Use of a multilayer structure or an object comprising at least one multilayer structure, to dampen shocks, vibrations and/or soundwaves, the said multilayer structure comprising at least two contiguous layers, called first and second layers, the first layer comprising at least one rigid material and the second layer comprising at least one supramolecular material having good adherence to the layer comprising the rigid material, and the said multilayer structure being obtained according to a method comprising at least the following steps: (i) a step of pouring a composition comprising at least one precursor of supramolecular material in contact with a layer comprising at least one rigid material, in order to form together two contiguous layers, the said precursor being obtained by at least the following successive steps: (a) the reaction of at least one at least trifunctional compound selected from trimers or mixtures of trimers and dimers of plant-derived fatty acids, with at least one compound having, on the one hand, at least one reactive group capable of reacting with the reactive functions of, and on the other hand, at least one associative group selected from the groups imidazolidonyl, triazolyl, triazinyl, bis-ureyl, ureido-pyrimidyl, (b) the mixing of the compound(s) obtained in step (a) with at least one at least difunctional compound, the reactive functional groups whereof are capable of reacting with the reactive functional groups of the compound during the curing stage (ii), in order to form ester or thioester bridges, alone or in combination with amide or urea bridges. the said rigid material being selected from glass, wood, metals or alloys thereof, ceramics, polar thermoplastic polymers, charged or not, thermosetting resins, concretes, mortars, plasterers, and (ii) a curing step performed so as to convert the said precursor into supramolecular material having a Delta tangent of more than 0.5, over a broad temperature range of at least 30°C, as measured by dynamic thermomechanical analysis. (i) a step of pouring a composition comprising at least one precursor of supramolecular material in contact with a layer comprising at least one rigid material, in order to form together two contiguous layers, the said precursor being obtained by at least the following successive steps: (a) the reaction of at least one at least trifunctional compound selected from trimers or mixtures of trimers and dimers of plant-derived fatty acids, with at least one compound having, on the one hand, at least one reactive group capable of reacting with the reactive functions of, and on the other hand, at least one associative group selected from the groups imidazolidonyl, triazolyl, triazinyl, bis-ureyl, ureido-pyrimidyl, (b) the mixing of the compound(s) obtained in step (a) with at least one at least difunctional compound, the reactive functional groups whereof are capable of reacting with the reactive functional groups of the compound during the curing stage (ii), in order to form ester or thioester bridges, alone or in combination with amide or urea bridges. the said rigid material being selected from glass, wood, metals or alloys thereof, ceramics, polar thermoplastic polymers, charged or not, thermosetting resins, concretes, mortars, plasterers, and (a) the reaction of at least one at least trifunctional compound selected from trimers or mixtures of trimers and dimers of plant-derived fatty acids, with at least one compound having, on the one hand, at least one reactive group capable of reacting with the reactive functions of, and on the other hand, at least one associative group selected from the groups imidazolidonyl, triazolyl, triazinyl, bis-ureyl, ureido-pyrimidyl, (b) the mixing of the compound(s) obtained in step (a) with at least one at least difunctional compound, the reactive functional groups whereof are capable of reacting with the reactive functional groups of the compound during the curing stage (ii), in order to form ester or thioester bridges, alone or in combination with amide or urea bridges. (ii) a curing step performed so as to convert the said precursor into supramolecular material having a Delta tangent of more than 0.5, over a broad temperature range of at least 30°C, as measured by dynamic thermomechanical analysis.