The stability of a slider-crank mechanism with an inhomogeneous coupler composed of transversely periodic arrays having linear viscoelasticity

The parametric instability of homogeneous couplers with and without viscoelasticity has been the subject of many interests. Recently, an attention is given to the use of nonhomogeneous links to reduce the happening of dynamic instability of mechanisms. Therefore, the objective of this study is to perform qualitative analysis of beam-like members composed of periodically embedded arrays in transverse direction to diminish the possibility of occurrence of large amplitude vibration. By assuming that the member is an inhomogeneous continuum, the periodicity and matching conditions across the interfaces of arrays and layers are taken into account by the Fourier series. The embedded arrays have different geometric and material properties and carry linear viscoelastic Kelvin–Voigt model. The proposed model is evaluated by applying it as a coupler into a slider-crank mechanism to examine the influence produced by arrays to the primary and secondary parametric instability. Result shows that the stiffness ratio between arrays and basic layers has visible effect on narrowing the regions of dynamic instability. Meanwhile, even if the damping of basic layer is light, increasing the damping ratio of arrays increases the capability of the coupler to suppress resonant peaks of vibration. As the damping of basic layer is moderate, the combination of stiffness ratio and damping ratio produces significant influence on diminishing the occurrence of large amplitude vibration, even though the fundamental frequency of the coupler is close to the resonant frequency. It is concluded that the growth of small amplitude vibration into large motion regime caused by parametric resonance can be effectively attenuated if the material and geometric properties between arrays and basic layers of the coupler are properly arranged.