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• A hybrid multi-scale/arbitrary Lagrangian-Eulerian finite element method is proposed. • The novel method is used for predicting nonlinear structural-acoustic responses. • The novel method offers valuable insights into structural-acoustic interaction mechanisms. This paper introduces a novel hybrid multi-scale/arbitrary Lagrangian-Eulerian finite element method (HMS/ALE-FEM) for addressing the nonlinear vibro-acoustic problem of a large-deformed beam in an infinite fluid. In the HMS/ALE-FEM, the vibrational response of the beam is tackled through modal superposition and a temporal multi-scale approach, while the acoustic wave emitted from the beam is addressed using the arbitrary Lagrangian-Eulerian finite element method (ALE-FEM). An alternating frequency/time domain technique is employed to handle the displacement and velocity of the moving mesh and the acoustic pressure on the beam surface. To validate the HMS/ALE-FEM, it is compared against the finite element method for beam response and the ALE-FEM for acoustic response, serving as a reference method. Taking the nonlinear vibro-acoustic problem of a buckled beam with 2:1 internal resonance as an example, the results of the HMS/ALE-FEM are compared with those of the reference method. The results show that the HMS/ALE-FEM is in good agreement with the reference method under different harmonic excitation amplitudes and frequencies. Due to the 2:1 internal resonance, double modes can be generated, and the second mode amplitudes of both beam displacement and acoustic pressure remain constant as the excitation amplitude varies. Notably, the HMS/ALE-FEM provides direct access to mode amplitude and phase information for beam displacement and acoustic pressure on the beam surface, offering valuable insights into fluid-structure interaction mechanisms in both single- and double-mode scenarios. [ABSTRACT FROM AUTHOR]

• A tunable sound absorber is proposed to dissipate energy of different intensities. • The neck and cavity are synchronously controlled and simultaneous tuning. • Relations between geometric parameters and impedance are established. • Energy dissipation mechanism is revealed under different sound excitations. • Absorption states and bandwidth are provided in the complex frequency plane. Noise reduction problem has been studied for decades with various novel sound absorbers proposed. Most existing absorbers are designed with fixed parameters, which cannot preserve a high absorption coefficient for acoustic waves with different sound pressure levels. This work designs a tunable sound absorber with a synchronously controlled neck and cavity to accommodate acoustic waves with different intensities. A nonlinear impedance model of the acoustic absorber based on an equivalent fluid method is established to quantify the relationship between the geometrical parameters, the levels of incident sound pressures, and the impedance of the absorber. Experiments on sound absorption performance are carried out to confirm the design and theoretical analysis of the absorber. The results show that the proposed absorber can maintain perfect sound absorption at designed frequencies by enlarging the cavity depth when the intensity of the acoustic wave increases. The sound reflection coefficient of the absorber is analyzed in a complex frequency plane. It is found that the sound absorption bandwidth of the absorber can be broadened with an increase in the sound excitation intensity as a larger cavity depth improves the upper bound of the sound absorption bandwidth. Physical insights into the energy dissipation mechanism of the absorber subject to different levels of sound excitation are provided. This work establishes a new approach to realizing perfect noise suppression performance of the absorber under different sound pressure levels without remanufacturing. [ABSTRACT FROM AUTHOR]

• Design a piezoelectric meta-shell shunted with digitally resonant circuits. • Establish the electrical-mechanical-acoustic coupling model of meta-shells. • Build an experimental set-up of the programable piezoelectric meta-shell. • The vibro-acoustic response of the underwater meta-shell is suppressed effectively. • Tunable and multiple bandgaps are attainable for controlling sound radiation. The vibration-induced sound radiation of shell structures has a significant influence on the acoustic-stealth performance of underwater vehicles. To tackle this challenge, a programmable meta-shell featuring periodically distributed piezoelectric shuntings is investigated in this research. Its tunable local-resonance (LR) bandgap, enabled by the digital shunting circuits, is utilized to mitigate the vibration and sound radiation of underwater shells. We establish an electrical-mechanical-acoustic coupling model for the meta-shell submerged in the unbounded heavy fluid. The quadratic velocity and the radiated sound power are computed to evaluate its global vibro-acoustic behaviors. It is demonstrated that, by strategically designing LR bandgaps around the wet-mode frequencies of meta-shells, both the vibration and the sound power could be effectively reduced at target modes. The impacts of electrical damping and poles on the vibro-acoustic reduction efficiency are also identified. Lastly, the experimental set-up of a piezoelectric meta-shell equipped with 48 independently controlled cells is built. The results achieved through underwater experiments validate the meta-shell's capability to programmably suppress vibro-acoustic response peaks associated with multiple wet modes. [ABSTRACT FROM AUTHOR]

• A partitioned numerical method for the fluid-structure-acoustic interaction problems is developed. • The flutter behaviors of composite laminated panel-cavity systems are analyzed. • Local mode coalescence is observed at a small range of aerodynamic pressure. • Physical insight into the acoustic resonance flutter behavior is provided. This paper is concerned with numerical modeling and nonlinear dynamics analyses of fluid-structure-acoustic interactions of an elastic composite laminated panel with a backed cavity in supersonic flow. To achieve strongly coupled solutions to the aeroelastic fluid-structure-acoustic interaction problem, an implicit partitioned arbitrary Lagrangian-Eulerian solution method is developed based on a finite volume model for the supersonic flow and a monolithic nonlinear finite element model for the composite panel-cavity system. A nonlinear higher-order shear deformation zig-zag theory is adopted to accommodate the large-deformable vibration of the composite panel, and the acoustic wave equation is employed for modeling the compressible fluid in the cavity. The method is verified by comparisons with benchmark results. Physical insights into the effects of the dynamic pressure, cavity depth, and the ply-angle of composite material on the aeroelastic behaviors of the panel-cavity system are provided. Some new phenomena are revealed. A special flutter behavior dominated by acoustic resonance is found for the composite panel with a backed cavity in supersonic flow, which is due to local mode coalescence as the mode frequencies of the acoustic cavity and the composite panel are close to each other. The transition between the aeroelastic flutters of the composite panel induced by the lower-order structural mode coalescence and the acoustic resonance of the cavity can be progressively adjusted by alerting the cavity depth and the ply-angle of the composite panel. [ABSTRACT FROM AUTHOR]

The analysis of deformations of structures immersed in water due to explosion waves is important for off-shore oil and marine applications. A challenging issue in these problems is the satisfaction of continuity conditions at the fluid/structure interface. We numerically analyze these transient problems by using the ghost fluid/solid method, and coupling the isobaric fixing technique with the real ghost fluid method. We verify accuracy of the developed algorithm by comparing predictions from it with the analytical solution for a one-dimensional problem in which a plane wave traveling in water impinges upon a water/solid interface. We show that the coupled method has first order accuracy. Numerical results for the propagation of a spherical wave interacting with a fluid/solid interface computed with the developed method are found to compare well with those from the commercial software, ANSYS, that uses the arbitrary Eulerian–Lagrangian method. It is found that the intensity of the reflected tensile wave at a solid/water interface is less than that at a solid/air interface. Factors motivating this work include (i) using only the finite difference method for numerically solving equations governing transient deformations of fluids and solids that employs the ghost fluid/solid method to accurately satisfy continuity conditions at the fluid–solid interface, (ii) avoiding the need to refine the grid near the fluid–solid interface, and (iii) having an in-house capability of modeling detonation of a charge and study the interaction of the shock wave produced with the deformable structure. A novelty of the work is that the pressure due to a shock wave is not modeled as the product of a function of time and a function of space coordinates but its spatial and temporal dependence is found by solving the fluid–structure interaction problem. [ABSTRACT FROM AUTHOR]

This paper presents a numerical method for analyzing the nonlinear structural and acoustic responses of a coupled stiffened composite laminated cylindrical shell and piecewise isolation system immersed in an infinite acoustic fluid. The cylindrical shell is reinforced by a series of circumferential rings and longitudinal stringers, which may be few or many in number, non-uniform or uniform in size, and arbitrarily distributed in space. The isolation system in the shell contains motion-limiting stops, and the restoring forces of the isolators are assumed as bi-linear functions of the isolator deformations. A modified variational approach for the shell combined with a discrete element method for the rings and the stringers is employed to establish the nonlinear dynamics model of the structural system. The exterior acoustic fluid is computed by a time-domain Kirchhoff boundary integral formulation. The structural and acoustic models are coupled together by considering the compatibility conditions on their interface. The validity of the present method for predicting the structural and acoustic responses of the coupled shell and isolator system is confirmed. The contribution of the grouped circumferential wave modes of the shell to the vibration and radiated sound of the coupled structural system is examined. The effects of the excitation frequency of the external load, as well as the stiffness ratio and the gap of the suspension springs in each isolator on the structural and acoustic responses of the coupled system are discussed. [ABSTRACT FROM AUTHOR]

Highlights • A novel numerical method is proposed for structural-acoustic analysis in time-domain. • Vibro-acoustic behaviors of elastic shell containing nonlinear subsystem are analyzed. • Contribution of circumferential wave modes of the shell to radiated sound is examined. • Physical insight into sub-harmonics, super-harmonics and combination harmonics is provided. Abstract This paper is concerned with the structural-acoustic analysis of a coupled sandwich cylindrical shell and nonlinear spring-mass-damper system immersed in an infinite acoustic medium. The restoring force of each spring in the spring-mass-damper system is assumed as a general polynomial function of the spring deformation, from which the nonlinear quadratic, cubic and quartic springs can be directly recovered. A modified variational approach is employed to formulate the nonlinear dynamics model of the coupled structural system, and the exterior acoustic fluid is computed by a time-domain Kirchhoff boundary integral formulation. The structural and acoustic models are coupled together through the compatibility conditions on their interface. The proposed model is validated by comparing the solutions obtained from the finite element/boundary element method and those available in the literature. Very good agreement between the predicted results and the reference solutions is achieved. Individual contributions of circumferential wave modes of the sandwich cylindrical shell to the vibration and acoustic responses of the coupled nonlinear structural system are examined. The effects of the amplitude and excitation frequency of the external loads, and different types of nonlinear springs (including the quadratic, cubic and quartic nonlinear springs) on the vibration and sound radiation behaviors of the structural system are investigated. [ABSTRACT FROM AUTHOR]

For a propeller vibrating in a fluid, the added mass and damping coefficients characterize the hydrodynamic forces and moments acting on the propeller, which are of great importance for evaluation of the vibration behaviors of submerged propellers. The present paper is concerned with the development of a numerical method for predicting the added mass and damping coefficients of a rotating marine propeller immersed in water. The three-dimensional panel method in frequency-domain is employed to establish the strongly coupled fluid-structure interaction models of the propellers to compute the added mass and damping coefficients. The relationship between the added mass and damping matrices due to the whole vibration of a rotating propeller and the local vibrations of the propeller blades is considered. Results of the present method are compared with those experimental and numerical data available in the literature. Very good agreement is achieved. The differences of the added mass and damping coefficients due to propeller vibrations of two types are analyzed. The results show that the added mass and damping coefficients of a submerged rotating propeller are functions of the ratio of oscillation frequency of rigid propeller f v to the blade frequency f b , and the advance ratio. In addition, the non-penetration boundary conditions should be imposed on the deformed blade surface for predicting the added mass and damping coefficients m 32 , m 62 , c 32 and c 62 , where m 32 ( c 32 ) and m 62 ( c 62 ) denote mass (damping) coefficients related to the lateral force and bending moment in the z direction induced by the transversal vibration in the y direction. Absolute values of all coefficients in the added mass matrix decrease as the ratio f v / f b is increased, and the absolute values of the coefficients in the added damping matrix increases with an increase in the advance ratio. [ABSTRACT FROM AUTHOR]

We present a robust sharp-interface immersed boundary method for numerically studying high speed flows of compressible and viscous fluids interacting with arbitrarily shaped either stationary or moving rigid solids. The Navier–Stokes equations are discretized on a rectangular Cartesian grid based on a low-diffusion flux splitting method for inviscid fluxes and conservative high-order central-difference schemes for the viscous components. Discontinuities such as those introduced by shock waves and contact surfaces are captured by using a high-resolution weighted essentially non-oscillatory (WENO) scheme. Ghost cells in the vicinity of the fluid–solid interface are introduced to satisfy boundary conditions on the interface. Values of variables in the ghost cells are found by using a constrained moving least squares method (CMLS) that eliminates numerical instabilities encountered in the conventional MLS formulation. The solution of the fluid flow and the solid motion equations is advanced in time by using the third-order Runge–Kutta and the implicit Newmark integration schemes, respectively. The performance of the proposed method has been assessed by computing results for the following four problems: shock-boundary layer interaction, supersonic viscous flows past a rigid cylinder, moving piston in a shock tube and lifting off from a flat surface of circular, rectangular and elliptic cylinders triggered by shock waves, and comparing computed results with those available in the literature. [ABSTRACT FROM AUTHOR]

This paper investigates the structural and acoustic responses of a coupled propeller-shafting and submarine pressure hull system under different propeller force excitations. The entire system, which consists of a rigid propeller, a main shaft, two bearings and an orthogonally stiffened pressure hull, is submerged in a heavy fluid. The shaft is elastically connected to the pressure hull by a radial bearing and a thrust bearing. The theoretical model of the structural system is formulated based on a modified variational method, in which the propeller, the main shaft and the bearings are treated as a lumped mass, an elastic beam and spatially distributed spring-damper systems, respectively. The rings and stringers in the pressure hull are modeled as discrete structural elements. The acoustic field generated by the hull is calculated using a spectral Kirchhoff-Helmholtz integral formulation. A strongly coupled structure-acoustic interaction analysis is employed to achieve reasonable solutions for the coupled system. The displacement of the pressure hull and the sound pressure of the fluid are expanded in the form of a double mixed series using Fourier series and Chebyshev orthogonal polynomials, providing a flexible way for the present method to account for the individual contributions of circumferential wave modes to the vibration and acoustic responses of the pressure hull in an analytical manner. The contributions of different circumferential wave modes of the pressure hull to the structural and acoustic responses of the coupled system under axial, transversal and vertical propeller forces are investigated. Computed results are compared with those solutions obtained from the coupled finite element/boundary element method. Effects of the ring and the bearing stiffness on the acoustic responses of the coupled system are discussed. [ABSTRACT FROM AUTHOR]

This paper develops a numerical method for predicting the nonlinear structural-acoustic interactions of a hyperelastic solid immersed in an unbounded compressible viscous fluid. The nonlinear acoustic wave model with perfectly matched layers adopted is proposed in an arbitrary Lagrangian-Eulerian frame to absorb acoustic waves at truncated fluid boundaries, whereas the geometric and material nonlinearities of the hyperelastic solid are characterized in a total Lagrangian form. Both the fluid and the solid are discretized by the finite element method, and both models are coupled together by the momentum equilibrium and kinematic compatibility on the common interface. The convergence and accuracy of the proposed method are assessed by comparing the computed results with existing solutions. A hyperelastic ring in a viscous fluid is analyzed to provide physical insights into the nonlinear dynamics behaviors of the coupled hyperelastic solid and acoustic fluid system. The hyperelastic ring in acoustic fluid exhibits deformation instability under a uniform distributed excitation load, producing a series of subharmonics, ultrasubharmonics, and superharmonics in the structural and acoustic responses. Nonlinear internal resonance and bifurcation phenomena in the vibration of the ring and the acoustic waves of the fluid are also discussed. • A numerical method for nonlinear structural-acoustic interaction of a hyperelastic solid immersed in an unbounded fluid is proposed. • Arbitrary Lagrangian-Eulerian technique is adopted for the nonlinear acoustic wave model in a time-dependent acoustic domain. • A loosely coupled serially staggered procedure for nonlinear structural-acoustic interaction is presented. • Internal resonance and bifurcation phenomena of a hyperelastic ring and the acoustic waves are discussed. [ABSTRACT FROM AUTHOR]

• Resonators with serrated necks are proposed to dissipate high-intensity sound. • Finite element analysis of nonlinear acoustic waves is performed. • Thermal conduction and vortex dissipation of resonators are evaluated. • Vortices generation in the serrated neck is beneficial for sound absorption. • Computed sound absorption coefficients agree well with experimental data. This paper focuses on the design and sound absorption analysis of Helmholtz resonators with serrated necks inspired by the leading edges of owl wings. Numerical models for predicting the sound absorption and the flow field of the resonators are established by a finite element method based on nonlinear acoustic wave equations. The thermal conduction and vortex energy dissipation of resonators with straight and serrated necks are evaluated. The effects of the geometrical parameters including the neck diameter, the serration height, and the serration pitch on the sound absorption behaviors of the resonator are discussed. It is found that for a lower-intensity acoustic excitation, the serration leads to periodic oscillations of the fluid in the resonator neck, and increases the acoustic resistance of the resonator. For a high-intensity sound excitation, the distributions of the velocity and vorticity in the resonator neck show that the serrated structure can produce more vorticities, which is beneficial for acoustic energy dissipation. The resistance of the resonators grows significantly and the reactance decreases slightly with an increase in intensity of the sound excitation. Sound absorption coefficients of resonators fabricated by three-dimensional (3D) printing are tested in an impedance tube for a large range of sound pressure excitations. The computed results of the sound absorption coefficients are in good agreement with the experimental data, and the superior sound absorption performance of the resonator with a serrated neck is confirmed. [ABSTRACT FROM AUTHOR]

This paper presents a semi-analytical method for the vibro-acoustic analysis of a functionally graded shell of revolution immersed in an infinite light or heavy fluid. The structural model of the shell is formulated on the basis of a modified variational method combined with a multi-segment technique, whereas a spectral Kirchhoff–Helmholtz integral formulation is employed to model the exterior fluid field. The material properties of the shell are estimated by using the Voigt׳s rule of mixture and the Mori–Tanaka׳s homogenization scheme. Displacement and sound pressure variables of each segment are expanded in the form of a mixed series using Fourier series and Chebyshev orthogonal polynomials. A set of collocation nodes distributed over the roots of Chebyshev polynomials are employed to establish the algebraic system of the acoustic integral equations, and the non-uniqueness solution is eliminated using a combined Helmholtz integral equation formulation. Loosely and strongly coupled schemes are implemented for the structure-acoustic interaction problem of a functionally graded shell immersed in a light and heavy fluid, respectively. The present method provides a flexible way to account for the individual contributions of circumferential wave modes to the vibration and acoustic responses of functionally graded shells of revolution in an analytical manner. Numerical tests are presented for sound radiation problems of spherical, cylindrical, conical and coupled shells. The individual contributions of the circumferential modes to the radiated sound pressure and sound power of functionally graded shells are observed. Effects of the material profile on the sound radiation of the shells are also investigated. [ABSTRACT FROM AUTHOR]

A semi-analytical method is developed to predict the vibration and acoustic responses of submerged coupled spherical–cylindrical–spherical shells stiffened by circumferential rings and longitudinal stringers. The structural model of the coupled stiffened shell is formulated using a modified variational method combined with a multi-segment partitioning technique, whereas a spectral Kirchhoff–Helmholtz integral formulation is employed to model the exterior fluid. The stiffened rings and stringers, which may be few or many in number, non-uniform or uniform in size, and non-uniformly or uniformly spaced, are treated as discrete elements. The displacement and sound pressure variables are expanded in the form of a double mixed series using Fourier series and Chebyshev orthogonal polynomials. This provides a flexible way for the present method to account for the individual contributions of circumferential wave modes to the vibration and acoustic responses of coupled stiffened shells in an analytical manner. The application of the method is illustrated with several numerical examples, and comparisons are made with available solutions obtained from the coupled finite element/boundary element method. The contributions of different circumferential wave modes to the vibration responses, sound power and the directivity of radiated sound pressure for coupled shells bounded by light or heavy fluid are examined. Effects of the rings and stringers on the vibration and acoustic responses of the coupled shells are investigated. [ABSTRACT FROM AUTHOR]

• Developing a vibro-acoustic coupling model for analyses of nonlinear acoustic wave behaviors of vibrational objects. • Numerical tests are carried out to confirm the validity of the developed coupling model. • Physical insights into the effects of high-order vibration responses on the nonlinear acoustic wave in the fluid are provided. • Effects of smooth and non-smooth nonlinearities on acoustic responses of vibrational objects are evaluated. This paper is concerned with numerical analyses of radiated sound behaviors of dynamic systems containing nonlinear vibrational objects immersed in a compressible and inviscid fluid of infinite extent. The vibrational solids are modelled by the Lagrangian description of motion, while the fluid surrounding the vibrational objects is formulated by the two-dimensional linearized Euler equations (LEEs). The nonlinear dynamic responses of the vibrational solids are computed by both the harmonic balance method (HBM) and direct time integration method. A fourth-order dispersion-relation-preserving (DRP) scheme is implemented on a fixed Cartesian grid to solve the governing equations of the fluid. A constrained moving least-squares sharp-interface immersed boundary method is adopted to impose the compatibility conditions on the common boundaries of the vibrational objects and the fluid. Selective filters are employed to suppress the spurious short waves appearing in numerical computations. Several numerical tests are carried out to confirm the validity of the developed vibro-acoustic coupling computational model by comparing the present solutions with the exact solutions. Nonlinear acoustic wave responses of vibrational objects with smooth and non-smooth nonlinearities are examined, including rigid cylinder-shaped oscillators resting on nonlinear mounts, ellipse-shaped objects suspended on nonlinear torsional springs, and rigid isolators with frictions and clearances. It is found that for vibrational objects containing nonlinearities, the amplitude-frequency responses of radiated sound pressure exhibit shifting resonance frequencies, secondary resonances and jump phenomenon. The intermittent collisions of the vibrational objects with clearances can result in abrupt fluctuations and distortions of the radiated acoustic waves in fluid. In addition, the radiation efficiency of high-order harmonics of nonlinear acoustic waves induced by stick/slip transitions of friction interfaces can reach to maximum with the friction coefficient. [ABSTRACT FROM AUTHOR]

[Display omitted] • Vibro-acoustic control of elastic ring structures in compressible fluid using programmable piezoelectric metamaterials is concerned. • Analytical method and FEM are established to predict the vibration and sound radiation behaviors. • High-order digital shunting circuits are designed to realize multi-band vibro-acoustic control. • Experiment of vibro-acoustic programmable control of the piezoelectric meta -ring is performed. In this paper, a programmable piezoelectric meta -ring equipped with high-order digital shunting circuits is designed for vibro-acoustic control. The structural and acoustic suppressing performance of the piezoelectric meta -ring in light fluid is tunable by re-programming transfer functions implemented in micro-controller units of the digital circuits. The radiated sound due to structural vibration of the meta -ring is attenuated in multiple local-resonance bandgaps, which is realized using high-order resonant circuits designed via the pole-zero placement method. An analytical model is developed for providing physical insights into vibro-acoustic behaviors of the piezoelectric meta -ring in light fluid. The analytical results agree well with numerical ones computed with the finite element method. The effects of electrical parameters such as gain parameter and electrical damping ratio on the sound radiation suppression of elastic rings are also discussed. To verify the programmability and high-order local-resonance bandgap performance of the piezoelectric meta -ring, the vibro-acoustic control experiment is carried out in the anechoic chamber. It is found that programmable bandgaps at different target frequencies of the piezoelectric meta -ring can be generated, which effectively suppress the structural–acoustic response peaks of the meta -ring. [ABSTRACT FROM AUTHOR]

A weak form variational based method is developed to study the vibro-acoustic responses of coupled structural-acoustic system consisting of an irregular acoustic cavity with general wall impedance and a flexible panel subjected to arbitrary edge-supporting conditions. The structural and acoustical models of the coupled system are formulated on the basis of a modified variational method combined with multi-segment partitioning strategy. Meanwhile, the continuity constraints on the sub-segment interfaces are further incorporated into the system stiffness matrix by means of least-squares weighted residual method. Orthogonal polynomials, such as Chebyshev polynomials of the first kind, are employed as the wholly admissible unknown displacement and sound pressure field variables functions for separate components without meshing, and hence mapping the irregular physical domain into a square spectral domain is necessary. The effects of weighted parameter together with the number of truncated polynomial terms and divided partitions on the accuracy of present theoretical solutions are investigated. It is observed that applying this methodology, accurate and efficient predictions can be obtained for various types of coupled panel-cavity problems; and in weak or strong coupling cases for a panel surrounded by a light or heavy fluid, the inherent principle of velocity continuity on the panel-cavity contacting interface can all be handled satisfactorily. Key parametric studies concerning the influences of the geometrical properties as well as impedance boundary are performed. Finally, by performing the vibro-acoustic analyses of 3D car-like coupled miniature, we demonstrate that the present method seems to be an excellent way to obtain accurate mid-frequency solution with an acceptable CPU time. [ABSTRACT FROM AUTHOR]

• A piezoelectric metamaterial beam with combined nonlinearity is proposed. • The shunting circuit incorporates cubic and fractional nonlinearities. • The proposed design widens the bandgap at both high and low excitation amplitudes. • The effects of the two nonlinearities on amplitude-dependent bandgaps are studied. Nonlinear metamaterials have been widely studied for their potential to broaden the bandgap for vibration suppression. However, the bandgap widening effect induced by nonlinearity vanishes when the excitation amplitude is insufficient to trigger the nonlinear behavior. In order to broaden the applicable range of excitation amplitude for nonlinear metamaterials, a novel design of a piezoelectric metamaterial beam shunted with combined nonlinear circuits is presented in this work, which incorporates fractional and cubic nonlinearities in circuits to achieve bandgap enhancement under both low and high excitation amplitudes. Theoretical and numerical models are established for predicting the nonlinear dynamics behaviors of the piezoelectric metamaterial beam, and their computational results are in good agreement. The amplitude-dependent bandgap of the metamaterial beam induced by combined nonlinearity is analyzed through the effective bending stiffness of a unit cell and validated through the frequency response of a piezoelectric metamaterial beam. It is found that based on the complementary nature of fractional and cubic nonlinearities in the amplitude-dependent characteristics, combined nonlinearity of the circuits can effectively improve the bandgap width of the beam under both low and high excitation amplitudes. In addition, the effects of the two nonlinearities on the amplitude-dependent characteristics of the bandgap are studied, and the interplay between the two nonlinearities within the combination is analyzed. The results show that the amplitude-dependent characteristics of the combined nonlinear design can be precisely tuned by adjusting the nonlinear coefficients of the circuits. Overall, a piezoelectric metamaterial beam with both fractional and cubic nonlinearities in circuits possesses superior vibration control performance than those with single nonlinear counterparts in circuits. [ABSTRACT FROM AUTHOR]

Broadband sound absorption has been a long-lasting concern in the field of noise engineering, yet to date remains challenging to cover a broad low-frequency range with ultra-thin materials of a few centimeters. A practicable approach is using coherently coupled resonators to constitute a compact coplanar metasurface absorber. However, this scheme leads to a tough inverse problem posed by the large number of design parameters since all have to be meticulously tuned to satisfy the critical coupling condition. We tackle this problem with the deep learning approach. An autoencoder-like neural network is built that, once maturely trained, significantly promote the inverse design process thanks to the highly efficient data-driven-based forward and inverse predictions. In the design, we have added a probabilistic model into the neural network to enhance its robustness for the normally ill-posed inverse design problems which require artificial and probably unreal spectrum as an input. This probabilistic network is capable of providing multiple ultra-thin (32 mm) and broadband metasurface designs. The optimized designs have been numerically and experimentally verified, showing the capacity of using solely nine resonators to achieve quasi-perfect sound absorption (absorption coefficient α ⩾ 0.9) in a band from 350 to 530 Hz. Our work is helpful to accelerate the design of metasurface absorbers targeted especially for broadband noise control at low frequencies. [ABSTRACT FROM AUTHOR]

• The piezo-metastructure is shunted with a one-way electrical transmission line. • Local-resonance bandgaps are maintained in opposite directions. • Nonreciprocal wave attenuation behaviors exist in the bandgap. • The presented nonreciprocal system is linear, adaptive and easily implemented. • Theoretical and experimental results verify nonreciprocity of the system. In contrary to elastic media, it is easy to attain one-way coupling feature among electrical elements, which enables unidirectional transmission of electrical wave. In this paper, we explore and exploit the interaction of a piezoelectric beam with a one-way electrical transmission line to facilitate nonreciprocal transmission of elastic wave in the linear fashion. Theoretical dispersion analysis and numerical simulations are performed to reveal transmission behaviors of elastic wave in the presented piezoelectric metastructure. It is uncovered that, when the one-way electrical coupling feature is introduced, local-resonance bandgaps are maintained in opposite directions of the piezoelectric metastructure. However, the bandgap attenuation capability in one direction is increased compared to conventional local-resonance metastructures, in which no electrical coupling exists between cells, while that in the other direction is decreased. Therefore, nonreciprocal transmission of elastic wave emerges in this system due to the distinct bandgap attenuation capability in opposite directions. It is also revealed that this sort of nonreciprocal wave attenuation capability is adaptive with the one-way electrical coupling coefficient and the resistance of electrical cells. An experimental set-up of the piezoelectric metastructure is built and experimental results verify the nonreciprocity property and its adaptiveness. Overall, the presented piezoelectric metastructure provides a linear and concise approach to realize adaptive nonreciprocal transmission of elastic wave. [ABSTRACT FROM AUTHOR]

• Study resonant passbands below the ring frequency of a piezoelectric meta-shell. • Negative dispersions appear in the passband due to negative bending rigidities. • Dispersion relations are computed using the plane-wave expansion method. • Perform energy flow analysis based on the Poynting vector. • Interplay of piezoelectric shunting and curvature leads to novel wave properties. The local-resonance (LR) mechanism is usually employed to induce bandgaps in the scope of metamaterials. On the contrary, we investigate LR passbands in this paper, which are located below the ring frequency of a piezoelectric meta-shell shunted with resonant circuits. The flexural wave properties of the meta-shell are investigated analytically through dispersion relations, and also verified by numerical results. It is observed that the piezoelectric shunting could induce longitudinal bandgaps above the ring frequency, while passbands below the ring frequency. Interestingly, negative dispersions may appear in this longitudinal passband when negative bending rigidity is induced through the piezoelectric bending effect, implying that the group velocity of flexural wave is opposite to its phase velocity. We demonstrate such rigidity-correlated dispersion behaviors through energy flow analysis based on the Poynting vector. It is also revealed that the curvature of shells impacts the width of negative-dispersion passbands, with the smaller radius leading to narrower passbands. Since the curvature couples in-plane vibrations and out-of-plane vibrations, it facilitates flexural-wave passbands below the ring frequency as well by introducing the piezoelectric tensional effect, but with dispersions maintaining positive. Moreover, we find that if the piezoelectric shunting induces the bending effect and the tensional effect simultaneously, their interplay at the overlap frequency range may create negative-dispersion passbands above the ring frequency, whereas cancels the impacts with each other below the ring frequency. The results in this research break the limitation that flexural wave propagation below ring frequencies of shells is conventionally not allowed in the longitudinal direction. It also offers the opportunity to implement unprecedent wave properties related to negative dispersions, such as negative refraction and superlensing, with single-negative curved metamaterials. [ABSTRACT FROM AUTHOR]

• Propose a piezoelectric meta-ring with digital shunting circuits. • Programmable local-resonance bandgaps are attainable in the digital meta-ring. • Establish a theoretical framework of the digital meta-ring. • Investigate two designing strategies of high-order local-resonance bandgaps. • Verify bandgaps of the digital micro-fiber-composite meta-ring experimentally. Representing a typical class of active metamaterials with unprecedented adaptiveness, piezoelectric metamaterials have received a lot of research efforts, but which are mostly focused on beam- and plate-types. In this research, we propose a piezoelectric meta-ring shunted with digital high-order resonant circuits, where the micro-fiber-composite (MFC) are used as the electrical-mechanical transducers. Due to the programmability of digital circuits, the bandgap behavior of the meta-ring is highly adaptive. The analytical dispersion relation of meta-ring cells is achieved with the transfer matrix method. To study dynamic response of the finite meta-ring system, we derive the six-order electrical-mechanical coupling equation, and also establish its discretized form using the assumed-mode expansion method. The finite-element simulations are performed to verify this analytical model. By homogenizing the meta-ring under the long-wavelength assumption, a simplified model is attained, so as to provide a convenient means to design the bandgaps and perform stability analysis. For the sake of implementing high-order local-resonance bandgaps, we investigate two manners based on the pole-zero placement to design digital circuits. The bandgap boundaries under these two scenarios are analytically identified. Additionally, the bandgap performance of the meta-ring is simulated, followed by a comprehensive investigation of the impacts of electrical parameters, including the gain, damping and poles-zeros. For the inversely designed digital circuits, the bifurcation phenomenon of poles of the electrical admittance is uncovered, which impacts the stability of circuits. Lastly, we build an experimental set-up of the digital MFC meta-ring. Its programmable and high-order local-resonance bandgap performance is validated experimentally. [ABSTRACT FROM AUTHOR]

This paper proposes a novel nonlinear dynamical system identification method based on the sparse regression algorithm and the separable least squares method. To effectively avoid solving the second derivative of the displacement signal and reduce the effect of noise, the Duhamel's integral is adopted to represent the dynamic relationship between the system input and output. In the expression form of Duhamel's integral, nonlinear dynamical system identification can be cast as a separable least squares problem. Thus, the separable least squares method is leveraged to separately identify the parameters of the linear subsystem and the coefficients corresponding to nonlinearities among the nonlinear dynamical system. During the identification process of nonlinear restoring forces, one complete set of nonlinear basis functions are used to represent the nonlinear restoring forces. Not all the candidate nonlinear terms are contributing, however, thus the sparse regression algorithm is adopted to select the actual contributing nonlinear components in the candidate nonlinear terms and eliminate the non-contributing nonlinear components, and then the corresponding parameters of contributing nonlinear components are estimated by the unbiased least squares method. Finally, one RKHS (Reproducing Kernel Hilbert Space)-based non-parametric de-noise method is further proposed to reduce the noise in the vibration displacement and obtain the noise-reduced velocity from the displacement signal. The numerical simulation about the identification of the rotating blade-casing system and the dynamic experiment of the HSLDS (high-static-low-dynamic stiffness) isolator system verify the effectiveness of the new identification method for nonlinear dynamical systems proposed in this paper. [ABSTRACT FROM AUTHOR]