When a body moves to and fro in a definite pattern then this motion is known as vibratory motion.
The particles of solids are closely packed and the empty spaces between the particles are very small.
Due to the close packing of the particles, they can only vibrate about their fixed positions because they cannot move freely.
When the solids are heated, the molecules move apart because the heat energy try to overcome the force of attraction between the molecules due to which the motion of solids increases.
When solid cools the molecules come close again and the motion of solids decreases.
But in the whole process, the molecules do not leave their place. Hence, the motion possessed by solids is known as vibratory motion.
Hence, vibratory motion is associated with solids.