International Journal of Applied Mechanics

This work deals with the mechanical response of circular microplates undergoing electrostatic actuation. A one degree-of-freedom model and Finite Element approaches are exploited in a nondimensional framework. First, a quasi-static conventional approach is adopted. From the one degree-of-freedom model a closed form solution for the plate electromechanical problem is obtained for the first time.

Then a strong attention is paid to pull-in phenomena in nonlinear dynamics. Dynamic behavior of the structure is explored, leading to the identification of a pull-in loading condition which is dependent on the quality factor Q. The outcomes are discussed and widely compared with those available in the literature for similar microsystems.

Further development of a novel mesh-free method for eigenvalue analysis of thin plate structures with complicated shapes is presented in this paper. A mesh-free method used the moving Kriging interpolation technique for constructing the shape functions, which possess the Kronecker's delta property, is formulated. Thus, it makes the present method efficient in enforcing the essential boundary conditions and none of any special techniques are required. The present plate theory followed the classical Kirchhoff's assumption and the deflection is in general approximated through the moving Kriging interpolation. Also, the mesh-free formulations for the vibration problem are formed in a simple way as finite element methods. The orthogonal transformation technique is used to implement the essential boundary conditions in the eigenvalue equation. A standard weak form is adopted to discrete the governing partial differential equation of plates. Some numerical examples are attempted to demonstrate the applicability, the effectiveness, and the accuracy of the method.

The thermopiezoelectrical behavior of a functionally graded piezoelectric medium (FGPM) is investigated in the present work. For the special case, the dynamic response of an FGPM rod excited by a moving heat source is studied. The material properties of the FGPM rod are assumed to vary exponentially through the length, except for specific heat and thermal relaxation time which are held constant for simplicity. The governing differential equations in terms of displacement, temperature, and electric potential are obtained in a general form that includes coupled and uncoupled thermoelasticity. The coupled formulation considers classical thermoelasticity as well as generalized thermoelasticity. Employing the Laplace transform and successive decoupling method, unknowns are given in the Laplace domain. Employing a numerical Laplace inversion method, the solutions are gained in the time domain. Numerical examples for the transient response of the FGPM rod are displayed to clarify the differences among the results of the generalized, coupled, and uncoupled theories for various nonhomogeneity indices. The results are verified with those reported in the literature.

The stress–strain relationship of biological soft tissues affected by Marfan's syndrome is believed to be nonconvex. More specifically, Haughton and Merodio recently proposed a strain energy density leading to localized strain-softening, in order to model the unusual mechanical behavior of these isotropic, incompressible tissues. Here we investigate how this choice of strain energy affects the results of some instabilities studies, such as those concerned with the compression of infinite and semi-infinite solids, slabs, and cylinders, or with the bending of blocks, and draw comparisons with known results established previously for the case of a classical neo-Hookean solid. We find that the localized strain-softening effect leads to early instability only when instability occurs at severe compression ratios for neo-Hookean solids, as is the case for bulk, surface, and bending instabilities.

The change in length of a muscle usually leads to a change in segment position. If a muscle is shortened the joint is being flexed. However bi-articular muscles are able to bend a joint as well as to stretch it by its contraction because of varied geometrical conditions. This phenomenon has already been analyzed in different surveys on M. biceps femoris. Until today such a consideration cannot be found for M. gastrocnemius, which is a bi-articular muscle, too. The weight- and speed-dependent activities of this muscle during fast and slow hopping, and also during running and walking, suggest that a movement-relevant function exists. This behavior pattern was the reason for a closer look on the actions of M. gastrocnemius from a geometrical point of view. The results clearly show a knee angle-dependent function. Moreover, a so-called critical angle area of the knee joint, from which the shortening of M. gastrocnemius leads from joint flexion to joint stretching, can be specified for the first time. At this, the position of the ankle joint seems to have little influence on the function of M. gastrocnemius.

The geometric effects on earthquake nucleation processes on bent dip-slip faults are studied using a slip strengthening and weakening friction law implemented in a two-dimensional quasi-static boundary integral model. The results show that the bend causes normal stress variations under tectonic loading on both the upper and lower segments. These stress variations differ from those on planar faults, leading to significant effects on earthquake nucleation location and time. Earthquakes tend to nucleate at shallower locations on thrust faults and at deeper locations on normal faults for steeper dipping angles on the lower fault segments. The elapsed time until nucleation on both thrust and normal faults is increased considerably as the bend angle becomes larger. For a thrust fault with a nearly horizontal lower segment, the time until nucleation can be more than 10 times larger than that for a corresponding planar fault. These findings may provide important insights for earthquake hazard analysis by taking the fault geometry effect into account when estimating hypocenter positions and time to instability.

Numerical simulations for local buckling and postbuckling behavior of plant stems are presented under two combined loading cases: (1) axial compression (caused by axial grains) combined with wind pressure; and (2) bending moment (caused by eccentric axial grains) combined with wind pressure. Based on its microstructure, a hollow plant stem is modeled as a stringer stiffened multiwalled shell. The material properties of the stem are assumed to be orthotropic. The nonlinear governing equations for buckling and postbuckling of plant stems are solved through arc-length method along with Newton–Raphson technique. The numerical calculations are carried out using the finite element package ABAQUS. The results show that the postbuckling equilibrium path is unstable for plant stems subjected to axial compression or bending combined with relatively low values of wind pressure. Large reduction in buckling load and in postbuckling strength can be found even if the applied wind pressure is relatively small, which results in the easy occurrence of stem lodging.

The paper shows a mathematical model for vibration analysis of soft mounted two-pole induction motors regarding electromagnetic excitation due to static rotor eccentricity. A static rotor eccentricity causes an electromagnetic force, acting on the rotor and on the stator and oscillating with the double supply frequency. This magnetic force is implemented into a simplified analytical machine dynamic model and the correlations between the rotor dynamics, electromagnetic, oil film characteristics of the sleeve bearings, and the stiffness and damping of a soft foundation are mathematically described. The derived results are clarified using an example that shows the influence of the rotor speed and the direction of the magnetic force on the vibration behavior. On one hand the aim of the paper is to show the mathematical correlations, based on a simplified model. On the other hand, the aim is to derive a method for calculating the forced vibrations — as a worst case — caused by a static rotor eccentricity. Therefore, the paper shall prepare the basis for implementing this method in more detailed numerical programs, e.g., finite element programs.

The free vibration problem of one-layered and two-layered metallic plates is investigated in this work. The thermomechanical effect is evaluated using a fully coupled thermomechanical model. The free frequency values of fully coupled problems are compared to the values of the pure mechanical problems. In pure mechanical models, the displacement is the only primary variable of the problem, while in fully coupled thermomechanical models, the temperature is also considered as a primary variable and the effect of the thermomechanical stiffness is evaluated. The thermoelastic coupling usually provides higher frequencies with respect to the pure mechanical case because it acts like a thermal source, which is proportional to the strain rate, which leads to a bigger global stiffness of the structure. Both thermomechanical and mechanical models are developed in the framework of Carrera's Unified Formulation (CUF). CUF permits several refined two-dimensional theories to be obtained with orders of expansion in the thickness direction, from linear to fourth-order, for both displacements and temperature. Both equivalent single layer and layer-wise approaches are considered for the multilayered plates. The thermomechanical effect is investigated, in terms of frequencies, for thick and thin one-layered and two-layered plates, and for lower and higher modes. It has mainly been concluded that the thermomechanical coupling: (a) Is correctly determined if both the thermal and mechanical parts are correctly approximated; (b) Is small for each investigated case; (c) Influences the various vibration modes in different ways; and (d) Has a limited dependence on the considered case, but this dependence vanishes if a global coupling is considered. Only fully coupled thermomechanical models allow to analyze this type of problem. The effect of the thermomechanical coupling on higher-order modes can only be investigated using refined two-dimensional theories.

When a cylinder specimen lies in the gaseous mixture under high temperature and high pressure, the ablation and the denudation may appear on the cylinder surface, which will lead to the mass loss and shape alteration. A combined model is developed for solving the mass loss rate resulted from the ablation and the denudation. In this model, three chemical formulas and ablation mechanism are presented to evaluate the mass loss rate; the core-spread vortex method is used to analyze the flow around the cylinder; and the particle trajectory equation is given to explore the traces of denudation particles. To obtain the mass loss rate of the cylinder in the two-phase flow, the simulations are performed well by using the written codes. Numerical results show that the Re number of gaseous mixture exerts significant effects on both the vortex street and the ablation rate. Furthermore, it is found that the vorticity determines the motion and distribution of denudation particles.