Free vibration of polar orthotropic circular plates with elastic growth stresses and drying stresses

This study was performed to analyze effect of transverse growth stresses and drying stresses on natural frequencies of transverse free vibration of thin tree disk with free boundary condition. Using Rayleigh–Ritz method and finite element method, explicit closed form expression was derived for homogeneous orthotropic circular plates with internal stresses, which enables to predict both the effects of growth stresses, drying stresses, and combined growth and drying stresses on the natural frequency changes. This model can be used for predicting growth stresses from known natural frequencies. The same approach can also be undertaken to validate models visco-elastic drying stresses.