The ideal acoustic black hole (ABH) can achieve wave gathering and zero reflection of elastic waves. In practice, ABHs have to be truncated, limiting their application in lower frequency range. Aiming at improving the ABH beam's vibration suppression ability at low frequencies, this study proposes a shunt damping-ABH composite beam by pasting shunt damping instead of ordinary damping on the ABH tip. The energy method is employed to solve the vibration equation of the ABH beam. The admissible function is the Mexican hat wavelet. The proposed method is verified by the finite element method. Compared with the uniform beam, the numerical results show the ABH beam has a noticeable attenuating effect in high-frequency range due to the ABH effect, but almost has no attenuating effect in the low-frequency range. Therefore, we introduce shunt damping to enhance the low-frequency vibration control. The shunt damping is composed of circuits connected to a piezoelectric patch. The effects of different circuits connected to the piezoelectric patch are discussed. The R–L shunt circuit and L–C parallel blocking circuit can simultaneously suppress the multimode vibration peak of the ABH beam at the low frequency successfully. Finally, a vibration experiment of ABH beam combined with shunt damping is implemented to verify the present method's feasibility and the shunt damping effect. The proposed shunt damping-ABH composite beam could improve the suppressing ability in both the low and high-frequency ranges.

This study investigates the use of a spring-bar mechanism (SBM) in a vibration suppression system to improve its performance. The SBM, comprising bars and springs, is configured with a conventional linear spring-damper isolator unit. The dynamic response, force transmissibility, and vibration energy flow behaviour are studied to evaluate the vibration suppression performance of the integrated system. It is found that the SBM can introduce hardening, softening stiffness, or double-well potential characteristics to the system. By tuning the SBM parameters, constant negative stiffness is achieved so that the natural frequency of the overall system is reduced for enhanced low-frequency vibration isolation. It is also found that the proposed design yields a wider effective isolation range compared to the conventional spring-damper isolator and a previously proposed isolator with a negative stiffness mechanism. The frequency response relation of the force-excited system is derived using the averaging method and elliptical functions. It is also found that the system can exhibit chaotic motions, for which the associated time-averaged power is found to tend to an asymptotic value as the averaging time increases. It is shown that the time-averaged power flow variables can be used as uniform performance indices of nonlinear vibration isolators exhibiting periodic or chaotic motions. It is shown that the SBM can assist in reducing force transmission and input power, thereby expanding the frequency range of vibration attenuations.

A theoretical method is employed to study the free vibration characteristics of a finite ring-stiffened elliptic cylindrical shell. Vibration equations of the elliptic cylindrical shell are derived based on Flügge shell theory, and the effects of the ring stiffeners are evaluated via “smeared” stiffener theory whereby the properties of the stiffeners are averaged over the shell surface. The displacements of the shell are expanded in double Fourier series in the axial and circumferential directions, and the circumferential curvature is expanded in single Fourier series in the circumferential direction. The partial differential characteristic equations with variable coefficients are converted into a set of linear equations with constant coefficients which couple with each other about the circumferential modal parameters. Then, the natural frequencies of the finite ring-stiffened cylindrical shell are obtained. To verify the accuracy of the present method, the finite ring-stiffened elliptic cylindrical shell is degenerated into two models: one of which is a ring-stiffened circular cylindrical shell and the other of which is an elliptic cylindrical shell without ring stiffeners. The present results of the two degenerated shells show good agreements with available results from the literature. The effects of main parameters, including the ellipticity, the shell length ratio, the stiffener's interval, the stiffener's depth, and the stiffener's eccentricity, on the free vibration of the ring-stiffened elliptic cylindrical shell are examined in detail. The ellipticity makes the difference between the symmetric and antisymmetric modal frequencies of the shell. The stiffeners have a greater influence on the free vibration at relatively higher order circumferential modal parameters. The circumferential modal parameters corresponding to the fundamental frequency are affected by the ellipticity, shell length, stiffeners' interval, and depth. The eccentricity of the ring stiffeners has a weak effect on the vibration of the structure.

The edge-based smoothed finite element method (ES-FEM) was proposed recently to improve the accuracy of the standard finite element method for solid mechanics. In the present paper, the ES-FEM is incorporated with the three-node Mindlin plate element (MIN3) to give a novel edge-based smoothed MIN3 (ES-MIN3) for plate analysis. The system stiffness matrix is computed by employing the edge-based strain smoothing technique over the edge-based smoothing domain. For the purpose of avoiding the transverse shear-locking, the MIN3 element is performed to calculate the strains in each element. From a series of selected numerical examples, it is found that the present ES-MIN3 possesses highly accurate solutions, and can be competitive with many existing plate elements.

Based on the principle of energy variation, a calculation model for the free vibration characteristics of a cylindrical shell with a finite submerged depth considering the influence of the free liquid surface is established in this paper. First, the Euler beam function is used instead of the shell axial displacement function to obtain the shell kinetic energy and potential energy. Then, by using the mirror image method, the analytical expression of the fluid velocity potential considering the free surface is obtained, and the flow field is added to the system energy functional in the form of fluid work. Then the energy functional is changed to obtain the shell–liquid coupled vibration equation. Solving the equation can obtain the natural frequencies and modes of the structure. The comparison with the finite element calculation results verifies the accuracy of the calculation model in this paper. The research on the influence of the free liquid surface shows that compared to the infinite domain, the free liquid surface destroys the symmetry of the entire system, resulting in a difference in the natural frequency of the positive and negative modes of the shell, and the circumferential mode shapes are no longer mutually uncoupled trigonometric functions. The existence of free liquid surface will also increase the natural frequency of the same order mode, and the closer to the free surface, the natural frequency is greater. As the immersion depth increases, the free vibration characteristics will quickly tend to the result of infinite domain. Additionally, when the immersion depth is equal to or greater than four times the radius of the shell structure, it can be considered that the free liquid surface has no effect. These law and phenomena have also been explained from the mechanism. The method in this paper provides a new analytical solution pattern for solving this type of problem.