Vibration analysis of sandwich beams with viscoelastic coating described by fractional constitutive equation

Numerical analysis of the dynamic characteristics of a fractional-order viscoelastic beam with fixed supports at both ends

“…Assuming that the fractional-order viscoelastic beam satisfies the Kelvin-Voigt fractional order model, its stress-strain relationship is given by (Xu et al, 2020a) s(x, z, t) = E 0 (x)e(x, z, t)…”

“…where, σ ( x , z , t ) is the stress at the point with a distance of z from the neutral axis on the cross-section. Assuming that the fractional-order viscoelastic beam satisfies the Kelvin-Voigt fractional order model, its stress-strain relationship is given by (Xu et al, 2020a)…”

“…For instance, Martin's improved variational iteration method has demonstrated notable proficiency in the dynamic analysis of simply supported viscoelastic beams utilizing the fractional Zener model, which has shown good performance in solving fractional differential equations (Olga, 2019). In recent work, Xu et al (2020aXu et al ( , 2022 explored the dynamic characteristics and steady-state response of fractional order viscoelastic beam structures employing the wave propagation method. Chen et al (2015) applied the wavelet method to solve nonlinear fractional differential equations, offering a different perspective on solving complex problems.…”

New control strategy for suppressing the local vibration of sandwich beams based on the wave propagation method

“…In our previous study (Xu et al, 2020a), the fractional dynamic equation of a viscoelastic film-covered sandwich beam under external excitation q(x, t) was established:…”

“…Guo et al (2020a) investigated the transient thermoviscoelastic response of viscoelastic laminated sandwich composite structures based on the fractional generalized thermo-viscoelasticity theory and formed a basis for subsequent theoretical research on the vibration control of composite structures under extreme nonisothermal conditions. In the recent work of authors, the wave propagation method was generalized to analyse the dynamic characteristics of viscoelastic beams (Xu et al, 2020b) and sandwich beams with viscoelastic membranes (Xu et al, 2020a), both of which were described by the fractional constitutive equation.…”