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An analytical model for the propagation of bending waves on a plant stem due to vibration of an attached insect

机译：由于附着昆虫的振动弯曲波在植物茎上传播的解析模型

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摘要

A mathematical model is presented to examine the propagation of bending waves on a plant stem that are induced by vibratory excitation from an attached insect. This idealized model represents the insect body as a mass and the legs as a linear spring along with a general time-varying force that is assumed to act in parallel with the spring. The spring connects the mass to a stem modeled as a beam having uniform geometric and material properties. The linearly elastic beam is assumed to undergo pure vibratory bending and to be infinitely long in each direction. The equations that govern the insect-induced, coupled motions of both the beam and the mass are solved for arbitrary time varying forces produced by the insect's legs. Solutions for the frequency response indicate that the response is dominated by frequency components near the natural resonant frequency of the attached insect while at higher frequencies the amplitude of the response is strongly influenced only by the properties of the stem.
机译：提出了一个数学模型来检查弯曲弯曲波在植物茎上的传播，该弯曲波是由附着昆虫的振动激发引起的。这个理想化的模型将昆虫身体表示为质量，将腿部表示为线性弹簧，并假设一般时变力与弹簧平行地作用。弹簧将质量块连接到建模为具有均匀几何和材料特性的梁的杆上。假定线性弹性梁经过纯振动​​弯曲，并且在每个方向上都无限长。对于由昆虫的腿产生的任意时变力，求解了控制昆虫引起的梁和物体耦合运动的方程。频率响应的解决方案表明，该响应受附着昆虫自然共振频率附近的频率分量支配，而在较高频率下，响应幅度仅受茎的特性强烈影响。

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