Dynamic instability of axially moving viscoelastic plate

Modeling and dynamic analysis of axially moving variable fractional order viscoelastic plate

“…Consider the external load perpendicular to the plate acting on the axially moving viscoelastic plate, as shown in Figure 1, where q(x, 𝑦, t) is the external excitation, w(x, 𝑦, t) as the displacement in the z direction, and h and v are the thickness and speed of the plate, respectively. Based on Zhou and Wang [31], the motion equation of axially moving viscoelastic plate under external excitation is obtained…”

“…Based on Zhou and Wang [31], the motion equation of axially moving viscoelastic plate under external excitation is obtained $$$$ \frac{\partial^2{M}_x}{\partial {x}^2}+2\frac{\partial^2{M}_{xy}}{\partial x\partial y}+\frac{\partial^2{M}_y}{\partial {y}^2}-\rho h\left(\frac{\partial^2w\left(x,y,t\right)}{\partial {t}^2}+2v\frac{\partial^2w\left(x,y,t\right)}{\partial x\partial t}+{v}^2\frac{\partial^2w\left(x,y,t\right)}{\partial {x}^2}\right)=q\left(x,y,t\right), $$$$ where $$$ \rho $$$ is volumetric mass density, $$$ {M}_x $$$ and $$$ {M}_y $$$ are bending moments, and $$$ {M}_{xy} $$$ is twisting moment; their relationship to stress is as follows: …”

Thermoelastic characteristics of moving viscoelastic nanobeams based on the nonlocal couple stress theory and dual-phase lag model

“…Their study examined the evolution of mathematical models for axially moving systems and vibration analysis methodologies during the last 60 years. Zhou and Wang [25] studied the transverse resonance and dynamic stability of a longitudinally moving viscoelastic plate with different boundary conditions. Shariati et al [26] investigated the vibrational behavior of an axially moving viscoelastic Rayleigh beams with variable material properties.…”

Stability and vibration analysis of an axially moving thin walled conical shell

“…For example, increasing the axial velocity will decrease the natural frequency. The vibration and dynamic stability of the axially moving viscoelastic plate have been investigated by Zhou and Wang (2019). Support of plate for two opposite edges was simple, and the other two opposite edges were simple or free.…”