Dynamics of 1D mass–spring system with a negative stiffness spring realized by magnets: Theoretical and experimental study

Realization of negative stiffness （NS） in damping low frequency acoustic and mechanical vibration is relevant in engineering applications. In this work, assemblage of two repelling magnets was used to produce negative magnetic spring （NMS）. A mass-spring system with NMS is experimented where the free and forced vibrations of the system are examined. The anti-phase movement is observed due to the presence of proposed NMS, confirming the analytical solution. We further showed the dynamics of the system containing NS spring could also be derived from Hamilton＇s principle.

Experimental study on interaction between a positive mass and a negative effective mass through a mass–spring system

We investigate the interaction between a positive mass and a negative effective mass through a three- mass chain connected with elastic springs, a pair of masses is designed to have an effective negative mass, and it interacts with the third positive one as if an equivalent two-mass chain. The dynamics of the equivalent two-mass chain shows that the two bodies may be self-accelerated in same direction when the effective mass becomes negative, the experiment is also conducted to demonstrate this type of motion. We further show that the energy principle （Hamilton＇s principle） is applicable if the energy of the negative mass unit is properly characterized. The result may be relevant to composite with cells of effective negative mass, their interaction with matrix may lead to more richer unexpected macroscopic responses.

Design of elliptical underwater acoustic cloak with truss-latticed pentamode materials

Pentamode acoustic cloak is promising for underwater sound control due to its solid nature and broadband efficiency,however its realization is only limited to simple cylindrical shape.In this work,we established a set of techniques for the microstructure design of elliptical pentamode acoustic cloak based on truss lattice model,including the inverse design of unit cell and algorithms for latticed cloak assembly.The designed cloak was numerically validated by the well wave concealing performance.The work proves that more general pentamode acoustic wave devices beyond simple cylindrical geometry are theoretically feasible,and sheds light on more practical design for waterborne sound manipulation.

Underwater Directional Acoustic Source Based on Pentamode Material

An underwater directional acoustic emitter is conceived with a highly anisotropic lattice material,whose acoustic characteristics manifest strong dependence on the orientation of the lattice material’s principal axis.Exploiting these features,a cylindrical structure made of such anisotropic lattice material is engineered to possess distinct impedance values in different directions,thereby facilitating wave emission along the principal axis while inducing reflection in other directions.Notably,through numerical simulations,it is demonstrated that the emission direction can be effectively manipulated by adjusting the principal axis orientation,concurrently enhancing the emitted power.In contrast to previous directional acoustic structures,the compact emitter presented in this study can get rid of the size-wavelength constraint,enabling effective control of low-frequency waves.

Some topics on elastic metamaterials

Acoustic metamaterials are composite materials that exhibit effective material properties beyond those of their constituent materials.By engineering negative properties,such as modulus,mass density,refractive index,and thermal expansion coefficient from positive constituents,these materials offer a range of mechanical and acoustic properties,as well as transport and stimuli-responsive characteristics.Wave mitigation and vibration suppression are popular applications of acoustic metamaterials,with band gap formation and artificial damping being the primary strategies.Recent research has also leveraged the principles of topological insulators in electronics and photonics to realize phononic topological phases,leading to robust mechanical boundary modes that are resistant to defects and geometric perturbations.Additionally,the emergence of acoustic nonreciprocity has led to new wave-related strategies such as acoustic diodes,unidirectional invisibility,and autonomous robots.

Odd elasticity realized by piezoelectric material with linear feedback

The systems exhibiting sustainable external energy exchange are abundant,e.g.,biological organisms’reaction to external stimuli while maintaining a constant energy exchange with the surrounding.In a linear mechanical system exhibiting an external energy gain or release,the recently proposed odd elasticity theory can characterize the overall stress and strain response.However,realizing the required odd elasticity is still challenging.In this work,we discovered that the smart materials with designed feedbacks can achieve this odd elasticity,thereby providing a practical platform to analyze the phenomenon related to this novel elasticity theory.We also demonstrated this idea by designing a non-reciprocal Rayleigh wave via odd elasticity and the equivalent piezoelectricity with linear feedback.The underpinned electric energy scenario was also examined.Our work establishes a method to easily realize the materials with odd elastic behaviors and explore the rich phenomena related to nonHermitian systems.

Acoustic cloak constructed with thin-plate metamaterials

We propose a strategy for designing the cylindrical acoustic cloak with thin-plate metamaterials.The inhomogeneous cloaking shell as derived by transformation acoustics is first discretized into a three-layer anisotropic metafluid,and their material parameters are optimized by minimizing the external scatterings.Then these metafluids are practically realized by thin-plate structures according to the metamaterial concept.As an example,an acoustic cloak is designed with nine layers of thin plate and totally 900 plate units.Numerical simulations are performed to assess the cloaking performance of the designed structure.

In-Plane Semi-Linear Cloaks with Arbitrary Shape

Soft materials with semi-linear strain energy function can be used as smart transformation media to manipulate elastic waves via finite pre-deformation. However, the intrinsic cons train ts involved in such materials limit the shapes of t ransformation devices to very sim - pie cases. In this work, combining theoretical and numerical analyses, we report an approach of achieving the in-plane elastodynamic cloak with arbitrary shape. We demonstrate that with the appropriate out-of^plane st retch applied on the semi-linear material, cloaking effec t can be achieved for both P- and SV-waves in the symmetrie plane of a 3D domain, and the performance of the cloak with arbitrary cross section can be guaranteed for relatively small in-plane rot at ion. In addition, we propose an empirical formula to predic t the deformation limit of the cloaks with semi-linear materials. This work may stimulate the experimental research on softmatter- based transformation devices. Potential applications can be anticipated in nondestructive testing, structure impact protection, biomedical imaging and soft robotics.

HEAT FLOW CONTROL BY TRANSFORMATION METHOD WITH GRID GENERATION METHOD

In the context of the transformation method, we propose a general approach to construct numerically the mapping generated by imposing specific boundary conditions with a targeted function, and the necessary material and heat source spatial distributions are then derived with the help of transformation method. The construction of mapping by grid generation method through solving partial differential equations circumvents the limitation of device geometry, which paves the way for designing more complex heat flow control devices. Two numerical examples are also given to show how to design material properties and heat source in order to control temperature patterns.