Journal of Computational Applied Mechanics

Dynamic Response and Damping of Viscoelastic Microtubules: Effects of N_S Configurations and Cytosolic Environments

Document Type : Research Paper

Authors

1 Ph.D. student Mech. Eng., Faculty of Mechanical Engineering, Kashan University, Kashan

2 Professor, Mech. Eng, Faculty of Mechanical Engineering, Kashan University, Kashan

3 MD student, Medical School. Medical university of Kashan, Kashan

Abstract

This study investigates the vibrational behavior of anisotropic microtubules (MTs) immersed in the viscous cytosolic fluid using both classical and higher-order beam theories (HOBTs). For the first time, multiple N_S configurations of MTs, along with their precise geometrical characteristics, are analyzed within a novel unified vibration–mechanics framework. The nonlocal strain gradient theory (NSGT) is employed to incorporate size-dependent effects, while surface elasticity theory ensures nanoscale accuracy. Viscoelastic models are integrated for both MTs and their surrounding medium.
The intrinsic structural damping of microtubules is examined via the Kelvin–Voigt viscoelastic damping coefficient (retardation time), and the influence of the cytosolic viscous fluid damping on both natural frequencies and damping ratios is thoroughly analyzed. Additional parameters such as the nonlocal parameter, material length scale parameter, microtubule length and various beam theory are also systematically explored. The governing equations and boundary conditions are derived from Hamilton’s principle and numerically solved using the Differential Quadrature (DQ) method, enhanced with a CBCGE scheme for efficient boundary implementation.
Results reveal that increasing either the structural damping of the MTs or the cytosolic fluid viscosity leads to greater overall damping and a reduction in natural frequencies. A critical retardation time is identified, beyond which the damping ratio rapidly increases, the natural frequencies sharply drop, and the system transitions to a non-oscillatory state. The magnitude of this critical time aligns well with previously reported nanoscale retardation times.
The same trend is also observed across different N_S configurations, indicating that smaller microtubules tend to possess higher natural frequencies. These findings highlight the importance of viscoelastic behavior—particularly retardation effects—in understanding cellular mechanics, cancer treatment, disease diagnosis, and bio-nanotechnology advancements.

Keywords

Main Subjects

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Journal of Computational Applied Mechanics
Volume 57, Issue 3
July 2026
Pages 473-496
  • Receive Date: 31 December 2025
  • Revise Date: 15 April 2026
  • Accept Date: 16 April 2026