Dynamic response of a 2-2 multi-layered cement-based piezoelectric composite under arbitrary mechanical load

Theoretical analyses of the dynamic properties of a 2-2 multi-layered cement-based piezoelectric composite are presented based on the theory of piezoelasticity and D'Alembert's principle. An arbitrary mechanical load acts on the free end of the composite in the form of pressure. The Taylor series expansion method is introduced for the arbitrary mechanical load, and the theoretical solutions of the composite are obtained mainly based on the eigenfunction expansion method, Duhamel integral, and Laplace transform. Comparisons between the theoretical results, numerical results, and four related theoretical studies are presented, and good agreements are found. Furthermore, the theoretical expression of magnification factors of the composite under the harmonic load are obtained and analyzed. In addition to providing a theoretical basis for the design and experimentation of 2-2 cement-based piezoelectric composites under the arbitrary loading, the theoretical methods presented in the article could be extended to analyze the dynamic characteristics of any multilayered composite structure.