设计了中点固结的余弦形预制双曲梁非线性隔振器，以用于船舶设备的主动与被动隔振.给出了余弦形预制双曲梁隔振器所受横向压力-位移关系解析表达式，分别建立了主动与被动隔振系统的非线性振动微分方程，利用谐波平衡法求得近似解析解，并与龙格-库塔法的数值解进行比较，给出了力传递率与位移传递率的表达式.同时，研究了在不同的非线性刚度系数、激励幅值、阻尼系数条件下，余弦形预制双曲梁隔振器的力传递率与位移传递率的变化规律.结果表明：谐波平衡法的解析解与龙格-库塔法的数值解基本吻合；所设计的非线性隔振器具有优良的低频隔振效果，其响应和隔振性能与激励幅值和阻尼有关.
Two prefabricated centrally-clamped cosine beams were proposed as a nonlinear vibration isolator for active and passive vibration isolation of marine equipment. The analytical expression of the beam’s force-displacement relationship was given, and the nonlinear differential equations of active and passive vibration isolation were established, respectively. The harmonic balance method (HBM) was applied to get the approximate analytical solutions of the differential vibration equations, and then the solutions were compared with those numerical ones obtained by the Runge-Kutta method. In order to characterize the vibration isolation capability of the isolator, the expressions of force transmissibility and displacement transmissibility were given. In addition, the effects of different nonlinear stiffness coefficients, excitation amplitudes and damping coefficients on force and displacement transmissibility were studied. The results show that HBM yields the same solution as the numerical method. The proposed nonlinear isolator has excellent performance of low-frequency vibration isolation, and its response and vibration isolation performance are affected by the excitation amplitude and damping coefficient.
［1］刘小彬. 船舶柴油发电机组浮筏隔振系统建模及振动特性分析［D］. 大连: 大连海事大学, 2013.
LIU Xiaobin. Modeling and vibration characteristics analysis of floating raft vibration isolation system of marine diesel generator set［D］. Dalian: Dalian Maritime University, 2013.
［2］朱海潮, 何琳, 霍睿, 等. 钢丝绳隔振器用于船舶主机隔振［J］. 中国造船, 2003(2): 35-40.
ZHU Haichao, HE Lin, HUO Rui, et al. Wire rope isolator used in vibration isolation of marine main propulsion engines［J］. Shipbuilding of China, 2003(2): 35-40.
［3］束立红, 周炜, 吕志强, 等. 钢丝绳隔振器在大型机械设备的振动冲击隔离设计中的应用［J］. 振动与冲击, 2006, 25(4): 78-81.
SHU Lihong, ZHOU Wei, L Zhiqiang, et al. Stainless steel wire-rope isolator used in vibration and impact isolation design for large machine equipment［J］. Journal of Vibration and Shock, 2006, 25(4): 78-81.
［4］QIU J, LANG J H, SLOCUM A H. A curved-beam bistable mechanism［J］. Journal of Microelectro-mechanical Systems, 2004, 13(2): 137-146.
［5］QIU J, LANG J H, SLOCUM A H. A centrally-clamped parallel-beam bistable MEMS mechanism［C］//14th IEEE International Conference on Micro Electro Mechanical Systems. Interlaken, Switzerland: IEEE, 2001: 353-356.
［6］鲍文博, 白泉, 陆海燕. 振动力学基础与MATLAB应用［M］. 北京: 清华大学出版社, 2015.
BAO Wenbo, BAI Quan, LU Haiyan. Foundation of vibration mechanics and application of MATLAB［M］. Beijing: Tsinghua University Press, 2015.
［7］NAYFEH A H, MOOK D T. Nonlinear oscillations［M］. New York: Wiley, 1979.
［8］HAYASHI C. Nonlinear oscillations in physical systems［M］. New York: McGraw-Hill, 1964.
［9］陈树辉. 强非线性振动系统的定量分析方法［M］. 北京: 科学出版社, 2007.
CHEN Shuhui. Quantitative analysis methods for strongly nonlinear vibration systems［M］. Beijing: Science Press, 2007.
［10］陈予恕. 非线性振动［M］. 北京: 高等教育出版社, 2002．
CHEN Yushu. Nonlinear vibration ［M］. Beijing: Higher Education Press, 2002.
［11］彭超, 程林, 王志海, 等. 基于谐波平衡法的非线性低频隔振系统振动特性研究［J］. 电子机械工程, 2015, 31(3): 1-6.
PENG Chao, CHENG Lin, WANG Zhihai, et al. Vibration characteristics analysis of nonlinear low-frequency vibration isolation system based on harmonic balance method［J］. Electro-Mechanical Engineering, 2015, 31(3): 1-6.
［12］刘兴天, 黄修长, 张志谊, 等. 激励幅值及载荷对准零刚度隔振器特性的影响［J］. 机械工程学报, 2013, 49(6): 89-94.
LIU Xingtian, HUANG Xiuchang, ZHANG Zhiyi, et al. Influence of excitation amplitude and load on the characteristics of quasi-zero stiffness isolator［J］. Journal of Mechanical Engineering, 2013, 49(6): 89-94.
［13］国家质量监督检验检疫总局.机械振动-客船和商船适居性振动测量、报告和评价准则: GB/T 7452-2007 ［S］. 北京: 中国标准出版社, 2002.
State Administration for Quality Supervision and Inspection and Quarantine. Mechanical vibration-guidelines for the measurement, reporting and evaluation of vibration with regard to habitability on passenger and merchant ships: GB/T 7452-2007 ［S］. Beijing: China Standards Press.
