Vibrations are caused by bit and drill string interaction with formations under ‎certain ‎drilling conditions. They are known as destructive loads and thus are leading to ‎downhole ‎fatigue failures, severe bottom hole ‎assembly and bit wear and may cause wellbore ‎instabilities. ‎Vibrations are affected by different parameters such as weight on bit, ‎rotary ‎speed, mud properties, bottom hole assembly and bit design as well as ‎formation ‎characteristics. During drilling operations, the drill bit interacts with different ‎formation layers ‎whereby each of those formations has usually different mechanical ‎properties. Vibrations are ‎also indirectly affected since the weight on bit and the rotary speed ‎of the drill string are ‎usually optimized against changing formations. Since uniaxial ‎compressive strength is one of ‎the representatives of the formations characteristics, axial ‎vibrations are expected to change ‎with the variations of the uniaxial compressive strength of ‎the formations. ‎ In this work the relationship between formation characteristics and drill string vibrations ‎in ‎laboratory scale have been studied. In addition, optimizing weight on bit and rotary speed ‎to ‎enhance the advance rate of drilling operations and manage vibrations has ‎been ‎considered as another main objective of this study. Non-linear models have also been ‎built to ‎establish a relationship between drill string vibration and other parameters. ‎ A fully automated laboratory scale drilling rig, the CDC miniRig, was used to ‎conduct ‎experimental tests. A vibration sensor sub attached to the drill string, above the bit, ‎recorded ‎the drill string vibrations during the tests and an additional sensor system ‎recorded ‎the drilling ‎parameters. Numerous uniform and layered concretes cubes as well as ‎different types of ‎uniform and layered rocks were ‎drilled by a double roller cone bit. The ‎uniaxial compressive ‎strength of the concretes and rocks were ‎measured prior to the ‎experiments. The experiments ‎were conducted using different combinations of weight on bit ‎and rotary speed. ‎Optimum ‎drilling parameter windows based on the experimental results of ‎uniform cubes, leading to ‎minimum drill string vibrations and maximum rate of ‎penetration, have been achieved. ‎Therefore monitoring the drill string vibrations can help ‎the driller to enhance the quality of ‎drilling operations and increase the rate of penetration.‎ Performing the layered experimental tests using the optimum drilling parameters ‎obtained ‎from uniform experiments and analysis the measured and calculated data (drill ‎string ‎vibrations and mechanical ‎specific energy) revealed the fact of changes in the axial ‎vibration ‎measurements due to variations of uniaxial ‎compressive strength of the layers. It is ‎concluded ‎that the formations can be recognized in real-time by incorporation of ‎the ‎vibration ‎measurements and allowed to differentiate the individual layers with different ‎strengths. ‎ Since linear equations are not sufficient to describe the relation between the drill ‎string ‎vibrations and other parameters, non-linear models like artificial ‎neural ‎networks in combination with sequential forward selection method were used. Different models to estimate the rate of penetration based on ‎the drilling ‎parameters, drill string vibrations and formation characteristics were built. ‎ The axial vibrations can be estimated using bit bounce models when they ‎are ‎being provided with drilling parameters and formation characteristics. ‎ Measured and calculated data from the uniform experimental tests formed the ‎formation ‎prediction model. Predicted (recognized) formation is the output of the model ‎when it is being ‎fed with the drilling parameters and drill string vibrations. ‎