Session: 03-02 Wave Propagation, Buckling, and Dynamic Response

Paper Number: 171943

171943 - Local Stiffness Variation and Natural Frequencies of Postbuckled Beams 

Lattice-based metamaterials can be designed to isolate vibrations within a certain band of frequencies (known as the bandgap) enabling selective reduction of undesirable vibration modes. As a metamaterial’s bandgap depends on the geometry and vibration properties of the metamaterial unit cells, the bandgap typically cannot be changed post-fabrication, which limits the potential applications. Alternatively, metamaterial unit cells with dynamically tunable bandgaps may be desirable to mitigate structural vibrations in spacecraft and automotive components. Because the metamaterial’s bandgap is influenced by the unit cell geometry, one method to dynamically tune the bandgap post-fabrication is by changing the unit cell’s shape through buckling. The metamaterial unit cells could be further simplified as a combination of compliant elements modelled as beams. Therefore, the investigation of the influence of a buckled beam’s local stiffness on its vibration characteristics is highly important.

In this study, we investigate the effect of locally varying the stiffness of a buckled beam on its buckled shape, and how the buckled shape then affects the beam’s vibration characteristics. In this study, two-dimensional solid beams with fixed-guided boundary conditions are considered using commercial finite element analysis (FEA) software. We begin by discretising the beam into equal sections along the length and then locally varying the stiffness of each section. Next, the buckling of the beams with various stiffness distributions is predicted using FEA. The results are then used in calculating the deviation of the postbuckled beam’s deformed shape from a user-defined baseline case using the shape error metric. Following the buckling analysis, the first natural frequency of the postbuckled beams is calculated in order to evaluate the change in their vibrational characteristics in relation to the baseline case. In parallel, we also investigate the extent to which local stiffness affects the postbuckled shape and vibration characteristics of the beam by varying the ratio of elastic moduli of low and high stiffness regions.

Results show that an asymmetric distribution of stiffnesses leads to an asymmetric postbuckling deformation of the beam. Similarly, symmetric distribution of stiffnesses leads to symmetric postbuckling deformation.  Moreover, the distinct postbuckled configurations possess distinct natural frequencies as well. Interestingly, the natural frequency of the postbuckled beam primarily depends on the effective elastic modulus of the beam, which is calculated using the area ratio of low and high stiffness regions in the beam. Nevertheless, the stiffness distribution has a small effect on natural frequency as well. In contrast, the target shape error in the postbuckled shape of the beam depend on the stiffness distribution, effective modulus, and the ratio of elastic moduli of the two materials in the beam. Also, both the shape error and first natural frequency increase with increasing ratio of elastic moduli.

Using the results of this study, the postbuckled shape can be tuned by varying the stiffness distribution of the beam. This tunability could be physically realized through the integration of lattice metamaterials with shape memory materials that tune the local stiffness thermally. This could, in turn, offer enhanced postbuckled shape control.  Thus, the results of this paper will enable the inverse design of a lattice metamaterial with improved bandgap via enhanced tunability of dynamically postbuckled shape of the compliant members.

Presenting Author: Prasanna Mondal The Pennsylvania State University

Presenting Author Biography: I am pursuing my PhD from Mechanical Engineering department of The Pennsylvania State University. My principal investigator is Dr. Mary Frecker. I joined the EDOG group in Fall 2024, to work on shape memory material-based lattice metamaterials. I am interested in mechanical design, strength of materials, engineering mechanics, structural dynamics, optimization, etc.
I enjoy writing stories, drawing, cooking and playing cricket in my leisure time. Also, I am curious about cultures and traditions of communities from various parts of the world.