International Journal of Applied Mechanics

This paper deals with the vibration characteristics and nonlinear aeroelastic response of the functionally graded (FG) multilayer composite plate reinforced with graphene nanoplatelets (GPLs) subjected to in-plane excitations and applied voltage. The different GPL nanofillers distribution patterns across the thickness are discussed, in which the effective Young’s modulus is determined by modified Halpin–Tsai model. Based on high-order shear deformation theory, the motion equations of the FG plate system considering the von Kármán geometric nonlinearity are derived using the Hamilton’s principle. The Galerkin method is applied to discretize the partial differential governing equations into the ordinary differential nonlinear system. The effects of many influential parameters, i.e., GPLs weight fraction, distribution pattern, geometry size, applied voltage and the number of layers, on the vibration and aeroelastic behaviors are presented in detail. Numerical results show that a small amount of GPLs reinforcement can have a significant enhancement effect on the performance of the composite plate structure. Moreover, the in-plane force and aerodynamic pressure play an opposite effect on the dynamic stability, and the jumping phenomena, quasi-periodic motion can be observed with the compressive force increased further.

Friction is a complicated phenomenon that plays a central role in a wide variety of physical systems. An accurate modeling of the friction forces is required in the model-based design approach, especially when the efficiency optimization and system controllability are the core of the design. In this work, a gyroscopic unit is considered as case study: the flywheel rotation is affected by different friction sources that needs to be compensated by the flywheel motor. An accurate modeling of the dissipations can be useful for the system efficiency optimization. According to the inertial sea wave energy converter (ISWEC) gyroscope layout, friction forces are modeled and their dependency with respect to the various physical quantities involved is examined. The mathematical model of friction forces is validated against the experimental data acquired during the laboratory testing of the ISWEC gyroscope. Moreover, in the wave energy field, it is common to work with scale prototypes during the full-scale device development. For this reason, the scale effect on dissipations has been correlated based on the Froude scaling law, which is commonly used for wave energy converter scaling. Moreover, a mixed Froude–Reynolds scaling law is taken into account, in order to maintain the scale of the fluid-dynamic losses due to flywheel rotation. The analytical study is accompanied by a series of simulations based on the properties of the ISWEC full-scale gyroscope.

Based on classical small deflection plate theory, the governing equation of functionally graded (FG) plates in thermal environment is derived by using Hamilton’s principle. Closed-form analytical solutions are obtained via separation-of-variable method for free vibration of rectangular FG thin plates with simply supported, clamped and guided edges, especially for the plates with two adjacent clamped edges in thermal environment. The normal modes and frequencies are in an elegant and explicit closed form. Comprehensive numerical comparison and results in dimensionless form validate the present method and reveal a few physical phenomena.

The problem about the indentation of the rigid spherical stamp into the cylindrical specimen was considered. The material of the specimen was assumed to be weakly compressible. The formulation of the problem was performed for the case of finite deformations. The method of construction of the constitutive relations in terms of logarithmic strain tensor for elastic media and the variant of the algorithm to take into account the variation of the contact zone were proposed. The expansion of Hencky tensor and its time derivative into the series in powers of Cauchy strain tensor were used to calculate correctly the components of these tensors. Within the indentation problem, we used the model of nonlinear elastic material which provides the best agreement between numerical solution and experimental data among other used types of constitutive relations including various elastic and hypoelastic models.

This paper aims to investigate the imperfection sensitivity of the post-buckling behavior and the free vibration response under pre- and post-buckling of nanoplates with various edge supports in the thermal environment. Formulation is based on the higher-order shear deformation plate theory, von Kármán kinematic hypothesis including an initial geometrical imperfection and Gurtin–Murdoch surface stress elasticity theory. The discretized nonlinear coupled in-plane and out-of-plane equations of motion are simultaneously obtained using the variational differential quadrature (VDQ) method and Hamilton’s principle. To this end, the displacement vector and nonlinear strain–displacement relations corresponding to the bulk and surface layers are matricized. Also, the variations of potential strain energies, kinetic energies and external work are obtained in matrix form. Then, the VDQ method is employed to discretize the obtained energy functional on space domain. By Hamilton’s principle, the discretized quadratic form of nonlinear governing equations is derived. The resulting equations are solved employing the pseudo-arc-length technique for the post-buckling problem. Moreover, considering a time-dependent small disturbance around the buckled configuration, the vibrational characteristics of pre- and post-buckled nanoplates are determined. The influences of initial imperfection, thickness, surface residual stress and temperature rise are examined in the numerical results.

The higher-order kinematic theory in conjunction with Green–Lagrange strain field has been incorporated to compute the nonlinear frequency parameter of the curved (single/doubly) graded (functionally) sandwich panel structure numerically via finite element technique. The current sandwich panel model is derived assuming the functionally graded carbon nanotube face sheets and isotropic (epoxy) core. The current mathematical model is generic in nature, i.e., the grading configurations of the face sheets and sandwich construction including the different geometrical shapes can be achieved easily. The governing equation of the sandwich structure is obtained and the subsequent weak form derived with the help of the isoparametric finite element method. The nonlinear solutions are computed via an original computer code using a robust numerical method (direct iterative method). The consistency and the accuracy of the current finite element solutions are established by executing different types of numerical examples. Also, the concurrence of current numerical solution is established by comparing the results with the available benchmark solutions. Finally, the effect of various design parameters on the nonlinear natural frequency values have been computed under the uniform temperature environment and the inferences provided in detail.

In the present research, we carry out a systematical experimental investigation on the strength, toughness and failure mechanism of the metal/silicone rubber/metal bonding system. For the case of the aluminum alloy cylinder/silicone rubber/aluminum alloy cylinder bonding system, we measure the tensile deformation and failure behaviors, including the dependence of the failure loading on the adhesive layer thickness and scarf angle. Through introducing a series of definitions, such as average normal stress, average shear stress, average normal strain and average shear strain, along the bonding interface, we realize the measurements on interfacial failure strength, and obtain the relationship between the interfacial strength and the interfacial scarf angle as well as adhesive layer thickness, and we further obtain the failure strength surface, interfacial fracture energy, as well as the energy release rate for the bonding system. The obtained results can provide a scientific basis for deeply understanding the strength and toughness properties as well as the failure mechanism of the metal-adhesive bonding system, and have an important guidance on optimization design and property evolution of the bonding system.

In this study, the ultra-low cycle fatigue (ULCF) behavior of a high-strength-ductile steel AerMet100 exposed to repeated high strain rate impact loadings is investigated. Three types of coupon-level experiments were performed, in which a three-point bending (TPB) specimen with a through-thickness notch was employed for multi-impact test. A special ratchet effect associated with complex stress state, dynamic impact loading and other physical mechanisms was observed through measured principal strain variations with a specific decay rate at the notch root surface. An improved ULCF predictive model based on the continuum damage mechanics was developed to quantify the relationship between the fatigue damage and the input of localized impact energy to the notch root. The model expressed in terms of damage growth rate introduces a new exponential term for better predictive accuracy and reduced number of nonlinear dynamic response analysis. As a computational efficient tool, the proposed model can predict impact fatigue life in acceptable timeframe for multiple critical locations in a complex engineering component.

In this paper, the static pull-in behavior of electrostatically actuated functionally graded (FG) micro-beams resting on an elastic medium is studied using the modified strain gradient (MSG) theory. To this end, the equilibrium equation along with classical and non-classical boundary conditions is obtained by considering the fringing field and elastic foundations effects within the principle of minimum total potential energy. Also, the elastic medium is composed of a shear layer (Pasternak foundation) and a linear normal layer (Winkler foundation). The governing differential equation is solved for cantilever and doubly fixed FG beams using an iterative numerical method. This method is a combination of the reduced-order technique, the fourth-order Runge–Kutta and shooting methods. The pull-in voltages of silicon beams obtained from the present model are compared with the experimental and theoretical results reported in the literature. It is seen that the MSG theory is able to reduce significantly the difference between pull-in voltages predicted by theoretical approaches based on the classical continuum theory and the experimental observations. Finally, a parametric study is carried out to analyze in detail the influences of power index, length scale parameters, coefficients of elastic foundations and boundary conditions on the pull-in behavior of FG micro-beams. Findings indicate that the size effect on the pull-in instability of FG micro-beams with both boundary conditions is significant; however, it is seen that the variation with the normalized length scale parameter of static pull-in voltages for doubly fixed beams is larger than cantilever beams. Also, it is shown that the increase of ceramic volume fraction can improve the pull-in resistance of beams. However, this influence becomes smaller with rise of power index for both cases.

The present work addresses with the cross-sectional design and analysis of fiber-reinforced multiscale composite beams of general cross-sectional shape and arbitrary anisotropic material properties and investigates the effect of carbon nanotubes (CNTs) on their stiffness properties. The three-dimensional strain field was formulated in terms of one-dimensional strains and a three-dimensional warping displacement. The bulk material properties of the multiscale composite were predicted using Halpin–Tsai equations and fiber micromechanics. The carbon nanotubes were assumed to be uniformly distributed and randomly oriented throughout the polymer matrix. The variational asymptotic beam section (VABS) was used to numerically evaluate the stiffness and mass matrices of four test cases: strip, circular pipe, box beam and airfoil. The influence of CNTs weight percentage and volume fraction of fibers was investigated through a detailed parametric study. The numerical results indicate that the inclusion of a small weight percentage of carbon nanotubes in the polymer matrix is sufficient to induce a significant improvement in stiffness properties.

The presence of part-through cracks with limited length is one of the prevalent defects in plate structures. The vibrational response of plates can be used to investigate the effect of crack presence. In this paper the modified line spring method (MLSM) is used to develop a nonlinear multi degree of freedom model of part-through cracked rectangular plate. After a convergence study in time series domain, tuning of the chaotic signal is conducted in two steps: (i) crossing of the Lyapunov exponents’ spectrums for the nonlinear model of the plate and the chaotic signal which assures the effectiveness of the model filter on the Lyapunov dimension of chaotic signal and (ii) varying the tuning parameter of chaotic signal to find a span in which tangible sensitivity in statistical parameters can be observed. Standard deviation, skewness and kurtosis are proposed as features to analyze the time series response of cracked plate. Damage characteristics such as: length, angle, location and depth of crack are considered as parameters to be varied in order to scrutinize the response of plates. Results show that by implementation of a tuned chaotic interrogator signal, tangible sensitivity and also near to monotonic behavior of statistical parameters versus damage characteristics are achievable.

The behavior of a coated asperity contacting with a rigid flat during the loading and unloading processes is investigated using the finite element method. The power-law hardening elastic–plastic substrate is considered, and the effect of the substrate hardening exponent and the coating thickness on the contact behavior is studied. It is shown that in the loading process, the contact load increases more slow and the contact area increases faster as the interference increases for smaller coating thickness and hardening exponent cases, and the coating thickness recovers more obviously after a rapid decrease. In the unloading process, the residual interference and the pileup effect of the asperity surface is larger for smaller coating thicknesses and hardening exponents, and the energy loss due to the plastic deformation is larger accordingly.