Extraction of nonlinear elastic parameters of paper from the amplitude-dependent frequency response of cantilever beams

Tuning the hygro-mechanical response of paper-based systems using glycerol

“…This kind of dynamic behavior shows a softening effect with the excitation amplitude. This amplitudedependent behavior has been already observed in paper-based mechanical systems (Cueva-Perez et al, 2019). Furthermore, this behavior is consistent with a lumped system with a non-linear quadratic stiffness term (Leadenham and Erturk, 2014).…”

“…where V sol is the liquid volume that saturates the hydrophilic region (unwaxed region) and P t is the porosity of the material. In this work, the porosity value for the chromatography paper without wax is assumed to have a value of 68.48% (Cueva-Perez et al, 2019). Therefore, a value of 4.7 mL must be used to saturate the hydrophilic region of Sample 1 and a value of 2.35 mL to saturate the hydrophilic region of Samples 2 and 3.…”

“…In a previous study (Cueva-Perez et al, 2019), the authors pointed out that the resonance frequency response of paper-based cantilever beams can be described with a quadratic stiffness model. Similarly, this approach is used to describe the dynamic behavior of a paper-based cantilever beam using a lumped-parameter model with a quadratic stiffness element that undergoes base harmonic motion.…”

“…In this diagram, F k 1 and F k 2 and F ceq represent the forces exerted by the linear spring, non-linear spring, and damper, respectively. Afterward, the equation of motion can be derived, assuming that the paper-based cantilever beam has a quadratic non-linear stiffness component that causes an amplitude-dependent softening effect (Cueva-Perez et al, 2019). Therefore, the k 2 term is negative to be compliant with this assumption.…”

“…It should be noted that these devices are subjected to static or quasi-static loads. However, some authors have recently started to explore the mechanical response of paper when subjected to dynamic loads (Cueva-Perez et al, 2019;Perez-Cruz et al, 2017b;Wang et al, 2018a) in response to the recent growing of devices oriented toward applications such as energy harvesting.…”