-ation Laws. 24th Symposium on Rock Mechnaics, 1983
12 A. Gosh, J. K. Deamen. Statistics-A Key to Better Blast Vibration Predictions, Proceedings of 27th US Symposium on Rock Mechanics, 1985,1141~1149
13胡宗武.工程振动分析基础.上海交通大学出版社, 1985
14李的林,高振儒,朱立新.爆破震动危害中几个重要因素分析.工程爆破, 1999, 5(3):64~67钱七虎,陈士海.爆破地震效应.爆破, 2004, 21(2):1~5
15 R. P. Dhakal, T. C. Pan. Response Characteristics of Structures Subjected to Blasting-induced Ground Motion. International Journal of Impact Engineering, 2003, 32(28):813~828
16霍永基,王湘均,费骥鸣.爆破地震效应及安全评定方法.土岩爆破文集(第二辑).冶金工业出版社, 1985, 184~187
17黄树棠,张雪亮.爆破地震效应.北京,地震出版社, 1981, 116~119
18叶海旺,房泽法,彭志刚.爆破地震对结构的影响.爆破, 2000, 20(1): 86~91
19庄金钊,杨仁树,李孝林.结构物爆破震动安全标准的探讨论,矿冶工程, 2003, 23(2):11~14
20贾光辉,王志军,张国伟,裴思行.爆破地震波对地下结构物的影响仿真研究.华北工学院学报, 2001, 17(6):445~448
21魏晓林.爆破震动对邻近建筑物的危害影响.爆破, 1998, 15(1):49~54
22曹孝君,张继春,吕和林.频率对爆破地震作用下结构的动力响应的影响研究.爆破, 2006, 23(2):14~19
23张志呈.爆破地震参量与振动持续时间.四川冶金, 2002(3):1~4
24 F. T. Richarl, T .T. Hall, R. Woods. Vibrations of soils and Foundations Frentice-Hall, Inc, Englewood, NJ, 1970, 89
25程运材,王太海,吴秀琼.延长平果铝土矿一期服务年限的研究,有色冶炼, 2002, 12, (6):125~135
26 G. W. Ma, H. Hao, Y. x. Zhou. Assessment of Structure Damage to Blasting Induced Ground Motions. Engineering Structures, 2000, 22:1378~1389
27李孝林,穆太升,董鑫,周东良,薛思读.频率在爆破震害中的作用及其影响因素分析.工程爆破, 2001, 7(3):15~18
28黄文华,徐全军,沈蔚,温蓉,季茂荣.小波变换在判断爆破地震危害中的应用.工程爆破, 2001, 3, 7(1):24~27
29陈士海.爆破地震动作用下结构震动响应研究现状与发展.爆破, 2003
30娄建武,龙源,徐全军.小波分析在结构爆破振动响应能量分析法中的应用.世界地震工程, 2003, 3, 11(1):64~67
31王小林,吴枫,徐书雷.建筑结构对爆破震动响应的动力学计算方法.西安科技学院学报, 2002, 22(14):411~413
32孔珍,张晓培,牛建军.应用于结构动力反应分析方法的对比研究.山西建筑, 2006, 32(18): 44~45
33王亚勇.关于设计反应谱、时程法和能量方法的探讨.建筑结构学报, 2000, 2, 21(1):21~28
34陈士海.工程爆破中防灾减灾与防护工程研究的几个主要问题.防灾减灾工程学报, 2003, 23(4):103~107
35爆破新技术与现场安全管理及强制性标准规范实务全书.当代中国出版社, 2006
36张义平,吴桂义.爆破地震波特性研究.矿业研究与开发, 2007, 27(6): 68~72
37郭学彬,肖正学,张继春,刘泉.论爆破地震波在传播过程中的衰减特性.中国矿业. 2006, 15(3):51~57
38李林峰.爆破震动的分析方法及测试仪器系统探讨.爆破, 2003.3
39史雅语,顾毅成.安托山B21-1及B21-2部分整治地块场平工程石方爆破与安全防护措施方案, 2003, 3
40陈寿如,肖清华.无线自记测震系统在露天矿山爆破地震控制中的应用.爆破器材, 1998, 2
41 Y. Lu, H. Hao, G.W. Ma. Simulation of structural response under high-frequency ground excitation. Earth-quake engineering structure dynamics, 2001, 30(3):307~325
42阳生权,廖先葵,刘宝琛.爆破地震安全判据的缺陷与改进.爆炸与冲击, 2001, 21(3): 224~227
43王民寿,郭庆海.用双随即变量回归改进爆破振速回归分析.爆破与冲击, 1998, 18(3): 283~288
44张志呈.浅谈评价爆破地震效应的方法和标准.爆破器材, 1998, 27(3):32~35
45 K. G. Hinzen. Modeling of blast vibration. Int J Rock Mech Min Sci& Geomnech Abstract. 1987, 25(6):439~445
46 A. Kavetsky. A model of acoustic pulse propagation and its application to determine Q for a rock mass. Int J Rock Mech Min Sci& Geomech Abstract. 1990 , 27(1):33~41
47王元丰,储德文.精细时程积分法在地震响应分析中的应用.土木工程学报, 2004, 37(1):20~23
48高层建筑混凝土结构技术规程.中国建筑工业出版社, 2002
49陈清军,徐植信.层状土介质中群桩及其上部结构体系对任意入射地震波的响应.地震工程与工程振动, 1994, 3, 14(1):36~43
50薄景山,李秀领,刘红帅.土层结构对地表加速度峰值的影响.地震工程与工程振动, 2003, 23(3):35~40
51陈跃庆,吕西林,侯建国,李培振.不同土性地基中地震波传递的振动台模型试验研究.武汉大学学报(工学版), 2005, 38(2):50~53
52冯希杰,全学申.场地土对基岩峰值加速度放大效应分析.工程地质学报, 2001, 9(4):385~388
53周芬,尚守平,杜运兴.有限元建模对结构自振频率计算的影响.湖南大学学报(自然科学版), 2006, 33(5):10~15
54陈波,吕西林,李培振,陈跃庆.用ANSYS模拟结构-地基动力相互作用振动台试验的建模方法.地震工程与工程振动, 2002, 22 (1):126-131
55赵全军,杨力.爆破震动速度微分与实测加速度的差异分析.西部探矿工程, 2005, 1:122~123
56岳祖润,周宏业,陈幼平.某花园大厦的三维地震反应分析.工程抗震, 1999, (6):3~7
57胡文源,邹晋华.时程分析法中有关地震波选取的几个注意问题.南方冶金学院学报, 24(4):25~27
58 R. P. Dhakal, T. C. Pan. Response Characteristics of Structures Subjected to Blasting-induced Ground Motion. International Journal of Impact Engineering, 2003, 28:813~828
59程桂胜.建筑抗震设计所需考虑的振型数.建筑技术开发, 1999, 26(6)
60薄景山,李秀领,刘红帅.土层结构对地表加速度峰值的影响.地震工程与工程振动, 2003, 23(3):35~40
61白川保友.对舒适度标准的重新评价.交通技术, 1980, 3:18~21
62宋志刚,金伟良.人对振动主观反应的模糊随机评价模型.应用基础与工程科学学报, 2002 ,10 (3):287~294
63 F. K. Chang. Human response to motion in tall buildings. Journal of the Structural Division, ASCE, 1973, 199(6):1259~1272
64唐传菌,张天侠,宋桂秋.基于烦恼率模型的振动舒适度评价方法.东北大学学报自然(科学版), 2006, 27(7):802~805
65 M J. Griffin. Handbook of human vibration. London: Academic Press. 1994, 353~355
66 International Standard 2631-2: Evaluation of human exposure to whole-body vibration-Continuous and shock-induced vibration in buildings, 1989
67 British Standard 6472: Guide to the evaluation of human exposure to vibration in building, British Standard Institute, 1984
68 G. S. Paddan, M. J. Griffin. Evaluation of Whole-body Vibration in Vehicles. Journal of Sound and Vibration, 2002 ,253(1):195~213
69宋志刚.基于烦恼率模型的工程结构振动舒适度设计新理论.杭州:浙江大学,2003
70涂瑞和,方丹群,战嘉恺.用模糊数学原理评价城市居民对环境振动的主观反应.国环境科学, 1990, 10(5):356~359
71宋志刚,金伟良.工程结构振动舒适度的抗力模型.浙江大学学报(工学版),2004, 8:966~370
72卢文波,赖世骥,舒大强,朱传云.关于爆破震动速度和加速度等效性问题的讨论.爆破, 17:11~14
2杨军,孙振.爆破振动对周围环境的影响.四川建筑, 2004, 24(3):103~105
3言志信,王永和,江平,王后裕.爆破地震测试及建筑结构安全标准研究. 2003, 22(1): 1907~1911
4 R. M. Wheeler. How Millisecond Delay Periods May Enhance or Deduce Blast Vibration Effects. Mining Engineering, 1988, 40(10):969~973
5 H. D. Charles. Monitoring and Control of Blast Effect. Mining Engineering Handbook,1990,746~760
6 C. L. Jimeno, A. A. Balkema. Drilling and Blasting of Rocks. Printed In Netherlands, 1995
7 A. J. Hendron, L. L. Oriard. Specification for Controlled Blasting And Civil Engineering Projects, Proceedings of North American Rapid Excavation And Tunneling Conference, AIME, 1972
8 C. H. Dowding. Blast Vibration Monitoring and Control. Practice Periodical on Structural Design and Construction, 2006, 12, 11(1):8~12
9 R. Holmberg, P. A. Persson. Design of Tunnel Perimeter Blasthole Patterns to Prevent Rock Damage, Proceedings Tunnelling, 1979
10 J. F. Devine. Effect of Charge Weight on Vibration Levels from Quarry Blasting. U. S. Bureau of Mine RI 6774. 1966
11 A. Gosh, J. K. Deamen. A Simple New Blast Vibration Predictor Based On Wave Propog-ation Laws. 24th Symposium on Rock Mechnaics, 1983
12 A. Gosh, J. K. Deamen. Statistics-A Key to Better Blast Vibration Predictions, Proceedings of 27th US Symposium on Rock Mechanics, 1985,1141~1149
13胡宗武.工程振动分析基础.上海交通大学出版社, 1985
14李的林,高振儒,朱立新.爆破震动危害中几个重要因素分析.工程爆破, 1999, 5(3):64~67钱七虎,陈士海.爆破地震效应.爆破, 2004, 21(2):1~5
15 R. P. Dhakal, T. C. Pan. Response Characteristics of Structures Subjected to Blasting-induced Ground Motion. International Journal of Impact Engineering, 2003, 32(28):813~828
16霍永基,王湘均,费骥鸣.爆破地震效应及安全评定方法.土岩爆破文集(第二辑).冶金工业出版社, 1985, 184~187
17黄树棠,张雪亮.爆破地震效应.北京,地震出版社, 1981, 116~119
18叶海旺,房泽法,彭志刚.爆破地震对结构的影响.爆破, 2000, 20(1): 86~91
19庄金钊,杨仁树,李孝林.结构物爆破震动安全标准的探讨论,矿冶工程, 2003, 23(2):11~14
20贾光辉,王志军,张国伟,裴思行.爆破地震波对地下结构物的影响仿真研究.华北工学院学报, 2001, 17(6):445~448
21魏晓林.爆破震动对邻近建筑物的危害影响.爆破, 1998, 15(1):49~54
22曹孝君,张继春,吕和林.频率对爆破地震作用下结构的动力响应的影响研究.爆破, 2006, 23(2):14~19
23张志呈.爆破地震参量与振动持续时间.四川冶金, 2002(3):1~4
24 F. T. Richarl, T .T. Hall, R. Woods. Vibrations of soils and Foundations Frentice-Hall, Inc, Englewood, NJ, 1970, 89
25程运材,王太海,吴秀琼.延长平果铝土矿一期服务年限的研究,有色冶炼, 2002, 12, (6):125~135
26 G. W. Ma, H. Hao, Y. x. Zhou. Assessment of Structure Damage to Blasting Induced Ground Motions. Engineering Structures, 2000, 22:1378~1389
27李孝林,穆太升,董鑫,周东良,薛思读.频率在爆破震害中的作用及其影响因素分析.工程爆破, 2001, 7(3):15~18
28黄文华,徐全军,沈蔚,温蓉,季茂荣.小波变换在判断爆破地震危害中的应用.工程爆破, 2001, 3, 7(1):24~27
29陈士海.爆破地震动作用下结构震动响应研究现状与发展.爆破, 2003
30娄建武,龙源,徐全军.小波分析在结构爆破振动响应能量分析法中的应用.世界地震工程, 2003, 3, 11(1):64~67
31王小林,吴枫,徐书雷.建筑结构对爆破震动响应的动力学计算方法.西安科技学院学报, 2002, 22(14):411~413
32孔珍,张晓培,牛建军.应用于结构动力反应分析方法的对比研究.山西建筑, 2006, 32(18): 44~45
33王亚勇.关于设计反应谱、时程法和能量方法的探讨.建筑结构学报, 2000, 2, 21(1):21~28
34陈士海.工程爆破中防灾减灾与防护工程研究的几个主要问题.防灾减灾工程学报, 2003, 23(4):103~107
35爆破新技术与现场安全管理及强制性标准规范实务全书.当代中国出版社, 2006
36张义平,吴桂义.爆破地震波特性研究.矿业研究与开发, 2007, 27(6): 68~72
37郭学彬,肖正学,张继春,刘泉.论爆破地震波在传播过程中的衰减特性.中国矿业. 2006, 15(3):51~57
38李林峰.爆破震动的分析方法及测试仪器系统探讨.爆破, 2003.3
39史雅语,顾毅成.安托山B21-1及B21-2部分整治地块场平工程石方爆破与安全防护措施方案, 2003, 3
40陈寿如,肖清华.无线自记测震系统在露天矿山爆破地震控制中的应用.爆破器材, 1998, 2
41 Y. Lu, H. Hao, G.W. Ma. Simulation of structural response under high-frequency ground excitation. Earth-quake engineering structure dynamics, 2001, 30(3):307~325
42阳生权,廖先葵,刘宝琛.爆破地震安全判据的缺陷与改进.爆炸与冲击, 2001, 21(3): 224~227
43王民寿,郭庆海.用双随即变量回归改进爆破振速回归分析.爆破与冲击, 1998, 18(3): 283~288
44张志呈.浅谈评价爆破地震效应的方法和标准.爆破器材, 1998, 27(3):32~35
45 K. G. Hinzen. Modeling of blast vibration. Int J Rock Mech Min Sci& Geomnech Abstract. 1987, 25(6):439~445
46 A. Kavetsky. A model of acoustic pulse propagation and its application to determine Q for a rock mass. Int J Rock Mech Min Sci& Geomech Abstract. 1990 , 27(1):33~41
47王元丰,储德文.精细时程积分法在地震响应分析中的应用.土木工程学报, 2004, 37(1):20~23
48高层建筑混凝土结构技术规程.中国建筑工业出版社, 2002
49陈清军,徐植信.层状土介质中群桩及其上部结构体系对任意入射地震波的响应.地震工程与工程振动, 1994, 3, 14(1):36~43
50薄景山,李秀领,刘红帅.土层结构对地表加速度峰值的影响.地震工程与工程振动, 2003, 23(3):35~40
51陈跃庆,吕西林,侯建国,李培振.不同土性地基中地震波传递的振动台模型试验研究.武汉大学学报(工学版), 2005, 38(2):50~53
52冯希杰,全学申.场地土对基岩峰值加速度放大效应分析.工程地质学报, 2001, 9(4):385~388
53周芬,尚守平,杜运兴.有限元建模对结构自振频率计算的影响.湖南大学学报(自然科学版), 2006, 33(5):10~15
54陈波,吕西林,李培振,陈跃庆.用ANSYS模拟结构-地基动力相互作用振动台试验的建模方法.地震工程与工程振动, 2002, 22 (1):126-131
55赵全军,杨力.爆破震动速度微分与实测加速度的差异分析.西部探矿工程, 2005, 1:122~123
56岳祖润,周宏业,陈幼平.某花园大厦的三维地震反应分析.工程抗震, 1999, (6):3~7
57胡文源,邹晋华.时程分析法中有关地震波选取的几个注意问题.南方冶金学院学报, 24(4):25~27
58 R. P. Dhakal, T. C. Pan. Response Characteristics of Structures Subjected to Blasting-induced Ground Motion. International Journal of Impact Engineering, 2003, 28:813~828
59程桂胜.建筑抗震设计所需考虑的振型数.建筑技术开发, 1999, 26(6)
60薄景山,李秀领,刘红帅.土层结构对地表加速度峰值的影响.地震工程与工程振动, 2003, 23(3):35~40
61白川保友.对舒适度标准的重新评价.交通技术, 1980, 3:18~21
62宋志刚,金伟良.人对振动主观反应的模糊随机评价模型.应用基础与工程科学学报, 2002 ,10 (3):287~294
63 F. K. Chang. Human response to motion in tall buildings. Journal of the Structural Division, ASCE, 1973, 199(6):1259~1272
64唐传菌,张天侠,宋桂秋.基于烦恼率模型的振动舒适度评价方法.东北大学学报自然(科学版), 2006, 27(7):802~805
65 M J. Griffin. Handbook of human vibration. London: Academic Press. 1994, 353~355
66 International Standard 2631-2: Evaluation of human exposure to whole-body vibration-Continuous and shock-induced vibration in buildings, 1989
67 British Standard 6472: Guide to the evaluation of human exposure to vibration in building, British Standard Institute, 1984
68 G. S. Paddan, M. J. Griffin. Evaluation of Whole-body Vibration in Vehicles. Journal of Sound and Vibration, 2002 ,253(1):195~213
69宋志刚.基于烦恼率模型的工程结构振动舒适度设计新理论.杭州:浙江大学,2003
70涂瑞和,方丹群,战嘉恺.用模糊数学原理评价城市居民对环境振动的主观反应.国环境科学, 1990, 10(5):356~359
71宋志刚,金伟良.工程结构振动舒适度的抗力模型.浙江大学学报(工学版),2004, 8:966~370
72卢文波,赖世骥,舒大强,朱传云.关于爆破震动速度和加速度等效性问题的讨论.爆破, 17:11~14