Archive of Applied Mechanics最新文献

The industrial standard in the design and development process of NVH (Noise Vibration Harshness) characteristic of brakes is the application of Finite Element (FE) models with a high number of degrees of freedom in the range of one or several millions. Nevertheless, parallel experimental investigations are still indispensable. On the other hand, minimal models with, due to the inclusion of the self-excitation process, at least two degrees of freedom are well known to be capable to explain qualitatively phenomena as instability of the desired non-vibrating solution or limit cycle oscillation but are in general very inaccurate in predicting the dynamics of a specific real brake. This is because the underlying physical assumptions are already too restrictive and model parameters (especially those referring to nonlinearities) are widely unknown. To overcome this problem, the data-driven modeling approach SINDy (Sparse Identification of Nonlinear Dynamics) is applied to identify appropriate nonlinear functions for a brake squeal minimal model. A problem thereby is the limited database. It turns out that the naive implementation of the method yielding the lowest possible residuum does not necessarily provide physically meaningful models and results, respectively. Instead, a constrained model that incorporates physical knowledge is used to robustly identify parameters and reproduce realistic dynamic behavior. Thereby, several appropriate models with coexisting limit cycles and stationary equilibrium are identified. In particular, it was found that the angular position of the brake drum has a significant influence on the model parameters and therefore must be taken into account in a model with long-term validity.

Peridynamics describes the material in a non-local form and is very suited for the simulation of dynamic fracture. However, one significant effect regarding dynamic fracture is the correct handling of elastic deformation, like the pressure and tension waves inside a body, due to dynamic boundary conditions like an impact or impulse. Many peridynamic material formulations have been developed with differences in this regard. This study investigates the elastic wave propagation characteristics of bond-based, ordinary state-based, continuum kinematics-inspired peridynamics and a local continuum consistent correspondence formulation. Multiple parameters of a longitudinal pressure wave inside an elastic bar are studied. While all formulations demonstrate adequate wave propagation handling, all except the correspondence formulation are sensitive to incomplete horizons. The local continuum consistent formulation does not suffer from the surface effect and models the wave propagation with perfect accuracy.

In this study, we propose a structural health monitoring and diagnostic method for layered (multi-story) structures using a convolutional neural network (CNN). The proposed method is a primary diagnostic one, and its purpose is to allow quick identification of the location of an abnormality after detecting it. An abnormality is defined as a decrease in the stiffness characteristics (spring constant) of the outer wall of a multi-story structure when it deteriorates or is damaged. The proposed method has the following features. A modal circle is generated by multiplying the frequency response functions (FRFs) simulated by a mathematical model and the FRFs from the actual structure, in frequency space, and then a CNN learns the features of the abnormality from the modal circle and diagnoses it in the actual multi-story structure. We first verified the validity of the proposed method by considering a three-story structure as a numerical example. When the method was applied to three types of abnormal conditions, it was shown that the abnormal diagnosis could be performed correctly. Next, we constructed an experimental model of a three-story structure, and realized three types of abnormal conditions similar to those in the numerical model. We verified the applicability of the proposed method and showed that correct diagnosis of an abnormality was possible. Both the validity and applicability of the proposed method were thus confirmed.

Resin-mineral composite materials (RMC) have attracted much attention due to their excellent dynamic properties. However, the mechanical models related to RMC have not fully considered the complex interactions between components and interface transition zones (ITZ), and have also given less consideration to the influence of initial defects in the material, resulting in lower prediction accuracy of RMC mechanical models. To address the problem, based on composite sphere model, generalized autonomous method, and improved Mori–Tanaka method, the theoretical prediction model of RMC elastic modulus considering the influence of ITZ and pores is established in this study. Then, based on the micromechanical analysis method and combined with the theoretical data, the numerical prediction model of RMC elastic modulus considering the impact of pores and ITZ is founded. Furthermore, the influence of ITZ, pore, aggregate, and matrix parameters on the elastic modulus of RMC is investigated. The research results indicate that: (1) The error between the predicted RMC effective elastic modulus and the corresponding experimental values is within a reasonable range, indicating that the theoretical and numerical models proposed in this study are theoretically feasible. (2) ITZ and pore parameters have remarkable impact on the effective elastic modulus of RMC, indicating that it is indispensable to take into account ITZ and pores. (3) It is the elastic modulus of RMC that can be sensitive concerning the volume fraction and effective modulus of aggregate and matrix. The research results provide a theoretical basis for the design and application of RMC.

In cold regions, the water in rock fissures may freeze due to external temperature, leading to crack expansion and propagation, which induces rock damage. In this work, the rock fracture due to uniaxial expansion of tension cracks under freezing conditions was studied, and different pressures acting on the crack surfaces were analyzed from the fracture mechanics perspective. The corresponding physical model was also developed. Considering the physical and mechanical degradation, the damage to fracture toughness caused by freeze-thaw cycles was determined, and improvements were made to the existing brittle phase field finite element model (PFM). Numerical simulations and calculations were carried out at different stages throughout the entire freeze-thaw cycle to obtain the crack expansion morphological features at different stages. The results showed that hydrostatic pressure and freezing pressure are the primary loads driving the crack expansion, with freezing pressure playing a dominant role, whereas hydrostatic pressure contributes relatively little. The freezing period is the main stage of crack expansion governing the crack morphology. The thawing period accelerates the crack propagation rate, leading to rock failure. Also, the inclination angle of cracks may significantly influence rock failure. In general, rock failure results from different combinations of the initiation, expansion and connection of primary cracks under freeze-thaw action .

Large strain analysis is a challenging task, especially in fictitious or immersed boundary domain methods, since badly broken elements/cells can lead to an ill-conditioned global tangent stiffness matrix, resulting in convergence problems of the incremental/iterative solution approach. In this work, the finite cell method is employed as a fictitious domain approach, in conjunction with an eigenvalue stabilization technique, to ensure the stability of the solution procedure. Additionally, a remeshing strategy is applied to accommodate highly deformed configurations of the geometry. Radial basis functions and inverse distance weighting interpolation schemes are utilized to map the displacement gradient and internal variables between the old and new meshes during the remeshing process. For the first time, we demonstrate the effectiveness of the remeshing approach using various numerical examples in the context of finite strain elastoplasticity.

Bubble-based metamaterials have been extensively studied both theoretically and experimentally thanks to their simple geometry and their ability to manipulate acoustic waves. The latter is partly dependent on the structural characteristics of the metamaterial and partly dependent on the incident acoustic wave. Initially, the selection of specific structural characteristics is explained by presenting the Fourier transformations of the reflected waves for different arrangements of a bubbly meta-screen subject to Gaussian excitation. Next, the numerical study focuses on the changes induced to the response of a bubbly meta-screen, subject to different excitation pulses. For complex frequency excitation the bubbles delay to return to their equilibrium position for a couple of moments, hence the energy is stored in the system during those moments. This research provides a new strategy to actively control the response of a bubbly meta-screen and seeks to inspire future studies towards further optimization of the incident pulse based on the functionalities in need.

The present article contributes a new novel mathematical model influenced with the memory effect that endeavours to record the thermal responses inside a living tissue exposed to an oscillatory heat input on its outer surface. Heat transport inside the tissue is modelled with the hyperbolic equation involving three relaxation times. Analytical solutions of the significant field quantities—temperature, displacement and thermal stress are determined in the frequency domain by adopting the Laplace transform mechanism. Computational results are derived by inverting the field quantities from frequency domain to the physical domain. Memory influences are forecasted on the propagation of the thermo-mechanical waves inside the tissue by obtaining the influences of the kernel functions and time-delay quantity on the physical fields. Impact of the relaxation times is pronounced on the variances of the waves’ constituents. Graphical outcomes speculate that inclusion of the phase lags in heat transfer model supresses and stabilizes the speed of the waves. This study may support to the medical practitioners during thermal therapy and to develop the precised clinical equipment.

The crux of the present investigation is to come up with a mathematical model for the analysis of moving interfacial crack caused by SH-wave propagating in a composite strip featuring dissimilar orthotropic material. Wiener–Hopf methodology along with complex variable transform technique has been applied to determine the closed form analytical expression of SIF (stress intensity factor). Two different types of loading constraints, viz. NHL (non-harmonic loading) and HL (harmonic loading), on the edges of the crack have been studied. In addition to this, some special cases, viz. constant loading and stress free condition, following aforementioned loading constraints have also been taken into account for the moving crack in the considered composite strip. The limiting case for static condition leading to resonance-type phenomena has been presented for the subject under investigation. When computed numerically and depicted graphically, the profound impacts of distinct material and geometrical parameters on SIF for distinct loading constraints have also been manifested. The computational results bring out the fact that stress intensity factor falls off with rise in crack velocity when the edges of the crack are under NHL, whereas SIF shows reverse nature for HL.

The primary objective of this paper is to introduce innovative orthogonal power function series aimed at obtaining accurate nonlinear analytical solutions for axisymmetric circular thin plates. The main features of this paper are as follows: The deflection is expanded by the innovative orthogonal power function series. The Airy stress function, which satisfies the geometric deformation compatibility equation, responds to the nonlinear coupling relationships between the plate deflection and the in-plane force or displacement boundary conditions. The nonlinear algebraic equations are obtained by the energy variational method. Many comparisons are made with the results of related researchers. The present accurate solutions not only allow the problems to be solved perfectly and provide the most reliable basis for engineering design but also set new benchmarks for the verification of various nonlinear numerical and approximate analytical solutions. The developed methodology represents a significant improvement, providing better accuracy and computational efficiency compared to historical approaches. Therefore, the present method is more worthy of promotion.