Applied Mathematics and Mechanics-English Edition最新文献

This research proposes a novel type of variable stiffness tuned particle damper (TPD) for reducing vibrations in boring bars. The TPD integrates the developments of particle damping and dynamical vibration absorber, whose frequency tuning principle is established through an equivalent theoretical model. Based on the multiphase flow theory of gas-solid, it is effective to obtain the equivalent damping and stiffness of the particle damping. The dynamic equations of the coupled system, consisting of a boring bar with the TPD, are built by Hamilton’s principle. The vibration suppression of the TPD is assessed by calculating the amplitude responses of the boring bar both with and without the TPD by the Newmark-beta algorithm. Moreover, an improvement is proposed to the existing gas-solid flow theory, and a comparative analysis of introducing the stiffness term on the damping effect is presented. The parameters of the TPD are optimized by the genetic algorithm, and the results indicate that the optimized TPD effectively reduces the peak response of the boring bar system.

In this paper, the interactions between the transverse loads and the electrical field quantities are investigated based on the nonlinear constitutive relation. By considering a composite beam consisting of a piezoelectric semiconductor and elastic layers, the nonlinear model is established based on the phenomenological theory and Euler’s beam theory. Furthermore, an iteration procedure based on the differential quadrature method (DQM) is developed to solve the nonlinear governing equations. Before analysis, the convergence and correctness are surveyed. It is found that the convergence of the proposed iteration is fast. Then, the transverse pressure induced electrical field quantities are investigated in detail. From the calculated results, it can be found that the consideration of nonlinear constitutive relation is necessary for a beam undergoing a large load. Compared with the linear results, the consideration of the nonlinear constitutive relation breaks the symmetry for the electric potential, the electric field, and the perturbation carrier density, and has little influence on the electric displacement. Furthermore, the non-uniform pressures are considered. The results show that the distributions of the electric field quantities are sensitively altered. It indicates that the electrical properties can be manipulated with the design of different transverse loads. The conclusions in this paper could be the guidance on designing and manufacturing electronic devices accurately.

Surface cracks are commonly observed in coatings and films. When structures with coatings are subject to stretching, opening mode cracks are likely to form on the surface, which may further lead to other forms of damage, such as interfacial delamination and substrate damage. Possible crack forms include cracks extending towards the interface and channeling across the film. In this paper, a two-dimensional numerical model is proposed to obtain the structural strain energy at arbitrary crack lengths for bilayer structures under uniaxial tension. The energy release rate and structural stress intensity factors can be obtained accordingly, and the effects of geometry and material features on fracture characteristics are investigated, with most crack patterns being confirmed as unstable. The proposed model can also facilitate the analysis of the stress distribution in periodic crack patterns of films. The results from the numerical model are compared with those obtained by the finite element method (FEM), and the accuracy of the theoretical results is demonstrated.

This paper is dedicated to applying the Fourier amplitude sensitivity test (FAST) method to the problem of mixed extension and inflation of a circular cylindrical tube in the presence of residual stresses. The metafunctions and the Ishigami function are considered in the sensitivity analysis (SA). The effects of the input variables on the output variables are investigated, and the most important parameters of the system under the applied pressure and axial force such as the axial stretch and the azimuthal stretch are determined.

The warping may become an important factor for the precise transverse vibrations of curved beams. Thus, the first aim of this study is to specify the structural design parameters where the influence of cross-sectional warping becomes great and the first-order shear deformation theory lacks the precision necessary. The out-of-plane vibrations of the first-order shear deformation theory are compared with the warping-included vibrations as the curvature and/or thickness increase for symmetric and asymmetric transversely-functionally graded (TFG) curved beams. The second aim is to determine the influence of design parameters on the vibrations. The circular/exact elliptical beams are formed via curved mixed finite elements (MFEs) based on the exact curvature and length. The stress-free conditions are satisfied on three-dimensional (3D) constitutive equations. The variation of functionally graded (FG) material constituents is considered based on the power-law dependence. The cross-sectional warping deformations are defined over a displacement-type FE formulation. The warping-included MFEs (W-MFEs) provide satisfactory 3D structural characteristics with smaller degrees of freedom (DOFs) compared with the brick FEs. The Newmark method is used for the forced vibrations.

A popular dynamical model for the vortex induced vibration (VIV) of a suspended flexible cable consists of two coupled equations. The first equation is a partial differential equation governing the cable vibration. The second equation is a wake oscillator that models the lift coefficient acting on the cable. The incoming wind acting on the cable is usually assumed as the uniform wind with a constant velocity, which makes the VIV model be a deterministic one. In the real world, however, the wind velocity is randomly fluctuant and makes the VIV of a suspended flexible cable be treated as a random vibration. In the present paper, the deterministic VIV model of a suspended flexible cable is modified to a random one by introducing the fluctuating wind. Using the normal mode approach, the random VIV system is transformed into an infinite-dimensional modal vibration system. Depending on whether a modal frequency is close to the aeolian frequency or not, the corresponding modal vibration is characterized as a resonant vibration or a non-resonant vibration. By applying the stochastic averaging method of quasi Hamiltonian systems, the response of modal vibrations in the case of resonance or non-resonance can be analytically predicted. Then, the random VIV response of the whole cable can be approximately calculated by superimposing the response of the most influential modal vibrations. Some numerical simulation results confirm the obtained analytical results. It is found that the intensity of the resonant modal vibration is much higher than that of the non-resonant modal vibration. Thus, the analytical results of the resonant modal vibration can be used as a rough estimation for the whole response of a cable.

The dispersion curves of bulk waves propagating in both AlN and ZnO film bulk acoustic resonators (FBARs) are presented to illustrate the mode flip of the thickness-extensional (TE) and 2nd thickness-shear (TSh2) modes. The frequency spectrum quantitative prediction (FSQP) method is used to solve the frequency spectra for predicting the coupling strength among the eigen-modes in AlN and ZnO FBARs. The results elaborate that the flip of the TE and TSh2 branches results in novel self-coupling vibration between the small-wavenumber TE and large-wavenumber TE modes, which has never been observed in the ZnO FBAR. Besides, the mode flip leads to the change in the relative positions of the frequency spectral curves about the TE cut-off frequency. The obtained frequency spectra can be used to predict the mode-coupling behaviors of the vibration modes in the AlN FBAR. The conclusions drawn from the results can help to distinguish the desirable operation modes of the AlN FBAR with very weak coupling strength from all vibration modes.

We present a study on the dynamic stability of porous functionally graded (PFG) beams under hygro-thermal loading. The variations of the properties of the beams across the beam thicknesses are described by the power-law model. Unlike most studies on this topic, we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent, simultaneously, by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory (NSGIT) which are strictly equipped with a set of constitutive boundary conditions (CBCs), and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed. All the variables presented in the differential problem formulation are discretized. The numerical solution of the dynamic instability region (DIR) of various bounded beams is then developed via the generalized differential quadrature method (GDQM). After verifying the present formulation and results, we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters, the static force factor, the functionally graded (FG) parameter, and the porosity parameter on the DIR. Furthermore, the influence of considering the size-dependent hygro-thermal load is also presented.

Wrinkles in flat graded elastic layers have been recently described as a time-varying Hamiltonian system by the energy method. Cylindrical core/shell structures can also undergo surface instabilities under the external pressure. In this study, we show that by treating the radial direction as a pseudo-time variable, the graded core/shell system with radially decaying elastic properties can also be described within the symplectic framework. In combination with the shell buckling equation, the present paper addresses the surface wrinkling of graded core/shell structures subjected to the uniform external pressure by solving a series of ordinary differential equations with varying coefficients. Three representative gradient distributions are showcased, and the predicted critical pressure and critical wave number are verified by finite element simulations. The symplectic framework provides an efficient and accurate approach to understand the surface instability and morphological evolution in curved biological tissues and engineered structures.

This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved. A novel approach is applied to the analysis of the natural vibrations of Euler-Bernoulli beams. The proposed algorithm, named as two-parameter multiple shooting method, is a new powerful numerical tool for calculating the natural frequencies and modes of multi-segment prismatic and non-prismatic beams with different boundary conditions. The impact of the axial force and additional point masses is also taken into account. Due to the fact that the method is based directly on the fourth-order ordinary differential equation, the structures do not have to be divided into many small elements to obtain an accurate enough solution, even though the geometry is very complex. To verify the proposed method, three different examples are considered, i.e., a three-segment non-prismatic beam, a prismatic column subject to non-uniformly distributed compressive loads, and a two-segment beam with an additional point mass. Numerical analyses are carried out with the software MATHEMATICA. The results are compared with the solutions computed by the commercial finite element program SOFiSTiK. Good agreement is achieved, which confirms the correctness and high effectiveness of the formulated algorithm.