Abstract:The nonlocal transverse parametric vibration and steady-state response of axially moving viscoelastic two-dimensional nanoplate-like structures are studied. The Hamilton’s principle is employed to derive the governing partial differential equations of the mathematical model. The instable behaviors of axially moving viscoelastic nanoplate with a periodic pulsation velocity are addressed using the method of multiple scales. The modal functions are determined by some specific boundary conditions and the method of complex mode, and then the effects of small-scale parameter on the natural frequencies of the axially moving nanoplates with uniform velocity are discussed. Subsequently, the analyses are mainly focused on the instable regions caused by summation and principal parametric resonances, respectively, of which the summation parametric resonance occurs when the harmonic frequency approaches the sum of any two mode natural frequencies, while the principal parametric resonance occurs when the harmonic frequency approaches two times of certain mode natural frequency. It is shown that the existence of small-scale parameter contributes to reduce the bending stiffness and natural frequencies of axially moving viscoelastic nanoplates, and further decreases the instable regions of summation parametric resonance, while increases the instable regions of principal parametric resonance. On the other hand, the small-scale parameter softens the influence of viscoelasticity on the instable regions of principal parameter resonance. Moreover, the effect of viscoelasticity on the instability of summation parametric resonance is more obvious, ceteris paribus.
刘金建,谢锋,姚林泉,李成. 基于非局部理论的轴向运动粘弹性纳米板的参数振动及其稳定性[J]. 振动与冲击, 2017, 36(19): 13-20.
LIU Jin-jian XIE Feng YAO Lin-quan LI Cheng . Vibration and stability in parametric resonance of an axially moving viscoelastic nanoplate base on nonlocal theory. JOURNAL OF VIBRATION AND SHOCK, 2017, 36(19): 13-20.
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