Applied Mathematics and Mechanics-English Edition最新文献

A multi-degree-of-freedom device is proposed, which can achieve efficient vibration reduction as the main objective and energy harvesting as the secondary purpose. The device comprises a multiscale nonlinear vibration absorber (NVA) and piezoelectric components. Energy conversion and energy measurement methods are used to evaluate the device performance from multiple perspectives. Research has shown that this device can efficiently transfer transient energy from the main structure and convert a portion of transient energy into electrical energy. Main resonance and higher-order resonance are the main reasons for efficient energy transfer. The device can maintain high vibration reduction performance even when the excitation amplitude changes over a large range. Compared with the single structures with and without precompression, the multiscale NVA-piezoelectric device offers significant vibration reduction advantages. In addition, there are significant differences in the parameter settings of the two substructures for vibration reduction and energy harvesting.

To improve the thermoelectric converting performance in applications such as power generation, reutilization of heat energy, refrigeration, and ultrasensitive sensors in scramjet engines, a thermoelectric film/substrate system is widely designed and applied, whose interfacial behavior dominates the strength and service life of thermoelectric devices. Herein, a theoretical model of a thermoelectric film bonded to a graded substrate is proposed. The interfacial shear stress, the normal stress in the thermoelectric film, and the stress intensity factors affected by various material and geometric parameters are comprehensively studied. It is found that adjusting the inhomogeneity parameter of the graded substrate, thermal conductivity, and current density of the thermoelectric film can reduce the risk of interfacial failure of the thermoelectric film/graded substrate system. Selecting a stiffer and thicker thermoelectric film is advantageous to the reliability of the thermoelectric film/graded substrate system. The results should be of great guiding significance for the present and upcoming applications of thermoelectric materials in various fields.

In a wide variety of mechanical and industrial applications, e.g., space cooling, nuclear reactor cooling, medicinal utilizations (magnetic drug targeting), energy generation, and heat conduction in tissues, the heat transfer phenomenon is involved. Fourier’s law of heat conduction has been used as the foundation for predicting the heat transfer behavior in a variety of real-world contexts. This model’s production of a parabolic energy expression, which means that an initial disturbance would immediately affect the system under investigation, is one of its main drawbacks. Therefore, numerous researchers worked on such problem to resolve this issue. At last, this problem was resolved by Cattaneo by adding relaxation time for heat flux in Fourier’s law, which was defined as the time required to establish steady heat conduction once a temperature gradient is imposed. Christov offered a material invariant version of Cattaneo’s model by taking into account the upper-connected derivative of the Oldroyd model. Nowadays, both models are combinedly known as the Cattaneo-Christov (CC) model. In this attempt, the mixed convective MHD Falkner-Skan Sutterby nanofluid flow is addressed towards a wedge surface in the presence of the variable external magnetic field. The CC model is incorporated instead of Fourier’s law for the examination of heat transfer features in the energy expression. A two-phase nanofluid model is utilized for the implementation of nano-concept. The nonlinear system of equations is tackled through the bvp4c technique in the MATLAB software 2016. The influence of pertinent flow parameters is discussed and displayed through different sketches. Major and important results are summarized in the conclusion section. Furthermore, in both cases of wall-through flow (i.e., suction and injection effects), the porosity parameters increase the flow speed, and decrease the heat transport and the influence of drag forces.

The electron-phonon interaction can reveal the microscopic mechanism of heat transfer in metals. The two-step heat conduction considering electron-phonon interaction has become an effective theoretical model for extreme environments, such as micro-scale and ultrafast processes. In this work, the two-step heat transfer model is further extended by considering the Burgers heat conduction model with the second-order heat flux rate for electrons. Then, a novel generalized electron-phonon coupling thermoelasticity is proposed with the Burgers electronic heat transfer. Then, the problem of one-dimensional semi-infinite copper strip subject to a thermal shock at one side is studied by the Burgers two-step (BTS) model. The thermoelastic analytical solutions are systematically derived in the Laplace domain, and the numerical Laplace inversion method is adopted to obtain the transient responses. The new model is compared with the parabolic two-step (PTS) model and the hyperbolic two-step (HTS) model. The results show that in ultrafast heating, the BTS model has the same wave front jump as the HTS model. The present model has the faster wave speed, and predicts the bigger disturbed regions than the HTS model. More deeply, all two-step models also have the faster wave speeds than one-step models. This work may benefit the theoretical modeling of ultrafast heating of metals.

The harmonic balance method (HBM) is one of the most widely used methods in solving nonlinear vibration problems, and its accuracy and computational efficiency largely depend on the number of the harmonics selected. The adaptive harmonic balance (AHB) method is an improved HBM method. This paper presents a modified AHB method with the asymptotic harmonic selection (AHS) procedure. This new harmonic selection procedure selects harmonics from the frequency spectra of nonlinear terms instead of estimating the contribution of each harmonic to the whole nonlinear response, by which the additional calculation is avoided. A modified continuation method is proposed to deal with the variable size of nonlinear algebraic equations at different values of path parameters, and then all solution branches of the amplitude-frequency response are obtained. Numerical experiments are carried out to verify the performance of the AHB-AHS method. Five typical nonlinear dynamic equations with different types of nonlinearities and excitations are chosen as the illustrative examples. Compared with the classical HBM and Runge-Kutta methods, the proposed AHB-AHS method is of higher accuracy and better convergence. The AHB-AHS method proposed in this paper has the potential to investigate the nonlinear vibrations of complex high-dimensional nonlinear systems.

The photo-induced buckling of axially periodic glassy nematic films with alternating stripped director domains is explored by the Föppl-von Kármán plate theory along with a modified kinetics approach. The effects of domain widths on the critical light intensity as well as the buckling morphology are examined numerically. It is found that in most cases the buckled film forms regularly aligned dimples and protrusions, but shows large scale bending perpendicular to the periodic axis if the widths of the stripes are nearly the same. In addition, change in light intensity is shown to alter the wavenumber of the buckling pattern. These results are expected helpful to the design of shape-shifting structures with glassy nematic films.

A nonlinear semi-analytical scheme is proposed for investigating the finite-amplitude nonlinear sloshing in a horizontally baffled rectangular liquid container under the seismic excitation. The sub-domain method is developed to analytically derive the modal behaviors of the baffled linear sloshing. The viscosity dissipation effects from the interior liquid and boundary layers are considered. With the introduction of the generalized time-dependent coordinates, the surface wave elevation and velocity potential are represented by a series of linear modal eigenfunctions. The infinite-dimensional modal system of the nonlinear sloshing is formulated based on the Bateman-Luke variational principle, which is further reduced to the finite-dimensional modal system by using the Narimanov-Moiseev asymptotic ordering. The base force and overturning moment induced by the nonlinear sloshing are derived as the functions of the generalized time-dependent coordinates. The present results match well with the available analytical, numerical, and experimental results. The paper examines the surface wave elevation, base force, and overturning moment versus the baffle parameters and excitation amplitude in detail.

A two-degree-of-freedom (2DOF) vibration isolation structure with an integrated geometric nonlinear inerter (NI) device is proposed. The device is integrated into an inertial nonlinear energy sink (INES), and its vibration suppression performance is examined by the Runge-Kutta (RK) method and verified by the harmonic balance method (HBM). The new isolator is compared with a traditional vibration isolator. The results show a significant improvement in the vibration suppression performance. To investigate the effects of the excitation amplitude and initial condition on the dynamics of the system, a series of transmissibility-frequency response analyses are performed based on the displacement transmissibility. The energy flow of the system is analyzed, and numerous calculations reveal a series of ideal values for the energy sink in the NI-INES system. This study provides new insights for the design of vibration isolators.

In this paper, we focus on the two-dimensional pulsating nanofluid flow through a parallel-plate channel in the presence of a magnetic field. The pulsating flow is produced by an applied pressure gradient that fluctuates with a small amplitude. A kind of proper transformation is used so that the governing equations describing the momentum and thermal energy are reduced to a set of non-dimensional equations. The analytical expressions of the pulsating velocity, temperature, and Nusselt number of nanofluids are obtained by the perturbation technique. In the present study, the effects of the Cu-H₂O and Al₂O₃-H₂O nanofluids on the flow and heat transfer in pulsating flow are compared and analyzed. The results show that the convective heat transfer effect of Cu-H₂O nanofluids is better than that of Al₂O₃-H₂O nanofluids. Also, the effects of the Hartmann number and pulsation amplitude on the velocity, temperature, and Nusselt number are examined and discussed in detail. The present work indicates that increasing the Hartmann number and pulsation amplitude can enhance the heat transfer of the pulsating flow. In addition, selecting an optimal pulsation frequency can maximize the convective heat transfer of the pulsating flow. Therefore, improved understanding of these fundamental mechanisms is conducive to the optimal design of thermal systems.

An efficient data-driven approach for predicting steady airfoil flows is proposed based on the Fourier neural operator (FNO), which is a new framework of neural networks. Theoretical reasons and experimental results are provided to support the necessity and effectiveness of the improvements made to the FNO, which involve using an additional branch neural operator to approximate the contribution of boundary conditions to steady solutions. The proposed approach runs several orders of magnitude faster than the traditional numerical methods. The predictions for flows around airfoils and ellipses demonstrate the superior accuracy and impressive speed of this novel approach. Furthermore, the property of zero-shot super-resolution enables the proposed approach to overcome the limitations of predicting airfoil flows with Cartesian grids, thereby improving the accuracy in the near-wall region. There is no doubt that the unprecedented speed and accuracy in forecasting steady airfoil flows have massive benefits for airfoil design and optimization.