Caglar Oskay delivered an invited lecture at the Ohio State University – 11/02/2018
Lecture Title: Viscoelastic Phononic Crystals: Unraveling Their Dynamic Behavior through Multiscale Modeling and Simulation
Location: Mechanical and Aerospace Engineering Department, Ohio State University, Columbus, OH.
Acoustic wave propagation in manufactured composite materials such as phononic crystals and metamaterials has been receiving tremendous interest from the research community as well as many industries. This is because of the opportunities these materials present for achieving unique dynamic properties within targeted frequency ranges, such as near-complete wave attenuation within acoustic band gaps. Such unique properties of these materials can be leveraged to create many novel engineering applications including acoustic cloaking, acoustic diodes, wave guides, impact mitigators and others. It has been recently recognized that employing viscoelastic constituents in design of phononic crystals and metamaterials could significantly expand possibilities by leveraging interactions between material damping and heterogeneity induced dispersion by shifting the stop band to lower frequencies and enhancing wave attenuation.
We present a multiscale computational methodology to simulate the transient wave propagation in phononic crystals, accounting for wave dispersion and attenuation due to material heterogeneity and damping. The proposed approach is formulated through asymptotic homogenization with higher order corrections incorporated to extend the applicability of the homogenization theory to short wavelength regime. We consistently derive a spatially and temporally nonlocal model that accurately captures the dispersive behavior of the composite up to the optical regime. We also propose a reduced order modeling approach that retains the dispersive character of the nonlocal model but efficiently simulates high frequency wave propagation at the structural scale without the numerical complications that come with using high order models. The capabilities of the approach are demonstrated in the context of multi-modal transient wave propagation in structures made of elastic and viscoelastic phononic crystals.