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

In recent years, paper has been used as an alternative to traditional substrate materials in the development of strain sensors and accelerometers due to its flexibility, disposability due to environment low footprint and low cost. A lack of knowledge about the sources of nonlinearity in the mechanical behavior of paper makes difficult to consistently predict its performance. The characterization procedures available in the literature are based on both static and dynamic loading as a first attempt to describe the elastic behavior of paper in sensing applications. However, these procedures do not reveal the necessary information to describe the elastic behavior of paper under dynamic excitation. In this work, the nonlinear dynamic response of a harmonically excited paper-based cantilever beam is studied. A lumped model with a quadratic nonlinearity is adopted to describe the nonlinear response of paper-based cantilever beams. The obtained results show that the nonlinear resonance frequency response is dependent on the intrinsic properties of paper when discarding hygrothermal variations of paper as the main source of nonlinear behavior. It was found that the estimation of two nonlinear elastic parameters, α p (hysteresis nonlinear parameter) and E 0 (linear elastic modulus) could yield an improved description of the elastic behavior of paper subjected to vibrations. It was concluded that the existing paper characterization standards should be adapted to better predict the dynamic behavior of paper-based mechanical systems. Different types of paper materials were analyzed to study the influence of the intrinsic characteristics of paper on the nonlinear parameters.