Free and Forced Vibration Characteristics of Axially Graded Multifunctional Viscoelastic Beams

Variable performance characteristics in a multifunctional structure may be achieved by identifying suitable material candidates, and spatially varying, or grading, their material properties along the structures. Additive manufacturing (e.g. 3D printing) offers various possibilities to fabricate/manufacture such graded structures. The material properties of multifunctional composite structures, such as beams or plates, are often graded along their thickness (laminate/sandwich) or distributed in a material matrix (fibers/nanoparticles). In recent years, it has been demonstrated that by tailoring the materials in other directions (axially/radially), superior mechanical behavior and structural stability can be realized. In this research, the modeling and analyses of axially graded polymeric beams to maximize their vibration performance for a large bandwidth of frequencies and damping is presented. Polymeric materials have frequency and temperature dependent viscoelastic properties (complex modulus, glass transition temperature etc.) which can be leveraged for different applications. The goal is to spatially combine these materials such that desired longitudinal vibration characteristics (natural frequencies, damping and modes) can be achieved. To this end, the modeling for the free and forced vibration of beams with spatially varying properties, is carried out by a piecewise uniform continuous model. The spectral characteristics (natural frequency, damping ratios, and frequency response functions) of the axially graded beams are computed by solving associated transcendental eigenvalues problems. The parametric studies included the grading of polymers which are regularly used for additive manufacturing, such as ABS, PLA, etc. These results demonstrate that the response of the system can be manipulated by axial grading and optimal design/fabrication (3D printing) of multifunctional smart structures may be developed for vibration control applications.