Nonlinear vibration behavior of metal foam structures

Metal foam structures (MFS) show promising static and dynamic performances with some initial real-life applications. However, the dynamic behavior of MFS is not thoroughly addressed yet, which is one of the reasons that limits their use. This thesis studies their nonlinear vibration behavior for better understanding and further development of this structural material. Theoretical models are developed in this thesis to study nonlinear free and forced vibrational behavior of beams with bidirectional porosities, where the voids are non-uniformly distributed through the length and thickness of the beam. Moreover, effect of porosities on nonlinear natural frequencies of cylindrical panels is studied as well. In addition, a few novel porosity distributions are proposed to improve the vibrational response of the metal foam structures. The dynamic governing equations are derived based on the third-order shear deformation theory, Hamilton’s principle and von Kármán geometrical nonlinearity. The governing equations are solved using numerical and analytical methods (method of multiple scales and harmonic balance method) based on the problem type. Generalized differential quadrature method (GDQM) is one of the utilized numerical methods due to its simplicity and low computational cost. However, the GDQM has some limitations in implementing boundary conditions, thus to overcome this issue, a novel and simple approach is proposed in this study. Elastic properties of the composite metal foams (CMFs) are evaluated using homogenization technique and finite element simulation. CMFs are a new class of closed-cell porous materials that can be produced by distributing metallic spheres in a metallic matrix. The CMFs have better mechanical performance than the regular metal foams. Studying the effect of microporosities in spheres’ wall and matrix of the CMFs revealed that the matrix microporosity has higher effect on the CMFs elastic modulus than the spheres’ microporosity. Furthermore, results revealed that increasing the packing factor and spheres wall thickness increases the CMFs elastic modulus. Finally, it is shown that the CMF structures could have better vibrational response in comparison to the regular metal foam structures. This allows widespread use of CMFs as a new and attractive type of metal foam.Applied Science, Faculty ofMechanical Engineering, Department ofGraduat