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Transient response of a hygrothermoelastic cylinder based on fractional diffusion wave theory

ABSTRACT A coupled fractional hygrothermoelasticity theory is formulated within the framework of fractional calculus. Both the classical Fourier’s and Fick’s laws are generalized to anomalous diffusion which is characterized by the time- fractional diffusion-wave equation. Based on the fractional hygrothermoelasticity theory, the transient response of an infinitely long cylinder subjected to hygrothermal loadings at the surface is analyzed. The finite Hankel integral transform method and decoupled technique are used to derive closed-form expressions for temperature, moisture, displacement, and hygrothermal stresses in the solid. The coupling effect of temperature and moisture on elastic fields is discussed. Numerical results of transient response of hygrothermoelastic fields are presented graphically for the cases of subdiffusion, normal diffusion, and superdiffusion, respectively.