International Journal of Applied Mechanics

Full waveform inversion (FWI) to estimate physical properties of a system is one of the major research topics in science and engineering. This study proposes a probabilistic approach toward these solutions by applying the unscented Kalman filter (UKF). The responses of the vertical displacements of a layered half-space subjected to a harmonic vertical disk load on the surface are calculated from an estimated profile of shear-wave velocities and compared with measurements or observations. In the calculation of the dynamic responses, the thin-layer method (TLM), which is efficient for layered media, is employed. In order to improve the solutions to the considered inverse problem, regularization terms are included in the observations so that the differences in the material properties between two consecutive layers vanish. The proposed UKF method is demonstrated with a variety of FWI problems in a layered half-space. The results show that the proposed method can estimate the material properties of a layered half-space accurately.

A strain gradient (SG) continuum theory of two-dimensional (2D) lattice metamaterials based on Padé approximation has been proposed, called PSGM hereafter, to predict their acoustic dispersion characteristics. Square and triangular elastic lattices have been investigated for a demonstrating purpose. By applying Padé approximation to the Taylor expansion of displacement field, the fourth- and eighth-order SG continuum models are established. The dispersion relations obtained by the proposed model are examined by comparing with the results by discrete analyses as well as existing SG theories. It is confirmed that the proposed theory is always more accurate than the existing SG counterpart with the same SG order. Furthermore, the present formulation is free of any unrealistic instability issue in dispersion, which has challenged the existing SG theories. The results also show that the accuracy of PSGM will be enhanced with increasing SG orders. Within the present parameter settings, it can be found that the eighth-order PSGM can successfully capture the dispersive properties of both lattices throughout the first irreducible Brillouin zone.

As an armor composite material, the damage mechanism, perforation resistance, damage evaluation and enhancement measures of steel-concrete are crucial to the protective design. In this paper, a modified prediction model of residual velocity and perforation resistance was proposed for the steel-liner-concrete composite target (SLCCT), which considered the fracture energy caused by steel liners and concrete. The numerical models were validated by comparing with previous penetration tests and the modified prediction model. Then LS-DYNA was used to analyze how the layer number (1–5) and rear-steel-liner layout influenced the projectile energy consumption, target damage and integral perforation resistance. The conclusions indicated that, when the reduction coefficient of fracture energy $(\xi )$ was taken as 0.1, the modified prediction model of residual velocity and perforation resistance for SLCCTs was firstly proposed and verified. Noteworthily, with regard to thin segmented SLCCTs (the ratio between layer thickness and projectile diameter was no more than 2.5), the structural perforation resistance was weakened with an increase of the layer number, where the ratio of residual and initial kinetic energy $(E_r/E_0)$ for five-layer target was approximately 17.9% higher than that of monolithic slab. Furthermore, as the ratio between layer thickness and projectile diameter was no more than 2, the perforation resistance provided by a rear steel liner was particularly prominent compared with each layer concrete in a SLCCT.

This paper investigates the fluid–solid interaction in an electrostatic microvalve to control the flow rate. A double clamped microbeam which has been considered as a microvalve by imposing a DC voltage on it in a capacitive system, is deflected and hence changes the boundary conditions of the fluid domain. So, in each step of increasing the voltage, the Navier–Stokes and Euler–Bernoulli equations have been solved simultaneously. To overcome the difficulties of the finite element solution in moving boundaries of the fluid domain, after each step, a mapping approach has been accomplished. Silicon and dielectric elastomer (DE) have been adopted as the microbeam’s material and capability of them to control the flow rate has been compared. The results have shown that DE can be an attractive candidate for microvalve instead of silicon due to the decreasing required applied voltage for achievement for a certain flow rate. The presented results can be also useful for modeling the FSI problems with moving boundaries in the fluid domain, especially in the microvalve design applications.

The optimum inertial amplifier tuned mass dampers (IATMD) for vibration reduction of linear and nonlinear dynamic systems are introduced in this paper. $H_2$ and $H_{\infty }$ optimization methods are applied to derive the exact closed-form expressions for optimal design parameters such as frequency and viscous damping ratios in simplified form mathematically for IATMD. From the parametric study, using these optimal closed-form solutions, a higher damper mass ratio, a higher amplifier mass ratio, and a lower inertial angle are recommended to design optimum IATMD to achieve robust dynamic response reduction capacity having moderate viscous damping and lower frequency ratios at an affordable range. The optimum IATMD systems are installed on top of linear and nonlinear single-degree-of-freedom systems to mitigate their dynamic responses of them. The linear dynamic responses are determined through transfer matrix formations, and nonlinear dynamic responses are derived using the harmonic balance (HB) method. $H_2$ optimized IATMD is significantly $44.78$ and $48.62$ superior to the $H_2$ optimized conventional tuned mass damper one (CTMD1) and conventional tuned mass damper two (CTMD2). Furthermore, $H_{\infty }$ optimized IATMD is significantly $39.98$ superior to the $H_{\infty }$ optimized conventional tuned mass damper (CTMD). According to the nonlinear dynamic analysis, $H_2$ optimized IATMD systems are significantly $35.33$, $76.97$, and $35.33$ superior to the $H_2$ optimized CTMD. Furthermore, $H_{\infty }$ optimized IATMD systems are significantly $25.92$, $73.64$, and $25.92$ superior to the $H_{\infty }$ optimized CTMD. The results of this study are mathematically accurate and feasible for practical applications.

In this study, the anti-cavitation performance and cavitation flow characteristics in a hydrodynamic levitated micropump were investigated based on numerical simulation and experiment. The cavitation characteristic curves and the development process of cavitation in the levitated micropump was firstly analyzed. Special emphasis was put on the effects of eccentricity on the anti-cavitation performance. The results show that as the eccentricity increases, the critical cavitation number gradually decreases, indicating that the eccentric rotation is beneficial to improve the anti-cavitation ability of the levitated micropump. The coupling effects between the radial force on the impeller and cavitation were also numerically studied. With the decrease of cavitation number, the radial force on the impeller gradually declines at first, then has a sudden increase and finally reduces with fluctuation. The drop of the radial force will lead to the decrease of eccentricity, resulting in the deterioration of cavitation further. In addition, the unsteady pressure pulsation was analyzed. The predominant frequencies of pressure pulsation are the blade passing frequency (BPF) and the harmonic frequency of BPF under both noncavitation and critical cavitation. Under critical cavitation, the amplitude of BPF has a drop, while the amplitude of low frequency less than BPF becomes larger.

In this study, a deeply buried circular tunnel supported with point-anchored rock bolts was investigated. Assuming that the effects of each rock bolt on the surrounding rock are simplified to two identical concentrated forces acting in opposite directions, a viscoelastic analytical solution for the axial forces of the rock bolts is presented herein based on the complex variable method and correspondence principle. First, in the solution process, the surrounding rock is considered as an elastic material. A linear equation system for the axial forces was established according to the deformation coordination condition between the surrounding rock and the rock bolts. Second, the surrounding rock was considered as a viscoelastic material. Based on the correspondence principle, Laplace transformation was performed for the equation system of the axial forces to obtain its expression in the Laplace domain, and the values of the axial forces in the Laplace domain could be determined by solving the obtained expression. Finally, the viscoelastic semi-analytical solution for the axial forces was established using the numerical method of the Laplace inverse transformation. The results obtained were also compared with the numerical methods of ANSYS. Accordingly, the effects of the lateral stress coefficient, rock mass Young’s modulus, rock bolt length, viscosity coefficient, and preload on the axial forces of the rock bolts were discussed.

The majority of ultrasonic characterizations are done on thermoplastics, with just a few articles available on the characterization of thermoset resin characteristics. A non-destructive methodology for monitoring fatigue and static deformation induced by mechanical loading on a fiber-reinforced plastic is presented. However, these materials’ dynamics of elastic waves are considerably more complicated. A large part was devoted to the calculation of dispersion curves of guided waves in composites. Therefore, this study presents a thorough description of the Glass/Epoxy system by comparing ultrasonic and mechanical data. Ultrasonic wave propagation at high frequencies, functioning as a dynamic mechanical deformation, may be utilized to calculate longitudinal and shear moduli during static and dynamic loading. The evolution of attenuation and velocity during loading is linked to the significant changes that occur during the aging process. The experimental transfer function is determined by the Fourier transform of all the obtained ultrasonic echoes.

This study establishes a novel three-dimensional dynamic model for functionally graded rotating microbeams simultaneously considering flapwise and chordwise shear effects based on a refined shear deformation theory and the modified couple stress theory. Five kinematic variables are introduced to describe the rotating microbeam’s axial, flapwise, and chordwise motions using a higher-order refined shear deformation theory. The related strain energy and kinetic energy functionals are discretized by the assumed mode method. Applying the Euler–Lagrange variational formulation, the governing equations for the rotating microbeam are obtained. Selective examples are provided to demonstrate the convergence and effectiveness of the proposed model. Finally, the impacts of slenderness ratio, rotation speed, material index, material length scale parameter (MLSP), and Poisson’s effect on the vibrational characteristics of the microbeam are examined. Numerical results indicate that the mode shape transition and frequency loci veering phenomena could easily occur under slight changes in the above factors when dense modes appear in the rotating microbeam; moreover, there is a positive/negative competitive relationship among the effects of rotation speed, MLSP, and shear deformation; Poisson’s effect seriously affects the coupling between axial and non-axial motions of the rotating microbeam. The results obtained are expected to provide data accumulation and methodological basis for the failure analysis and vibration shape determination of micro air vehicles.

This paper deals with flow field prediction in a blade cascade using the convolution neural network. The convolutional neural network (CNN) predicts density, pressure and velocity fields based on the given geometry. The blade cascade is modeled as a single interblade channel with periodic boundary conditions. In this paper, an algorithm that enforces periodic boundary conditions onto the CNN is presented. The main target of this study is to parametrize the CNN model depending on the Reynolds number. A new parametrization approach based on a so-called hypernetwork is employed for this purpose. The idea of this approach is that when the Reynolds number is modified, the hypernetwork modifies the weights of the CNN in such a way that it produces flow fields corresponding to that particular Reynolds number. The concept of the hypernetwork-based parametrization is tested on the problem of a compressible fluid flow through a blade cascade with variable blade profiles and Reynolds numbers.