Understanding the mechanical properties of bio-adsorbates at the pathological state is important in mechanobiology and medical diagnosis. With the development of biodetection technology, the mechanical properties of bio-adsorbates can be detected at microscale. The paper presents an integro-partial-differential theoretical model to elucidate the effect of adsorbate viscoelasticity on vibrational properties of elastic–viscoelastic microcantilever. A differential method in the temporal domain and a variable separation method or a differential quadrature method (DQM) in the spatial domain are combined to obtain the relevant analytical solutions for free vibration with a complete adsorption and numerical solutions for forced vibration with a local adsorption. The present results agree well with the previous studies in the case of complete elastic adsorption. The study shows that the amplitude of a weakly damped free vibration of the microcantilever is positively correlated with the reciprocal of relaxation time of adsorbate film; the dissipative mechanical property of adsorption film with a standard linear solid constitutive relation endows the forced vibration of the microcantilever subjected to a transverse harmonic load with a double-peak resonance; and the sensitivity of microcantilever-based dynamic detection can be improved remarkably if the excitation frequency, film-to-substrate thickness/modulus ratio, adsorption position/area are carefully controlled.
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