Present research includes damping as well as vibration evaluations of advanced sandwich nanotube. This nanostructure comprised of carbon nanotube (CNT) contains internal and external layers composed of ZnO provided as sensor and actuator. The structure is subjected to 2D magnetic and electric field as well. In order to presume this sandwich structure much more realistic, Kelvin model will be utilized and it is surrounded by visco-Pasternak foundation. Further, non-local piezoelasticity theory is employed regarding small scale influence. Gurtin-Murdoch model is noticed to account surface stresses. Besides zigzag shear-deformation theory for modeling the structure mathematically, Hamilton principle is applied to achieve motion equations. Generalized differential quadrature method (GDQM) is employed as numerical method for calculating sandwich structure's natural frequency and damping. So as to show accuracy of methods and validate, the obtained results are compared by another simplified cases. Finally, the influences of diverse traits and variables covering surface stresses, small scale parameter, magnetic and electric fields, surrounding medium and their effects on natural frequency will be studied. Citing the results, rise of nonlocal parameter results in reduction of natural frequency and regarding stress of surfaces leads to increase in natural frequency.