Abstract This study investigates the dynamic behaviour and vibration transmission of impact oscillators with nonlinear motion constraints. The proposed nonlinear motion constraint with geometric stiffness nonlinearity is created by a linear spring embedded in a diamond-shaped linkage mechanism (DSLM). The harmonic balance (HB) approximations and numerical integrations are both employed to obtain the steady-state response of the systems subjected to harmonic force excitations. The force transmissibility and time-averaged power flows are used as indices to quantify and evaluate the vibration transmission and dissipation in impact oscillators. For a single-degree-of-freedom (SDOF) impact oscillator, it is found that the use of the nonlinear constraint can lead to a higher response amplitude but a substantially lower force transmissibility than those of the corresponding linear constraint case. For a two-degree-of-freedom (2DOF) impact oscillator, an extra peak is found in the curves of relative displacement between masses and in those of the force transmissibility to the secondary mass, while a local minimum point may exist near the extra peak. The inclusion of nonlinear motion constraint can lead to a higher proportion of the input power dissipated at interface compared to the linear constraint case. It is shown that the level of vibration power flow transmission within impact oscillators can be tailored by adjusting design parameters of the nonlinear constraint. It is also found that the nonlinear constraint may lead to bifurcations as well as super-harmonic and sub-harmonic response components. The findings from the study provide an in-depth understanding of the effects of design parameters and locations of nonlinear constraints on the vibration transmission in impact oscillators and assist in superior dynamic design of such systems for desirable vibration performance.

中文翻译：

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菱形连杆机构非线性运动约束冲击振子的振动传递与能流

摘要 本研究研究了具有非线性运动约束的冲击振荡器的动态行为和振动传递。所提出的具有几何刚度非线性的非线性运动约束是由嵌入菱形连杆机构 (DSLM) 的线性弹簧创建的。谐波平衡 (HB) 近似和数值积分都用于获得系统在谐波力激励下的稳态响应。力传递率和时间平均功率流被用作指标来量化和评估冲击振荡器中的振动传递和耗散。对于单自由度 (SDOF) 冲击振荡器，结果表明，与相应的线性约束情况相比，非线性约束的使用可以导致更高的响应幅度，但力的传递率却大大降低。对于双自由度（2DOF）冲击振子，在质量之间的相对位移曲线和到次级质量的力传递曲线中发现了一个额外的峰值，而在额外的附近可能存在一个局部极小点。顶峰。与线性约束情况相比，包含非线性运动约束会导致在界面处消耗的输入功率的比例更高。结果表明，可以通过调整非线性约束的设计参数来调整冲击振荡器内的振动能流传输水平。还发现非线性约束可能导致分叉以及超谐波和次谐波响应分量。研究结果提供了对设计参数和非线性约束位置对冲击振荡器振动传输的影响的深入理解，并有助于此类系统的卓越动态设计以获得理想的振动性能。