This paper reports the development of a novel semi-analytical model for solving the transient and steady-state contact responses of a rigid sphere sliding/rolling on a viscoelastic layer-elastic substrate system. The displacement transmissions at the layer-substrate interface are affected by spring-like or dislocation-like defects. The analytical transient and steady-state viscoelastic frequency response functions (FRFs) are derived from the elastic solutions with imperfect interfaces. The solutions are so formulated that fast numerical techniques, such as the conjugate gradient method (CGM) and the discrete convolution-fast Fourier transform (DC-FFT) algorithm, can be incorporated for computation efficiency. The developed model is employed to investigate the effects of layer thickness, modulus, sliding velocity, and the degree of interface imperfection on the viscoelastic contact response of the material system, including pressure distributions, displacements, viscoelastic dissipation, and subsurface stresses.

本文报道了一种新型的半解析模型的开发，该模型用于解决在粘弹性层-弹性基底系统上滑动/滚动的刚性球体的瞬态和稳态接触响应。层-基体界面处的位移传递受到弹簧状或位错状缺陷的影响。瞬态分析和稳态粘弹性频率响应函数（FRF）是从界面不完善的弹性解中得出的。制定解决方案的方式，可以结合快速数值技术，例如共轭梯度法（CGM）和离散卷积-快速傅里叶变换（DC-FFT）算法，以提高计算效率。所开发的模型用于研究层厚度，模量，滑动速度，