It is expected that automated vehicles will gradually penetrate on public roads, resulting in mixed traffic in the next decades. This can impact traffic flow operations, especially the roadway capacity and flow stability. It is of paramount importance to understand and predict the implications of automated driving systems on traffic flow at the early design phase to avoid disruptive impacts on traffic. String stability properties of automated vehicle platoons are a fundamental block to understand their traffic flow stability impact. Previous reports on string stability analysis focussed on homogeneous vehicle strings and simplify the time delays in vehicle systems. This work propose an analytical approach to determine string stability conditions for non-connected vehicle platoons with heterogeneous parameters. To this end, a third-order linear vehicle dynamics model is used in the control design and Laplace transform of the spacing and speed error dynamics in time domain to frequency domain enables the determination of sufficient string stability criteria of heterogeneous vehicle strings. The analytical string stability conditions give new insights into the relationship between the string stability properties of vehicle strings in relation to the system properties of time delays and controller design parameters of feedback gains and desired time gap. Analytical results are verified via systematic simulation of both homogeneous and heterogeneous strings. Simulations demonstrate the predictive power of the analytical string stability conditions.