Abstract: Abstract This paper provides a general solution for a torsion problem of bar composed of confocally elliptical dissimilar layers. Complex variable method is used to study the problem. The continuity conditions for the warping function and the normal shear stress along the interfaces are suggested. By using the transfer matrices, we can exactly link all sets of undetermined coefficients in the complex potentials defined for layers. Finally, from the conditions imposed on the interior inclusion and the exterior boundary, the solution is obtainable. Numerical examples are carried out to show the influence of the different shear moduli defined on different layers to the stress distribution. The applied torque at the ends of bar is evaluated. PubDate: 2020-03-01

Abstract: Abstract The tuned mass damper (TMD) is a widely used passive control device which is attached to a main system to suppress undesired vibration. In this paper, a non-traditional form of TMD system is investigated. Unlike the traditional TMD configuration, the considered TMD system has a linear viscous damper connecting the absorber mass directly to the ground instead of the main mass. There have been some studies on the optimization design of the non-traditional TMD (NT-TMD) for undamped main structures. Those studies have indicated that the NT-TMD provides better performance than the traditional TMD does. When there is a frequency shifting in the structural frequency or tuning frequency of TMD, to the best knowledge of the authors, there has been no study on the performance of the NT-TMD. The main idea of the study is to investigate the effect of frequency detuning on the control performance of the NT-TMD. The optimum parameters of the NT-TMD system and corresponding effectiveness are obtained for different mass ratios of the NT-TMD system. The numerical results indicate that the NT-TMD with high mass ratio provides better robustness to the changes in the target frequency ratio than the traditional TMD. PubDate: 2020-03-01

Abstract: Abstract The bending vibration of transmission shafting directly influences dynamic performance of mechanical systems. The adoption of carbon fiber-reinforced plastics (CFRP) hollow shaft in the long-span transmission shafting can effectively reduce bending vibration. This paper aims to modify the transfer matrix method (TMM) for the CFRP/Steel composite transmission shafting system based on lamination theory and layer-wise beam theory. The dynamic kinetic equations of the steel and CFRP segments of the composite transmission shafting were modeled; then the bending vibration was solved by combining the boundary conditions of the CFRP/Steel composite transmission shafting. The experimental tests have been carried out in the CFRP/Steel composite transmission shafting to obtain the critical speed of rotation. Moreover, the results of modified TMM were compared with experimental tests, finite element method, and simply supported beam model. The comparison results show that the modified TMM proposed in this paper can effectively calculate the bending vibration characteristics of the CFRP/Steel composite transmission shafting system. PubDate: 2020-03-01

Abstract: Abstract This paper presents a theoretical investigation on the temperature and thermal stress distributions developed in simply supported laminated open cylindrical panels subjected to thermal load. Cylindrical panels were divided into several thin layers, where the radial variable r in heat conduction equation and elasticity equations was approximately replaced by the center coordinate of each layer. The analytical expressions in terms of temperature, displacements and stresses can be then deduced in a thin layer. Transfer matrix method was used to recursively generate the relations of temperature, displacements and stresses between outermost and innermost surface for the laminated panel. The panel surface condition was thereafter used to determine the coefficients in the solutions. These coefficients were substituted in solutions for each thin layer to obtain the distributions of temperature, displacements and stresses in the panel. The number of the terms of series was used to check the solution convergence. The validity and feasibility of the proposed method were verified by comparing the theoretical results with the numerical results from the finite element method. The effects of surface temperatures, panel thickness, number of laminated layers and material properties were detailed and investigated with respect to the temperature, displacement and stresses distributions in the panel. PubDate: 2020-03-01

Abstract: Abstract Introducing the fractional \(\Lambda \)-derivative, with the corresponding \(\Lambda \)-fractional spaces, the fractional beam bending problem is presented. In fact, non-local derivatives govern the beam bending problem that accounts for the interaction of microcracks or materials non-homogeneities, such as composite materials or materials with fractal geometries. The proposed theory is implemented to the fractional bending deformation of a simply supported beam and a cantilever beam under continuously distributed loading. PubDate: 2020-03-01

Abstract: Abstract The dynamic properties of bridges can be extracted from the dynamic responses of the vehicles passing on these bridges. This paper proposes a method for the vehicle–bridge interaction analysis of continuous beam bridges with different spans and variable cross sections using numerical methods that are high in computational efficiency. Herein, the vehicle is simplified as a spring–damper–mass system and coupled to the bridge by its interactional force in the governing equations based on the Timoshenko beam theory. According to the symplectic orthogonality of the state vectors, the orthogonality of the mode shapes of the Timoshenko beams is proved, and the dynamic responses of the continuous beam bridges with different spans and variable cross sections can be solved by the mode superposition method. More complicated factors, such as harmonic load on vehicles, noise in measurement, and roughness of pavements, can also be conveniently taken into account. Finally, the proposed method is demonstrated using some numerical examples and applied to a real bridge. The results indicate that the method is convenient, efficient, and precise for engineering applications. PubDate: 2020-03-01

Abstract: Abstract In this contribution, a new form of the strain energy function is proposed to describe the hyperelastic behavior of rubber-like materials under various deformation. The proposed function represents an invariant-based model and contains two material parameters. The model was tested with the experimental data of vulcanized rubbers, collagen and fibrin. The material parameters are kept constant for a material subjected to different types of loading. Good agreement between model and experimental data was obtained for all materials. PubDate: 2020-03-01

Abstract: Abstract Bone remodeling is a key process in vertebrate organisms, since it is responsible for maintaining skeleton’s integrity. However, in some pathological conditions, such as osteoporosis or Paget’s disease, bone’s function becomes compromised. To gain a better understanding about these conditions, bone remodeling has become a determinant subject of research. Remodeling implies resorption of bone by osteoclasts followed by formation of new tissue by osteoblasts. The interaction between these two bone cells is reproduced in this work by extending the bone remodeling model of Ayati et al. (Biol Direct 5:28, 2010. https://doi.org/10.1186/1745-6150-5-28). Also, for the first time, a discrete numerical method—finite element method (FEM)—is applied to solve the remodeling equations and analyze the results. A single cycle of remodeling is simulated using a two-dimensional bone patch. Results show that the developed mathematical model is able to correlate bone cell dynamics with different phases of the remodeling process, allowing to obtain the transient spatial distribution of bone’s apparent density along time. Thus, the presented model reveals itself as a successful approach, producing an accurate temporal-spatial evolution of bone cells during an event of bone remodeling. PubDate: 2020-03-01

Abstract: Abstract The nonlinear energy sink (NES) is a lightweight, strongly nonlinear dynamical attachment coupled to a (typically linear) large-scale primary structure for passive vibration mitigation. There are two nonlinear mechanisms governing the dynamics of the coupled system: irreversible targeted energy transfer (TET) from the primary structure to the NES, where energy is confined and locally dissipated, and NES-induced nonlinear energy scattering between the structural modes of the primary structure. In the literature, different NES designs have been investigated to optimize their nonlinear effects on the primary structures. One such design is the rotary NES consisting of a small mass inertially coupled to the primary structure through a rigid arm; another is the vibro-impact NES with non-smooth nonlinearities and inelastic collisions with the primary structure. These types have been found to achieve strong and rapid TET and are less sensitive to energy fluctuations. In this work, a hybrid NES design is proposed based on the synergetic synthesis of the rotary and impact-based NESs in a single rotary-impact NES (RINES). The RINES incorporates a fixed rigid barrier attached (typically) to the top floor of the primary structure to inflict impacts between its rotating mass and the top floor. An analytical study to evaluate its capacity to engage in resonance capture with a primary structure is presented first, followed by numerical investigations of cases when the RINES is attached to the top floors of small- and large-scale linear primary structures under impulsive excitation. The non-smooth nonlinearities induced through the consecutive impacts resulted in effective broadband shock mitigation at highly energetic response regimes, whereas the nonlinear inertial coupling enables similar beneficial mitigation capacity at lower-energetic response regimes. Hence, the combined effect of non-smooth and inertial nonlinearities enables effective passive mitigation capacity for a broad range of applied impulsive energies. PubDate: 2020-03-01

Abstract: Abstract An efficient procedure based on the semi-analytical finite strip method with invariant matrices is developed and applied to analyze the initial post-buckling of thin-walled members. Nonlinear strain–displacement equations are introduced in the manner of the von Karman assumption for the classical thin plate theory, and the formulations of the finite strip methods are deduced from the principle of the minimum potential energy. In order to improve the computational efficiency, an analytical integral of the stiffness matrix is transformed into matrix multiple calculation with introducing invariant matrices which can be integrated in advance only once. Three commonly employed benchmark problems are tested with proposed method and other state-of-the-art methods. The corresponding comparison results show that: (1) this finite strip method is proved to be a feasible and accurate tool; (2) compared with the calculation process of the conventional finite strip methods, the proposed procedure is much more efficient since it requires the integration of the stiffness matrix only once no matter how many iterations are needed; and (3) the advantage of time-saving is greatly remarkable as the number of iterations increases. PubDate: 2020-03-01

Abstract: Abstract In an important class of linear viscoelastic media the stress is the superposition of a Newtonian term and a stress relaxation term. It is assumed that the creep compliance is a Bernstein class function, which entails that the relaxation function is LICM. In this paper, the effect of Newtonian viscosity term on wave propagation is examined. It is shown that Newtonian viscosity dominates over the features resulting from stress relaxation. For comparison the effect of unbounded relaxation function is also examined. In both cases, the wave propagation speed is infinite, but the high-frequency asymptotic behavior of attenuation is different. Various combinations of Newtonian viscosity and relaxation functions, and the corresponding creep compliances are summarized. PubDate: 2020-03-01

Abstract: Abstract A novel three-dimensional progressive damage model based on generalized mixed finite element method (GMPDM) was established to investigate the strength and failure behavior of notched composite laminate plate. Firstly, the stress distribution of notched isotropic plate under tension is studied, and the results are compared with the analytical solution to verify the high accuracy of the generalized mixed finite element method. Then, the strength and failure modes of three notched composite laminates are studied. The results are compared with the several groups of results to verify the high-precision of the developed GMPDM method, respectively. PubDate: 2020-03-01

Abstract: Abstract This paper studies analytically the problem of the sudden failure of a number of stays through a suitable mathematical model, based on the analytical method exposed by authors in previous publications and extended in this study through a 3D analysis. The analysis is carried out by the modal superposition method, and the gathered equations of the problem are solved through the Galerkin procedure and the Duhamel’s Integrals. Characteristic examples are solved and useful diagrams and plots are drawn, while interesting results are obtained. PubDate: 2020-02-20

Abstract: Abstract Studied in this paper is the surface tension-induced stress field around two nanoscale holes in an infinite, elastic matrix. The complex variable method is adopted to describe the assumed plane-strain deformation of the structure. The stress boundary conditions at the surfaces of the holes are formulated via the integral-type Gurtin–Murdoch model. The stress field is finally obtained with the aid of conformal mapping and series expansion methods. Numerical examples are demonstrated for the case of one approximately triangular, smooth hole and one approximately square, smooth hole. A detailed discussion is carried out about the influence of the distance between the two holes on the stress field. PubDate: 2020-02-20

Abstract: Abstract The present paper takes up the underlying nonlinear initial value problem from a preceding author’s work about the dynamics of a single bubble in a highly viscous liquid medium under different pressure impacts. The arising ordinary differential equation is mainly based on the constitutive relation of a second-order liquid that in particular includes two non-Newtonian material constants. In this article, the significance of these coefficients is mathematically analyzed in detail by proving the existence of stable solutions of the named initial value problem. This is achieved by special transformations of the differential equation at hand and the introduction of appropriate Lyapunov functions. It particularly turns out that a combined condition of the non-Newtonian coefficients and diverse restrictions to the external pressure impact are decisive for the validity of the existence results. Furthermore, the convergence speed of solutions is investigated by considering the linearized equation associated with the present initial value problem and by applying a special variant of Gronwall’s lemma. The main theoretical result, being the prementioned strong condition for the non-Newtonian coefficients, is finally compared to real data sets. PubDate: 2020-02-17

Abstract: Abstract In recent years to overcome many limitations of drilling operations, composite drill strings as high-tech rotors with complex dynamic behavior are under development. In this research, the fully coupled nonlinear vibration of composite drill strings, which consist of orthotropic layers, is investigated using the Lagrangian approach and the finite element method. In addition to the main nonlinear terms and particularly the geometric stiffening effect, which resulted from the interaction of the drill string weight and the axial bit force, the gyroscopic effect has also been taken into account. The analysis ability of the dynamic model, which is intended to furnish a basic model for the further development of a more comprehensive model, is examined. The fully coupled nonlinear vibrations and modal analysis of the composite drill strings due to various fiber orientations and stacking sequences in the different drilling conditions are studied, and are compared with the steel drill string. PubDate: 2020-02-17

Abstract: Abstract We consider the linear thermo-piezoelectric properties of a ceramic matrix with cylindrical empty pores distributed periodically. The asymptotic homogenization method is applied to an elliptical tensor-weighted boundary value problem in the Stress-Charge-Entropy formulation of the constitutive relations with rapidly oscillating coefficients and free boundary conditions on the surfaces of the pores. For different shapes of the pore cross section, we solve the local problems via finite element method to compute the effective coefficients as functions of the physical properties of the matrix, the shape of the pore cross section and their volume fraction. The numerical results show excellent agreement with analytical formulae. When the effective coefficients are transformed to the Strain-Charge-Entropy formulation of the constitutive relations, they become independent of the shape of the cross section, which further validates the importance of the analytical formulae. We compute the piezoelectric and pyroelectric figures of merit for energy-harvesting applications, which depend on the effective coefficients and are compared with recent experimental results. This contribution could be useful for fine-tuning the properties of this class of materials for energy-harvesting applications. PubDate: 2020-02-14

Abstract: Abstract Vibration characteristics of elastic nanostructures embedded in fluid medium have been used for biological and mechanical sensing and also to investigate the materials mechanical properties. The fluid medium surrounding the nanostructure is typically modeled as a Newtonian fluid. A novel approach based on the exact theory has been developed in this paper, to accurately predict the various vibration scenarios of an elastic sphere, in a compressible viscous fluid. Then, the analysis is extended to a viscoelastic medium using the Maxwell fluid model. To demonstrate the accuracy of the present approach, a comparison is made with the published theoretical results in the literature in some particular cases, which shows a very good agreement. The effects of fluid compressibility and viscoelasticity are discussed in details, and we demonstrate that the fluid compressibility plays a significant role in the vibration modes of an elastic sphere. Results also show that the different vibration modes of a sphere trigger a viscoelastic response in water–glycerol mixtures similar to that of literature. In addition, the obtained results can serve as benchmark solution in design of liquid sensors. PubDate: 2020-02-11

Abstract: Abstract A Legendre polynomial-based stochastic micromechanical framework is proposed to quantify the unbiased probabilistic behavior for the unsaturated concrete repaired by the electrochemical deposition method (EDM). By following the authors’ previous works, a deterministic micromechanical model with new multilevel homogenization scheme for the repaired unsaturated concrete is presented based on the material’s microstructures. With the stochastic descriptions for the microstructures of the repaired unsaturated concrete, the deterministic framework is extended to stochastic. The unbiased probabilistic behavior of the repaired concrete is reached by incorporating the Legendre polynomial approximations and the Monte Carlo simulations. The predictions herein are then compared with the available experimental data, existing models and the commonly used probability density functions, which indicate that the presented stochastic micromechanical framework is capable of characterizing the EDM healing process for unsaturated concrete considering the material’s random microstructure. Finally, the statistical effects of the deposition products and unsaturated pores are discussed. PubDate: 2020-02-11

Abstract: Abstract Human drivers take instant decisions about their speed, acceleration and distance from other vehicles based on different factors including their estimate of the road roughness. Having an accurate algorithm for real-time evaluation of road roughness can be critical for autonomous vehicles in order to achieve safe driving and passengers comfort. In this paper, we investigate the problem of interactive road roughness identification. We propose a novel inverse algorithm based on the knowledge of a vehicle dynamic characteristics and dynamic responses. The algorithm construct the road profile in time using one-iteration to update the wheels forces which are then used to identify the road roughness. The relation between the forces and the road profile is defined by a system of ordinary differential equations that are solved using the composite Gaussian quadrature. To reduce the error accumulation in time when noisy data is used for the vehicle response, a bidirectional filter is also implemented. We assume a simple model that is based on four degrees-of-freedom system and vibration acceleration measurements to evaluate the road roughness in real time. Although we present the results for this specific model, the algorithm can also be utilised with models of any number of degrees of freedom and can deal with models where the dynamic response is only available at some of the degrees of freedom. This is achieved by introducing a matrix reduction technique that is discussed in details. Furthermore, we evaluate the impact of uncertainty in the vehicle parameters on the algorithm estimation accuracy. The proposed algorithm is evaluated for different types of road roughness. The simulation results show that the proposed method is robust and can achieve high accuracy. The algorithm offers excellent potential for road roughness estimation not only for autonomous vehicle but also for vehicles and roads designing purposes. PubDate: 2020-02-10