Free longitudinal vibrations of a viscoelastic growing rod in both lateral and axial directions are considered in terms of the classical model. Exact and approximate WKB solutions are obtained for the single-mode case for both undamped and damped vibrations of the rod. The coupled multi-mode system is investigated numerically. It is shown that because of the rod’s growth in the axial direction, the amplitude of vibration tends to increase, and vice versa, because of the rod’s growth in the lateral direction its amplitude tends to decrease. The notion of ”critical damping” of a growing rod is introduced. At critical damping, the vibration amplitude remains constant. It is found that because of initial excitation of the lower-order vibration modes, the coupled higher-order mode amplitudes decrease with the growth of the mode number. However, with the growth of the mode number, the initial excitation of higher-order modes in the rod’s vibrations induces an effective amplitude increase in the lower-order modes.

根据经典模型考虑了粘弹性生长棒在横向和轴向上的自由纵向振动。对于杆的无阻尼和阻尼振动的单模情况，获得了精确和近似的 WKB 解。对耦合多模系统进行了数值研究。结果表明，由于杆在轴向方向上的增长，振动幅度趋于增加，反之，由于杆在横向方向上的增长，其幅度趋于减小。“临界阻尼”的概念介绍了一个生长棒。在临界阻尼下，振幅保持恒定。发现由于低阶振型的初始激发，耦合的高阶振型振幅随着振型数的增加而减小。然而，随着模式数的增长，杆振动中高阶模式的初始激发导致低阶模式的有效振幅增加。