In this study, we investigated dispersion curves and the band gap structure of a multiresonator mass-in-mass lattice system. The unit cell of the lattice system consists of three separate masses connected by linear springs. It was demonstrated that the band gaps can be shifted by varying the spring constant and the magnitude of the internal masses. By using the conventional monatomic (single mass) lattice model as an equivalent system, the effective mass was found to become negative for frequencies in the band gaps. An attempt was made to represent the two-resonator mass-in-mass lattice with a microstructure continuum model. It was found that the microstructure continuum model can capture the dispersive behavior and band gap structure of the original two-resonator mass-in-mass system.

Elastic metamaterials have been extensively investigated due to their significant effects on controlling propagation of elastic waves. One of the most interesting properties is the generation of band gaps, in which subwavelength elastic waves cannot propagate through. In the study, a new class of active elastic metamaterials with negative capacitance piezoelectric shunting is presented. We first investigated dispersion curves and band gap control of an active mass-in-mass lattice system. The unit cell of the mass-in-mass lattice system consists of the inner masses connected by active linear springs to represent negative capacitance piezoelectric shunting. It was demonstrated that the band gaps can be actively controlled and tuned by varying effective stiffness constant of the linear spring through appropriately selecting the value of negative capacitance. The promising application was then demonstrated in the active elastic metamaterial plate integrated with the negative capacitance shunted piezoelectric patches for band gap control of both the longitudinal and bending waves. It can be found that the location and the extent of the induced band gap of the elastic metamaterial can be effectively tuned by using shunted piezoelectric patch with different values of negative capacitance, especially for extremely low-frequency cases.

A microstructure design of anisotropic resonant inclusions is investigated for the elastic metamaterial plate with the aid of the numerically based effective medium model. Experimental validation is then conducted in the anisotropic metamaterial plate through both harmonic and transient wave testing, from which the anisotropic effective dynamic mass density, group, and phase velocities are determined as functions of frequency. The strongly anisotropic mass density along two principal orientations is observed experimentally and the prediction from the experimental measurements agrees well with that from the numerical simulation. Finally, based on the numerically obtained effective dynamic properties, a continuum theory is developed to simulate different guided wave modes in the elastic metamaterial plate. Particularly, high-order guided wave coupling and repulsion as well as the preferential energy flow in the anisotropic elastic metamaterial plate are discussed.

Elastic waves, especially guided waves, generated by a piezoelectric actuator/sensor network, have shown great potential for on-line health monitoring of advanced aerospace, nuclear, and automotive structures in recent decades. Piezoelectric materials can function as both actuators and sensors in these applications due to wide bandwidth, quick response and low costs. One of the most fundamental issues surrounding the effective use of piezoelectric actuators is the quantitative evaluation of the resulting elastic wave propagation by considering the coupled piezo-elastodynamic behavior between the actuator and the host medium. Accurate characterization of the local interfacial stress distribution between the actuator and the host medium is the key issue for the problem. This paper presents a review of the development of analytical, numerical and hybrid approaches for modeling of the coupled piezo-elastodynamic behavior. The resulting elastic wave propagation for structural health monitoring is also summarized.

In the study, a retrieval approach is extended to determine the effective dynamic properties of a finite multilayered acoustic metamaterial based on the theoretical reflection and transmission analysis. The accuracy of the method is verified through a comparison of wave dispersion curve predictions from the homogeneous effective medium and the exact solution. A multiresonant design is then suggested for the desirable multiple wave band gaps by using a finite acoustic metamaterial slab. Finally, the band gap behavior and kinetic energy transfer mechanism in a multilayered composite with a periodic microstructure are studied to demonstrate the difference between the Bragg scattering mechanism and the locally resonant mechanism.