Dynamic bending of an oak board due to a moisture content gradient

When an oak board is exposed to moisture on only one of its surfaces, an asymmetric moisture content profile induces differential expansion over the thickness. Consequently, a bending moment causes the board to curve. Meanwhile, moisture transport takes place, which results in a continuously changing bending moment. When exposed to a step change in the moisture content, the end of the board deflects to a maximum, after which the board, due to moisture transport, deflects back to its initial x-position. The y-position of the free end of the board changes continuously too, but reaches a different value eventually due to a different moisture content. In real-life applications, however, objects are most often exposed to continuous or cyclic changes in the relative humidity. It is shown that the deflective step response of the board contains information about its frequency behavior. When assuming linear system behavior, the frequency response can be predicted from the step response. Experiments with a sinusoidal fluctuation in relative humidity at different frequencies confirm the prediction from the step response.