A tapered nanobeam is modelled by Euler–Bernoulli beam theory and nonlocal theory of elasticity. A solution technique based on homotopy perturbation method is proposed to analyse the dynamic behavior of the tapered nanobeam. Beam becomes tapered along the width exponentially. The effects of flexible and rigid supports on the vibration of tapered nanobeam are analysed. Influences of tapered ratio and nonlocal parameter on the shape mode of deflection are also scrutinized. Homotopy perturbation method shows its effectiveness in this analysis. The results reveal that the effects of nonlocal parameter and tapered ratio are significant for the dynamic behavior of tapered nanobeam.

锥形纳米束通过Euler–Bernoulli束理论和非局部弹性理论建模。提出了一种基于同伦摄动法的求解技术来分析锥形纳米束的动力学行为。光束沿宽度成指数锥状。分析了柔性和刚性支撑对锥形纳米束振动的影响。还研究了锥度比和非局部参数对挠曲形状模式的影响。同伦摄动法在该分析中显示了其有效性。结果表明，非局部参数和锥形比的影响对于锥形纳米束的动力学行为具有重要意义。