Cheng Jianchun

Complete Band Gaps for Lamb Waves in Cubic Thin Plates with Periodically Placed Inclusions

We present a theoretical study for propagation of Lamb waves in cubic thin plates consisting of solid inclusions placed periodically in the host material. The dispersion curves of Lamb waves propagating parallel to the surfaces of the plates are calculated based on the plane wave expansion method for triangular lattices. We realize the existence of full band gaps in the systems composed of W cylinders embedded in a Si matrix with filling ratio f = 0.176 for different thickness ratios of h/a, where h is the plate thickness and a is the lattice spacing.

Investigation of a silicon-based one-dimensional phononic crystal plate via the super-cell plane wave expansion method

The super-cell plane wave expansion method is employed to calculate band structures for the design of a silicon-based one-dimensional phononic crystal plate with large absolute forbidden bands. In this method, a low impedance medium is introduced to replace the free stress boundary, which largely reduces the computational complexity. The dependence of band gaps on structural parameters is investigated in detail. To prove the validity of the super-cell plane wave expansion, the transmitted power spectra of the Lamb wave are calculated by using a finite element method. With the detailed computation, the band-gap of a one-dimensional plate can be designed as required with appropriate structural parameters, which provides a guide to the fabrication of a Lamb wave phononic crystal.

The Band Gaps of Plate-Mode Waves in One-Dimensional Piezoelectric Composite Plates: Polarizations and Boundary Conditions

Theoretical studies are presented for the band structures of plate-mode waves in a one-dimensional (1-D) phononic crystal plate consisting of piezoelectric ceramics placed periodically in an epoxy substrate. The dependences of the widths and starting frequencies of first band gaps (FBG) on the filling fraction and the thickness to lattice pitch ratio are calculated for different polarizations of piezoelectric ceramics under different electric boundary conditions, i.e., short circuit (SC) and open circuit (OC). We found that the FBG always is broadened by polarizing piezoelectric ceramics, and the FBG widths with SC always are larger than that with OC for the same polarization. Our research shows that there are three critical parameters which determine the FBG: the polarized directions, the filling fraction, and the ratio of the plate thickness to the lattice pitch, respectively. Therefore, we can control the width and starting frequency of the FBG in the engineering according to need by choosing these parameters of the system.

Elastic Wave Propagation in Two-Dimensional Ordered and Weakly Disordered Phononic Crystals

Elastic wave propagation in two-dimensional solid-solid ordered and weakly disordered phononic crystals is studied by using finite-difference time-domain method. Theoretical results show that obvious band gaps in the ordered crystal could be found, while in the weakly disordered ones the band gaps could partially vanish. Furthermore, with increase of disorder, band gaps are destructed badly and prominently in the high frequency regime while slightly in the low regime. Comparing the energy transmission dependent on time, we find that the coda wave phenomenon is prominent in the ordered crystal while weakened in the weakly disordered ones, and the physical properties are discussed.

Modelling of Laser-Generated Guided Waves in Bonded Plates with a Weak Interface by the Two-Layer Normal Mode Expansion Method

The two-layer normal mode expansion method is employed to analyse the laser-generated elastic guided waves in bonded plates accounting for the adhesive bond layer in terms of a weak interface with the spring model. The sensitivity of dispersion and transient characteristics of the guided wave to the stiffness coefficients characterizing the cohesive quality is analysed in details. This method provides a new promising way for the characterization of the cohesive quality in bonded plates.

Experimental and Theoretical Evidence for the Existence of Broad Forbidden Gaps in the Three-Component Composite

The influence of localized resonance on the properties of band-gaps of the two-dimensional periodic composite are analysed numerically and experimentally by comparing the two-component phononic crystal with the three-component one. The three-component composite which exhibits localized resonance in the elastically soft coating ring is composed of a square array of coated cylinders embedded in an epoxy resin. The coated cylinders consist of a steel inner core and a rubber coating, which has much smaller wave velocity and mass density than the matrix and the inner material. The measured transmission power of the three-component composite drops to the noise level in a broad ultrasonic frequency interval in contrast to the binary composite, which is in good agreement with the calculation using the finite element method.

Local resonant characteristics of a layered cylinder embedded in the elastic medium

Three kinds of resonant modes of a single layered circular elastic cylinder embedded in the elastic medium are analysed by considering the oscillation of the scatters core, based on the fact that the core moves as a rigid body when the shell material is very compliant. The resonant frequencies of the single resonator acquired by our method are in good agreement with those calculated by the local interaction simulation approach (LISA) for the local resonant phononic crystal. Therefore, the local resonant characteristics of a single layered circular elastic cylinder can be used to evaluate the resonant frequencies of the phononic crystal. The effects of the geometrical and physical parameters of the shell and the core are also studied in details. This work is significant for designing the locally resonant phononic crystal based on the local resonant characteristics of the single resonator and the resonant frequencies can be tuned by selecting the geometrical sizes and the materials.

Concealing a Passive Sensing System with Single-Negative Layers

We propose a multi-layer structure for concealing an electromagnetic sensing system (a sensor is wrapped with a transparent protective layer), using single-negative (SNG) materials whose material parameters are completely independent of those of the host matrix as well as the concealed system. The numerical results show that only three different kinds of SNG materials are sufficient to yield the cloaking effect even in the presence of weak loss. This may significantly facilitate the experimental realization of a well-performing sensor-cloaking device.

A Unique Method to Describe the Bonding Strength in a Bonded Solid–Solid Interface by Contact Acoustic Nonlinearity

We present a unique method to describe the bonding strength at a bonded solid–solid interface in a multilayered composite material by contact acoustic nonlinearity (CAN) parameter. A CAN model on the bonded solid–solid interface is depicted. It can be seen from the model that CAN parameter is very sensitive to the bonding strength at the interface. When an incident focusing acoustic longitudinal wave scans the interface in two dimensions, the transmitted wave can be used to extract CAN parameter. The contour of the bonding strength for a sample is obtained by CAN parameter. The results show that the region with weak bonding strength can be easily distinguished from the contour.

Homogenization of Two-Dimensional Phononic Crystals at Low Frequencies

Effective velocities of elastic waves propagating in two-dimensional phononic crystal at low frequencies are analysed theoretically, and exact analytical formulas for effective velocities of elastic waves are derived according to the method presented by Krokhin et al. [Phys. Rev. Lett. 91 (2003) 264302]. Numerical calculations for phononic crystals consisted of array of Pb cylinders embedded in epoxy show that the composites have distinct anisotropy at low filling fraction. The anisotropy increases as the filling fraction increases, while as the filling fraction closes to the limitation, the anisotropy decreases.