The performance of the cantilever beam autoparametric vibration absorber with a lumped mass attached at an arbitrary point on the beam span is investigated. The absorber would have a distinct feature that in addition to the two-to-one internal resonance, the one-to-three and one-to-five internal resonances would also occur between flexural modes of the beam by tuning the mass and position of the lumped mass. Special attention is paid on studying the effect of these resonances on increasing the effectiveness and extending the range of excitation amplitudes at which the autoparametric vibration absorber remains effective. The problem is formulated based on the third-order nonlinear Euler–Bernoulli beam theory, where the assumed-mode method is used for deriving the discretized equations of motion. The numerical continuation method is then applied to obtain the frequency response curves and detect the bifurcation points. The harmonic balance method is also employed for detecting the type of internal resonances between flexural modes by inspecting the frequency response curves corresponding to different harmonics of the response. Parametric studies on the performance of the absorber are conducted by varying the position and mass of the lumped mass, while the frequency ratio of the primary system to the first mode of the beam is kept equal to two. Results indicated that the one-to-five internal resonance is especially responsible for the considerable enhancement of the performance.

中文翻译：

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弯曲模式的非线性相互作用对梁自参数减振器性能的影响

研究了悬臂梁自参数减振器的性能，该悬臂梁在梁跨度的任意点处均附有集总质量。吸收器将具有一个明显的特征，即除了二对一内部共振之外，通过调整光束的质量和位置，在梁的弯曲模式之间还会发生一对三和一对五内部共振。集总质量。要特别注意研究这些共振对提高效率和扩大自动参量吸振器保持有效的激发幅度范围的影响。该问题是根据三阶非线性Euler–Bernoulli束理论公式化的，其中使用假定模式方法来推导离散的运动方程。然后应用数值连续法获得频率响应曲线并检测分叉点。谐波平衡方法还用于通过检查与响应的不同谐波相对应的频率响应曲线来检测弯曲模式之间的内部谐振的类型。通过改变集总质量的位置和质量来进行吸收体性能的参数研究，而主系统与光束的第一模的频率比保持为2。结果表明，一对五的内部共振是性能显着提高的主要原因。谐波平衡方法还用于通过检查与响应的不同谐波相对应的频率响应曲线来检测弯曲模式之间的内部谐振的类型。通过改变集总质量的位置和质量来进行吸收体性能的参数研究，而主系统与光束的第一模的频率比保持为2。结果表明，一对五的内部共振是性能显着提高的主要原因。谐波平衡方法还用于通过检查与响应的不同谐波相对应的频率响应曲线来检测弯曲模式之间的内部谐振的类型。通过改变集总质量的位置和质量来进行吸收体性能的参数研究，而主系统与光束的第一模的频率比保持为2。结果表明，一对五的内部共振是性能显着提高的主要原因。而主系统与光束的第一模的频率比保持等于2。结果表明，一对五的内部共振是性能显着提高的主要原因。而主系统与光束的第一模的频率比保持等于2。结果表明，一对五的内部共振是性能显着提高的主要原因。