【作者】 陈钢；

【导师】 崔洪宇； 陈立；

【作者基本信息】 大连理工大学 ， 海洋工程， 2025， 硕士

【摘要】 舰艇设备振动传递特性的识别与分析对于提升结构噪声控制水平与隔振系统设计具有重要的工程意义。传统传递路径分析方法受限于激励不可测、测点布局有限、非线性影响未充分考虑等因素,难以满足现代舰载结构复杂隔振系统的动态特性识别需求。针对上述问题,本文基于互易原理,构建适用于非线性隔振系统的传递函数互易性分析方法体系,围绕非线性互易性条件、误差度量指标与反演工程实现路径,开展了系统性理论推导与试验验证研究,力求为舰艇设备激励辨识与路径反演提供一种高效、实用、可扩展的新方法。首先,本文在多自由度系统建模基础上,推导了考虑非线性刚度影响下的互易性传递函数表达式,明确了互易性成立所依赖的动力学约束条件,构建了可量化评估互易性误差的频域指标,为后续非线性系统互易性分析提供了理论依据。通过引入龙格-库塔法对二自由度与三自由度非线性系统进行数值求解,系统研究了非线性刚度幅值、非线性参数对称性、非线性比例因子、上下阻尼比等关键因素对传递函数互易误差的影响规律。其次,在实验方面,本文设计并实施了BE40与BE60橡胶隔振器的静态与动态压缩试验,识别其等效线性刚度与非线性力-位移特性,采用表格函数构建非线性刚度模型;随后基于典型舱段结构搭建模态实验平台,开展了传递函数测量与互易性试验。试验结果显示,在低频段范围内(0–300Hz),系统在正反激励路径下传递响应高度一致,验证了互易原理在实船构型隔振系统中的适用性。进一步开展的激励力反演试验结合Tikhonov正则化方法,初步实现了激励源识别,证明了路径反演方案的工程可行性。最后,基于试验识别结果构建了验证性有限元仿真模型,分别开展了线性与非线性系统下的正反工况互易性仿真。线性系统采用谐波分析直接计算传递函数,非线性系统则采用扫频正弦激励并提取时域响应计算频域传递函数,仿真结果与试验趋势高度一致,进一步验证了非线性参数对互易误差的影响机制。结果表明:当非线性刚度幅值适中、结构基本对称时,系统仍可维持良好互易性,阻尼则在一定程度上对非线性诱发的互易性误差具有抑制作用。本文构建了从理论建模、实验识别到仿真验证的非线性传递函数互易性分析闭环流程,提出了工程化、量化的互易性评估与激励反演方法,为舰艇等复杂结构中振动源识别与非线性动力学建模提供了理论支撑与工程实践参考。更多还原

【Abstract】 The identification and analysis of vibration transmission characteristics in shipboard equipment are of great engineering significance for improving structural noise control and the performance of isolation system design.Traditional Transfer Path Analysis(TPA)methods are often constrained by unmeasurable excitations,limited sensor placement,and insufficient consideration of nonlinear effects,making them inadequate for capturing the dynamic behavior of complex marine isolation structures.To address these limitations,this study establishes a transmission function reciprocity analysis framework for nonlinear isolation systems based on the reciprocity principle.It systematically investigates reciprocity conditions,error quantification metrics,and practical excitation inversion strategies through theoretical modeling,numerical simulation,experimental validation,and finite element analysis.First,a multi-degree-of-freedom dynamic model incorporating nonlinear stiffness was developed,and the corresponding reciprocal transmission function expressions were derived.The study clarified the dynamic constraints required for reciprocity to hold and introduced a frequency-domain metric to quantitatively evaluate reciprocity errors.Numerical simulations using the Runge-Kutta method were performed on both 2-DOF and 3-DOF systems to examine the influence of nonlinear stiffness magnitude,symmetry of parameters,stiffness ratio,and damping asymmetry on the transmission function reciprocity.Secondly,on the experimental side,static and dynamic compression tests were conducted on BE40 and BE60 rubber isolators to identify their equivalent linear stiffness and nonlinear force–displacement behavior.A piecewise tabular function was used to model the nonlinear stiffness.A modal testing platform was then built based on a representative ship segment to carry out frequency response measurements and reciprocity validation.Results show that,in the low-frequency range(0–300 Hz),the transmission responses under forward and reverse excitations are highly consistent,verifying the engineering feasibility of applying the reciprocity principle to ship-mounted isolation systems.Furthermore,an excitation inversion test based on the Tikhonov regularization method was implemented,achieving initial source identification and validating the effectiveness of the proposed path inversion approach.Finally,a finite element model was constructed based on the identified experimental parameters to perform forward and reverse simulations under linear and nonlinear conditions.For the linear system,harmonic excitation analysis was directly applied,while the nonlinear system used a frequency sweep sinusoidal input and post-processed time-domain responses to obtain frequency-domain transmission functions.Simulation results were consistent with experimental trends and further confirmed the influence mechanism of nonlinear parameters on reciprocity errors.The findings indicate that when the nonlinear stiffness magnitude is moderate and system structural symmetry is preserved,good reciprocity performance can still be maintained.High damping levels were also found to suppress the amplification of reciprocity errors induced by nonlinear behavior.This study establishes a closed-loop workflow for reciprocity analysis in nonlinear isolation systems,spanning theoretical derivation,experimental identification,and simulation validation.The proposed framework offers a quantitative,engineering-oriented approach to vibration source recognition and path inversion,providing both theoretical insight and practical support for dynamic modeling of nonlinear ship structures.更多还原