In this work, we present a systematic method to design layered periodic composites (PCs) for a prescribed elastodynamic response. Our focus is on optimization problems with equality and/or inequality constraints. Constrained optimization problems are reduced to unconstrained problems, and a genetic algorithm is used to find the optimal design. Symmetric 3-phase layered PCs are considered and the thickness of each phase is chosen as a design parameter. Three cases are presented for illustration purposes: (1) the design of an acoustic filter for maximum bandwidth, (2) the design of an acoustic filter for maximum attenuation, and (3) the design of a PC for maximum attenuation and minimum reflection of acoustic waves.
In this paper we present a method to design composites which are acoustically impedance matched with a homogeneous
medium at a desired frequency. We use dynamic homogenization of layered elastic composites to calculate their
effective acoustic impedance. It is shown that the microstructure of a layered composite can be designed so that its
acoustic impedance matches the impedance of the homogeneous medium at the desired frequency. As a result, the
reflection at the interface of such a composite with the homogeneous medium is minimized. Transfer matrix calculation
and finite element modeling of wave propagation through a layered periodic composite sandwiched between two
homogenous media are done. It is observed that at the design frequency where the composite has matched impedance
with homogenous media the reflection at the interfaces is almost zero.
In this paper we show that the bandstructure of a periodic elastic composite, in addition to being dependent upon the
micro-constituents and their microarchitecture, may also be controlled by changing the temperature. The essential idea
is to fabricate a periodic composite with constituent materials which have temperature dependent elastic properties. As
temperature is changed, such a composite is expected to exhibit a bandstructure which changes with the temperature
dependent properties of its micro-constituents. For our purpose, we use polyurea and steel to make a 1-D periodic
composite. Ultrasonic measurements are done on the sample from 0.5 kHz to 1.5 MHz under changing temperature
and the change in the second passband is studied. It is observed that the change in the bandstructure is significant when
the temperature is changed from -50°C to 50°C. Experimental results are compared with the theoretical calculations
and it is shown that good agreement exists for the observed bandstructure.
A small volume fraction of Carbon Nanotubes (CNTs) added in a polymeric matrix increases significantly the
mechanical properties of the polymers. It is experimentally determined from the TEM images of CNT-based
nanocomposites that nanotubes don't stand straight in their embedded matrix and they have some curvature in their
shape. The load transfer mechanism between CNT and polymer matrix is also one of the most important issues which is
not understood explicitly, yet. In this paper a wavy Single Walled Carbon Nanotube (SWCNT) is modeled as inclusion
in a polymer matrix and its effective mechanical properties is studied. This model is based on using 3-D Representive
Volume Element (RVE) with long wavy CNT inclusions. The CNT is modeled as a continuum hollow cylindrical shape
elastic material with some curvature in its shape. The effect of the waviness of the CNT inclusions and its parameters is
studied. We used a new approach in the modeling of interaction between the CNT/matrix at the interface. This approach
consists of modeling the physical interaction between CNT and polymeric matrix from point of view of the classical
contact phenomenon between two flexible bodies. The results of this new approach are compared with perfectly bonded
interface and also those obtained from the rule of mixtures. Results show that the Effective Young Modulus (EYM) of
the CNT-based nanocomposites for modeling the interaction of CNT/polymer from the point of view of classical contact
approach is slightly smaller than the perfectly bonded condition and is more near to experimental reports. It is also
showed that increasing the amplitude of wavy CNT or decreasing its wavelength decreases the EYM of the CNT-based
nanocomposites s which is in good agreement with the literature. There were also, a linear relation between the EYM of
the CNT-based nanocomposites and the volume fraction of CNT inclusions which was observed by the other authors.
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