Nonlinear Vibration Control and Stability Analysis of a Cantilever Composite Laminated Plate in Hygrothermal Environment

Composite plates find extensive use in aerospace and marine industries due to light weight, high strength-to-weight ratio and large stiffness. Their stiffness or natural frequency changes due to variation in environmental conditions such as temperature and moisture, and thus their dynamic performance can be adversely affected. Therefore, a nonlinear energy sink (NES) based vibration absorber is proposed that remains effective in a wide range of frequency change.

A cantilever composite laminated plate (CCLP) is modelled using classical laminate plate theory. Moreover, dynamics of the plate-NES system is expressed by Euler–Lagrange equation; discretized in two fixed-free and two free-free modes using the Galerkin method. As the free end is more prone to vibration under excitation, first two resonant peaks in free-free direction of the plate are extensively studied in hygrothermal environment- with and without NES. The particle swarm optimization is used to optimize the NES parameters.

Numerical analysis shows that the optimal NES decreases the first mode’s peak amplitude by about 70% and dissipates 68% of the vibration energy, for temperature variation of 20 K and the moisture change of 0.10%. Moreover, the second peak is also reduced by 66.67% for the same hygrothermal conditions. From the numerical analysis, quasi-periodic and phase-locked responses are seen at some points in the amplitude–frequency curve; further explored through post-transient phase portraits, time histories, and Poincaré maps. Moreover, the changes in qualitative behaviour of the CCLP-NES system by varying the NES parameters are examined from the amplitude–frequency curves. A higher NES stiffness and mass increase resonant amplitudes and therefore, the unstable band. Conversely, increased NES damping reduces resonant peaks and the unstable band.

The NES works effectively for a range of temperature and moisture variation as well as excitation amplitudes. The study notes jump phenomena near nonlinear resonance peaks at higher NES stiffness and excitation amplitudes, which also widens the unstable band between Limit-Point bifurcation points. Physical realization of the proposed NES can be the focus of the future research.