Free-space optical (FSO) communication, considered as a last-mile technology, is widely used in many urban scenarios. However, the performance of urban free-space optical (UFSO) communication systems fades in the presence of system vibration caused by many factors in the chaotic urban environment. In this paper, we develop a dedicated indoor vibration platform and atmospheric turbulence to estimate the Bifurcated-Gaussian (B-G) distribution model of the receiver optical power under different vibration levels and link distances using nonlinear iteration method. Mean square error (MSE) and coefficient of determination ($R^2$) metrics have been used to show a good agreement between the PDFs of the experimental data with the resulting B-G distribution model. Besides, the UFSO channel under the effects of both vibration and atmospheric turbulence is also explored under three atmospheric turbulence conditions. Our proposed B-G distribution model describes the vibrating UFSO channels properly and can easily help to perform and evaluate the link performance of UFSO systems, e.g., bit-error-rate (BER), outage probability. Furthermore, this work paves the way for constructing completed auxiliary control subsystems for robust UFSO links and contributes to more extensive optical communication scenarios, such as underwater optical communication, etc.