A self-consistent particle-in-cell simulation study is performed to investigate the effect of driving frequency on the electric field non-linearity, electron heating mechanism, and electron energy distribution function (EEDF) in a low pressure symmetric capacitively coupled plasma (CCP) discharge at a constant electron plasma frequency maintained by adjusting the discharge voltage. The driving frequency is varied from 27.12 MHz to 100 MHz for a fixed discharge gap of 3.2 cm and at a gas pressure of 1 Pa. The simulation results provide insight into higher harmonic generations in a CCP system for a constant electron response time. The spatio-temporal evolution and spatial time-averaged electron heating are presented for different driving frequencies. The simulation results predict that the electric field non-linearity increases with a rise in driving frequency along with a concurrent increase in higher harmonic contents. In addition to the electron heating and cooling near to the sheath edge, a positive <J.E> is observed in to the bulk plasma at higher driving frequencies. The EEDF illustrates enhancement in the population of mid-energy range electrons as driving frequency increases thereby changing the shape of EEDF from bi-Maxwellian to nearly Maxwellian. For the constant ion flux on the electrode surface, a decrease in the ion energy by more than half is observed with an increase in driving frequency.