Journal of Solid Mechanics
Volume:15 Issue: 2, Spring 2023

In this paper, the analysis of nonlinear free vibrations of beams made of functionally graded materials with magnetorheological fluid as core is investigated. It is assumed that the beam is made of three layers including constraining layer, magnetorheological fluid and base layer and is located on Simply-Simply, Clamped-Simply and Clamped–Clamped supports. The governing equations of the beam are derived using the Hamilton’s principle. To obtain the vibrational frequencies, the theory of Timoshenko beam is used by the Generalized Differential Quadrature method. The effects of magnetic field intensity, power law exponents, core thickness and constraining layer thickness and the length of the beam on natural frequency and modal loss factor related to different frequencies modes for the three boundary conditions have been investigated. The results show the effects of physical and geometrical parameters regarding the natural frequency and modal loss factor of the sandwich beam with different modes. Also, the frequency and loss factor values obtained from Generalized Differential Quadrature method are very close to the results obtained by the Finite Element method. This shows the accuracy and precision of this method.

The undulated characteristics of the irregular boundaries in the layered structure with piezoelectric materials generate some prominent effects on wave propagation.  On the other hand, initial stress in the layered structure also play an important role in velocity characterization of the surface seismic waves. In light of the above, this paper studies the Rayleigh-type wave propagation in a composite structure with piezoelectric materials. Mathematical expressions for the mechanical displacement and electric potential function are obtained for both the piezoelectric layer and elastic substrate with the aid of coupled electromechanical field equations. Frequency equations for the waves are derived for both electrically open and short cases. The effects of the corrugation parameters, initial stress, piezoelectric constant, dielectric constant and thickness of the piezoelectric layer on the phase velocity of Rayleigh-type wave are discussed graphically for both the electrically open and short cases. Numerical examples and discussions are made to exhibit the findings graphically. The validation of the problem is made with the classical result.

Due to their continuous material variation and eliminating the mismatch stress field in the thickness direction, Functionally Graded Materials (FGMs) have found wide applications in aerospace and mechanical engineering. This article presents closed-form solution for thick functionally graded plate based on three-dimensional elasticity theory. To this end, first, the characteristic equation of FG plate is derived and general closed-form is obtained analytically. Both positive and negative discriminant of characteristic equation is considered and solved. The presented method is validated with finite element results by considering isotropic thick plate. Several parametric studies are carried out to investigate the effect of geometric and material parameters. The aim of this research is to present analytical solution form for thick FG plate and work out the problem of inconsistency for corresponding displacements field. The presented solution can be used to examine accuracy of various plate theories such as first-order, third order shear deformation theories and other equivalent plate theories.

Graphene without defects exhibits extraordinary mechanical properties, while defects such as vacancies and Stone-Wales usually impose a suffering effect on graphene's properties. On the other hand, strictly two-dimensional crystals are expected to be unstable due to the thermodynamic requirement for the existence of out-of-plane bending with interatomic interaction generating a mathematical paradox. This paper researches the fracture strength and the stretching stiffness of a rippled defective graphene that is placed under the loading pressure of uniaxial tensile. With the purpose of replicating a model for carbon atoms’ covalence bonding, a molecular dynamics simulation is carried out. This is sorted according to the adaptive intermolecular reactive bond order potential function. The degree of the temperature of the system throughout the experiment is contained through the Nose-Hoover thermostat. The software package large-scale atomic/molecular massively parallel simulator is utilized for the aim of simulation the desired bond formation in the graphene layer structure. The present study offers a physical insight into the mechanisms of topological mechanical defects of graphene, and we propose static ripples as one of the key elements to accurately understand the thermo-mechanics of graphene. The results revealed that the fracture strength of a rippled graphene is significantly reduced when it contains defects, and fracture stress and strain with different vacancy defects are presented and compared.

In this research, a multi-scale model was used to analyze the vibrational behavior of the atomic force microscope (AFM) on a graphene sheet sample. Cantilever and silicone tip base were simulated based on the continuum mechanics using finite element modeling and the tip apex were modeled based on the Tersoff potential by the structural mechanics modeling. The contact behavior between the tip and graphene was investigated using measuring friction force during the tip movement on the graphene layer, and its results were compared to the results obtained from molecular dynamics simulation and experimental test. The friction force between the tip and graphene increases by enhancing the tip radius and the contact surface between the tip and the sample. Moreover, the friction force dwindles by heightening the number of graphene layers as a result of sliding graphene layers on each other and diminishing the Poker effect (wrinkling). With the initial distance displacement of the tip from the sample, two curves of the tip vibration amplitude variations and the phase change between tip vibration and excitation vibration were plotted, and the effect of crack and its location in the cantilever was studied. The results showed that the crack in the cantilever can dramatically influence the tip vibration amplitude and the phase change between the tip vibration and the excitation signal.

This paper deals with the analysis of temperature, deflection and thermal stresses of a multilayered annular disk. The thermo-mechanical properties of the disk are taken to be temperature dependent. Using Kirchhoff’s variable transformation, the non-linear heat conduction equation is reduced to a linear form. Finite integral transform, Fourier series and Fourier transform techniques are used to solve the heat conduction equation and the desired solution is obtained in series form. Deflection, thermally induced resultant moments and the corresponding thermal stresses are determined. Numerical analysis is carried out for a three layered annular disk and the results are depicted graphically. Thermosensitivity plays a vital role in the thermal profile of the multilayered disk. In the temperature dependent case, the radial stress suddenly becomes compressive in the middle region, whereas it is tensile throughout all the regions in the temperature independent case. Due to the inhomogeneous thermal conductivity considered in the form of exponential function, the temperature and the corresponding thermoelastic quantities shows the lag along radial direction.

In this paper, an arbitrary angle waveguide bend made of a new heterostructure phononic crystal has been studied. By creation of line defects in the proposed heterostructure which is composed of square and rhombus phononic crystals, a simple structure waveguide bend with arbitrary angles is made. Analyzing the proposed bend showed that by creating line defects in the composition of the square and equilateral triangle lattices, 30˚ waveguide bend can be realized. Also the study showed that by creating line defects in the composition of the square and rhombus lattices, 40˚ (20˚) waveguide bend could be obtained if the angular constant of the rhombus lattice is 80˚ (40˚). The 40˚ and 20˚ waveguide bends have a narrow pass band which can be utilized as a filter to separate a specific frequency and guide it along a defined pass. Also the study shows that by incorporation of 90˚ bend within the presented heterostructure bends, waveguide bends can be realized that guide elastic waves in the arbitrary angles greater than 90˚.

In this paper, the mechanical fracture problem of a half-plane made of functionally graded material (FGM) with a coating of a homogeneous layer containing multiple interface cracks is investigated in order to determine the dynamic stress intensity factors (DSIFs) under transient in-plane loading. According to exponential law, the properties of functionally graded material change continuously along y-direction. Initially, integral transformations and dislocation of the Volterra type of climbing and sliding edges on the interface of a FG half-plane with a homogeneous coating leads to the numerical solution of a system with singular integral equations. These equations which have the Cauchy type-singularity are then obtained using the distributed dislocation technique (DDT). Using the inversion technique in the Laplace domain, the dislocation density on the crack faces is obtained which has led to the determination of the DSIFs. Finally, in order to show the accuracy and validity of this research, the final results in the form of graphs have been compared with other references and a very acceptable conformity has been observed. The influences of the FG parameter, coating thickness, crack length, the variation of time and the interaction between of cracks on the DSIFs are studied.