Could a pure-transverse acoustical-wave propagate? This is the Wikipedia definition of acoustic waves:

Acoustic waves are a type of energy propagation through a medium by means of adiabatic compression and decompression

Rayleigh surface waves (solid-surface-borne sounds) are a mix of transverse and longitudinal mechanical waves which propagates through compression/decompression, so they are acoustical by definition.
However, what about the transverse component alone of a solid-surface-borne mechanical wave (e.g. seismic S-wave)? While there are compression and decompression along the transverse component, there isn't any compression/decompression of particle in the direction of propagation (longitudinal). So I have 3 related questions:

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*Do pure transversal mechanical wave exist in practice or is there always a small component of longitudinal wave that allows the propagation with compression/decompression?

*If it is possible to have no longitudinal component at all in mechanical pure-transverse waves, how do they propagate?

*I guess the wave could propagate through the friction of particles that belong to a different transverse plane. In this case, since the propagation is not directly performed through compression/decompression but via friction, could we say that pure transversal mechanical waves are not part of acoustics?
Some animations of longitudinal, transversal or a mix of the two help to think about it.
 A: It would be a misconception to hold that shear isn't a way for a general material to be loaded or for a wave to propagate, or that materials generally resist shear deformation through friction, or that S-waves are surface waves (rather, they are body waves).
Note that some of these statements are true for ideal fluids, which have a shear modulus of zero; that is, any infinitesimal shear stress is completely (and fairly quickly) relieved through flow as mediated by the viscosity. There are no long-range S-waves in fluids.
However, solids and so-called complex fluids can indeed have a well-defined shear stiffness; these materials maintain a resistance not only to dilatational loads (i.e., compressive loads) that tend to change the material's size but also to deviatoric loads (i.e., shear loads) that tend to change the material's shape. Broadly, this stiffness arises from long chains of bonding that maintain long-range order. (This effect is distinct from friction, which does not typically refer to cohesive forces within materials.)
A further nuance is that for some crystal symmetries (or lack thereof), a shear stress can cause both shear and normal strains. For simplicity, and since it doesn't alter the main thrust of this answer, let's assume sufficient symmetry (e.g., orthotropy) such that normal stresses produce only normal strains and shear stresses produce only same-plane shear strains.
Thus, applying a shear or tractional load to some plane of a material causes the adjacent region to change shape, as mediated by the shear modulus. Since that region is bonded in place, fully three other loads must arise on the side of any constituent element to prevent it from translating or rotating:


This is the essence of the shear stress state.
In turn, the tractional loads tend to shear the adjacent regions and then their adjacent regions, as mediated in part by their inertia (i.e., their density). This is the essence of the S-wave, whose velocity increases with increasing shear modulus and decreasing density.
The definition of an "acoustical wave" is merely a matter of convention; I'd be interested to see if any reference excludes shear waves other than Wikipedia, the encyclopedia that anyone can edit™. What other examples have you found in your research?
