In regards to what? Acoustical vibration is not a proper term, so it would be hard to define. I would need some context for how the term was used.
There is a class of vibration problems particularly in reciprocating compressors that are due to the acoustic energy in the gas pumped down the piping system interacting with the piping system and causing the pipe to vibrate. Than may be what was meant by acoustical vibration.
Vibration acoustics Structural Acoustics and Vibration is the study of how sound and mechanical structures interact and includes the transmission of sound through walls and the radiation of sound from vehicle panels.
Kinsler,L.E. & Frey,A.R.,1962, Fundamentals of Acoustics, 2nd Ed. states " In a broad sense, acoustics may be defined as the generation, transmission and reception of energy in the form of vibrational waves in matter...Many different types of vibration occur in the generation and propagation of acoustic waves.In a narrow sense, their frequency is limited to the range from about 20 cycles per second to 15,000 cycles per second, which produce the auditory sensation of sound for the average person... In a broader sense they also include both ultrasonic frequencies above 15,000 cps and inaudible infrasonic frequencies below 20 cps."
