We study wave propagation in periodic materials with dissipation using two different formulations. An -formulation yields complex frequency solutions for nonvanishing dissipation whereas a -formulation leads to complex wave numbers. For small (realistic) levels of material dissipation and longer wavelengths, we show that the two formulations produce nearly identical results in terms of propagation constant and wave decay. We use the -formulation to compute loss factors with dissipative bandgap materials for steady-state wave propagation and create simplified diagrams that unify the spatial loss factor from dissipative and bandgap effects. Additionally, we demonstrate the applicability of the -formulation for the computation of the band diagram for viscoelastic composites and compare the computed loss factors for low frequency wave propagation to existing results based on quasi-static homogenization theory.
Skip Nav Destination
Article navigation
August 2013
Research-Article
Analysis of Phononic Bandgap Structures With Dissipation
Jakob S. Jensen
Jakob S. Jensen
e-mail: jsj@mek.dtu.dk
Department of Mechanical Engineering,
Department of Mechanical Engineering,
Technical University of Denmark
,Building 404
, 2800 Denmark
Search for other works by this author on:
Jakob S. Jensen
e-mail: jsj@mek.dtu.dk
Department of Mechanical Engineering,
Department of Mechanical Engineering,
Technical University of Denmark
,Building 404
, 2800 Denmark
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 14, 2012; final manuscript received February 12, 2013; published online June 6, 2013. Assoc. Editor: Massimo Ruzzene.
J. Vib. Acoust. Aug 2013, 135(4): 041015 (8 pages)
Published Online: June 6, 2013
Article history
Received:
May 14, 2012
Revision Received:
February 12, 2013
Citation
Andreassen, E., and Jensen, J. S. (June 6, 2013). "Analysis of Phononic Bandgap Structures With Dissipation." ASME. J. Vib. Acoust. August 2013; 135(4): 041015. https://doi.org/10.1115/1.4023901
Download citation file:
Get Email Alerts
Reduced-Order Modeling in Rotordynamics and Its Robustness to Random Matrix Perturbation
J. Vib. Acoust (February 2024)
Reviewer's Recognition
J. Vib. Acoust (February 2024)
Active Regulation of Elastic Waves in a Type of Two-Dimensional Periodic Structures With Piezoelectric Springs
J. Vib. Acoust (February 2024)
Related Articles
Tuning Band Structures of Two-Dimensional Phononic Crystals With Biasing Fields
J. Appl. Mech (September,2014)
Wave Directionality in Three-Dimensional Periodic Lattices
J. Appl. Mech (January,2018)
Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook
Appl. Mech. Rev (July,2014)
Band Gap Formation and Tunability in Stretchable Serpentine Interconnects
J. Appl. Mech (September,2017)
Related Proceedings Papers
Related Chapters
Electronic Properties of a Two-Dimensional Ring-Shaped Kronig-Penney Lattice with a Positional Disorder
International Conference on Mechanical and Electrical Technology, 3rd, (ICMET-China 2011), Volumes 1–3
Conclusion
Introduction to Finite Element, Boundary Element, and Meshless Methods: With Applications to Heat Transfer and Fluid Flow
Fast Fracture Simulated by Conventional Finite Elements: A Comparison of Two Energy-Release Algorithms
Crack Arrest Methodology and Applications