Ginsberg Jerry H
5661 Woodsong Drive, Dunwoody, Georgia 30338, USA.
J Acoust Soc Am. 2020 Oct;148(4):2223. doi: 10.1121/10.0002160.
Considered herein is a small wedge-shaped block that contacts a rough surface on its angled face, with contact maintained by precompressed springs. The wedge is connected to a large mass that is subjected to a harmonic excitation. The development begins with a derivation of equations for the normal and friction forces, which are shown to depend on the displacement and acceleration of the wedge as well as the external force. Enforcing Coulomb's law for sliding leads to a differential equation of motion in which the effective inertia and stiffness coefficients switch values according to whether the wedge advances or retreats. Algebraic expressions for the displacement in either state are supplemented by an assessment of sticking based on Coulomb's static friction rule. The solutions for motion and the assessment of sticking are assembled in a simple, yet general, algorithm that only requires calculation of algebraic formulas. Transient waveforms of displacement, acceleration, and transmitted force are calculated for a harmonic excitation at the natural frequency of the frictionless system. It is found that very large viscous damping ratios would be required to obtain the same steady-state amplitude.
本文考虑的是一个小的楔形块，其斜面与粗糙表面接触，通过预压缩弹簧保持接触。楔形块连接到一个受到谐波激励的大质量块上。推导从法向力和摩擦力的方程开始，结果表明这些力取决于楔形块的位移和加速度以及外力。应用库仑滑动定律得到一个运动微分方程，其中有效惯性系数和刚度系数根据楔形块前进还是后退而切换值。基于库仑静摩擦规则对粘着的评估补充了两种状态下位移的代数表达式。运动解和粘着评估被整合到一个简单但通用的算法中，该算法只需要计算代数公式。针对无摩擦系统的固有频率下的谐波激励，计算了位移、加速度和传递力的瞬态波形。结果发现，要获得相同的稳态振幅，需要非常大的粘性阻尼比。
