Infinte Periodic Structure of Lightweight Elements: Representation of Wave Propagation

Lightweight wooden structures have become more popular as a sustainable, environmental- friendly and cost-effective alternative to concrete, steel and masonry buildings. However, there are certain drawbacks regarding noise and vibration due to the smaller weight and stiffness of wooden buildings. Furthermore, lightweight building elements are typically periodic structures that behave as filters for sound propagation within certain frequency ranges (stop bands), thus only allowing transmission within the pass bands. Hence, traditional methods based on statistical energy analysis cannot be used for proper dynamic
assessment of lightweight buildings. Instead, this paper discusses and compares the use of finite element analysis and a wave approach based on Floquet theory.
The present analysis has focus on the effect of periodicity on vibration transmission within semi-infinite beam structures. Two models of a semi-infinite Euler-Bernoulli and Timoshenko beam structure with periodic variation of the cross-sectional properties are analyzed. In case of the Euler-Bernoulli beam, vibrational behavior is studied in two dimensions by finite element analysis and Floquet theory. Wave propagation within the two-dimensional periodic Timoshenko beam structure is studied with a finite-element approach and compared with the periodic Euler-Bernoulli beam. The computations are carried out in frequency domain with the load acting as an impact load at the end of a semi-infinite beam. Results of various beam models and analytical approaches are compared and analyzed. A vibration-level distribution and propagation characteristics within the beam are presented for excitation frequencies
up to 2 kHz.