Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect

Abstract

In recent years, the static and dynamic response of micro/nanobeams made of hyperelasticity materials received great attention. In the majority of studies in this area, the strain-stiffing effect that plays a major role in many hyperelastic materials has not been investigated deeply. Moreover, the influence of the size effect and large rotation for such a beam that is important for the large deformation was not addressed. This paper attempts to explore the free and forced vibrations of a micro/nanobeam made of a hyperelastic material incorporating strain-stiffening, size effect, and moderate rotation. The beam is modelled based on the Euler–Bernoulli beam theory, and strains are obtained via an extended von Kármán theory. Boundary conditions and governing equations are derived by way of Hamilton’s principle. The multiple scales method is applied to obtain the frequency response equation, and Hamilton’s technique is utilized to obtain the free undamped nonlinear frequency. The influence of important system parameters such as the stiffening parameter, damping coefficient, length of the beam, length-scale parameter, and forcing amplitude on the frequency response, force response, and nonlinear frequency is analyzed. Results show that the hyperelastic microbeam shows a nonlinear hardening behavior, which this type of nonlinearity gets stronger by increasing the strain-stiffening effect. Conversely, as the strain-stiffening effect is decreased, the nonlinear frequency is decreased accordingly. The evidence from this study suggests that incorporating strain-stiffening in hyperelastic beams could improve their vibrational performance. The model proposed in this paper is mathematically simple and can be utilized for other kinds of micro/nanobeams with different boundary conditions.

A review on the nonlinear dynamics of hyperelastic structures

“…(Permission obtained from ELSEVIER) nano-/micromaterials [123][124][125][126], which have crucial importance in new technologies. For instance, microscale beam structures made by hyperelastic materials have been studied by Alibakhshi et al [127] using the Euler-Bernoulli beam theory, modified couple stress theory (which have been used previously for studying small-scale elastic structures [128][129][130][131][132]), and Gent strain energy density model. It was shown that the force-amplitude response of the structure is highly sensitive to the stiffness parameter of Gent model (Fig.…”

Application of Surface Stress-Driven Model for Higher Vibration Modes of Functionally Graded Nanobeams

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Application of the Higher-Order Hamilton Approach to the Nonlinear Free Vibrations Analysis of Porous FG Nano-Beams in a Hygrothermal Environment Based on a Local/Nonlocal Stress Gradient Model of Elasticity

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