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We explain the vibrations of a Frenkel–Kontorova (FK) model under Shapiro steps by the action of an external alternating force. We demonstrate Shapiro steps for a case with soft ‘springs’ between an 8-particles FK chain. Shapiro steps start with a single jump over the highest    $$\hbox {SP}_4$$  SP 4 in the global valley through the PES. They finish with doubled, and again doubled oscillations. We study in this part I a traditional FK model with periodic boundary conditions.

Description of Shapiro steps on the potential energy surface of a Frenkel–Kontorova model Part I: The chain in a variable box