Summary

This paper presents some results on the parameter estimation of a fixed-distance joint. Such joints are of interest in various fields of applied mechanics such as mechanisms, vehicle and human body dynamics. The corresponding geometrical parameters are positions of the points of connected bodies, which are kept at constant distance during the movement. The problem is solved using kinematical information on a certain number of points belonging to the connected bodies. The conditioning problem, and, consequently, the accuracy of the results, depends on the relative movement of the bodies and also on possible a priori information. The case of planar motion is investigated in more detail; a numerical example is provided and discussed.

Since Green’s matrices are widely used for solution of the theoretical and applied problems in science and engineering, it is important to get efficient methods for their calculation. Therefore, a new efficient algorithm for the calculation of Green’s matrices for the boundary value problem (BVP) for the system of ordinary differential equations (ODE) of the first order has been developed here. For any well-defined BVP, a fundamental matrix has to be constructed first; then, using a simple algorithm the corresponding Green’s matrix is calculated. For the fundamental matrix calculation an approach based on the matrix exponential is used. To demonstrate the effectiveness and robustness of the algorithm, Green’s matrices for elastic bar, Euler–Bernoulli, Timoshenko’s and Vekua’s beams have been calculated. All of the presented calculations have been done using the computed algebra software Mathematica. In the cases of the elastic bar, Euler–Bernoulli, Timoshenko’s beams corresponding Green’s functions have been presented in analytical form as the Mathematica output. In the case of the Vekua’s beams analytical expressions for Green’s functions are relatively long; they have been calculated numerically, by using the proposed algorithm. The Green’s matrices for Timoshenko’s and Vekua’s beams have been verified by comparing the solution of the corresponding BVP obtained using Green’s function method with the numerical solution obtained using Mathematica function NDSolve. Proposed algorithm can be applied for solution of the BVP for any linear and some classes of nonlinear systems of the ODE using the Green’s matrices approach.

In order to obtain the equations of motion of vibratory systems, we will need a mathematical description of the forces and moments involved, as function of displacement or velocity, solution of vibration models to predict system behavior requires solution of differential equations, the differential equations based on linear model of the forces and moments are much easier to solve than the ones based on nonlinear models, but sometimes a nonlinear model is unavoidable, this is the case when a system is designed with nonlinear spring and nonlinear damping. Homotopy perturbation method is an effective method to find a solution of a nonlinear differential equation. In this method, a nonlinear complex differential equation is transformed to a series of linear and nonlinear parts, almost simpler differential equations. These sets of equations are then solved iteratively. Finally, a linear series of the solutions completes the answer if the convergence is maintained; homotopy perturbation method (HPM) is enhanced by a preliminary assumption. The idea is to keep the inherent stability of nonlinear dynamic; the enhanced HPM is used to solve the nonlinear shock absorber and spring equations.

Summary

Failure of earth structures or laboratory specimens of soils is often characterized by the existence of bands or surfaces at which strain localizes. Numerical simulation of shear band development has attracted the attention of many research groups during past years. Here it is proposed that adaptive remeshing techniques can be applied to better simulate strain localization problems in geotechnique. The algorithm has been previously applied to compressible fluid dynamics problems to capture discontinuities such as shocks. A new refinement functional has been introduced to improve quality of produced meshes. Finally, the algorithm is applied to solve inception and development of shear bands on both homogeneous stress fields and non-homogeneous stress fields.

In this paper, a size-dependent Timoshenko beam is developed on the basis of the couple stress theory. The couple stress theory is a non-classic continuum theory capable of capturing the small-scale size effects on the mechanical behavior of structures, while the classical continuum theory is unable to predict the mechanical behavior accurately when the characteristic size of structures is close to the material length scale parameter. The governing differential equations of motion are derived for the couple-stress Timoshenko beam using the principles of linear and angular momentum. Then, the general form of boundary conditions and generally valid closed-form analytical solutions are obtained for the axial deformation, bending deflection, and the rotation angle of cross sections in the static cases. As an example, the closed-form analytical results are obtained for the response of a cantilever beam subjected to a static loading with a concentrated force at its free end. The results indicate that modeling on the basis of the couple stress theory causes more stiffness than modeling by the classical beam theory. In addition, the results indicate that the differences between the results of the proposed model and those based on the classical Euler–Bernoulli and classical Timoshenko beam theories are significant when the beam thickness is comparable to its material length scale parameter.

Summary

 We consider the air contained in a pneumatic tyre with the purpose of investigating its inertial oscillations. We model the tyre as a torus limited by a membrane in contact with the ground. According to this model, we prove that the flow within this torus may be considered as one at low Mach number and that it is ruled by oscillations of incompressible rotating fluid. Investigating such inertial oscillations, we show that the geostrophic oscillation is resonant, and we study the resonance phenomenon.

The dynamical stability of carbon nanotubes embedded in an elastic matrix under time-dependent axial loading is studied in this paper. The effects of van der Waals interaction forces between the inner and outer walls of nanotubes are taken into account. Using continuum mechanics, we apply an elastic layered shell model to solve the transverse parametric vibrations of a carbon nanotube. Both the Gaussian wide-band axial temperature changes and physically realizable temperature changes with known probability distributions are assumed as the tube axial loading. The energy-like functionals are used in the stability analysis. The emphasis is placed on a qualitative analysis of dynamic stability problem. Stability domains in the space of geometric, material and loading parameters are presented in analytical forms.

Vibration absorbers are usually designed using the finite element (FE) model of structures. It is generally believed that the modal models are more accurate than FE models, because in modal testing the model is built by direct measurement of the test structure. In this paper, a method is proposed to design a translational vibration absorber using the measured frequency response functions of a primary structure. The designed vibration absorber imposes a node on the structure when it is excited by a harmonic force. The method is based on the structural modification using experimental frequency response functions technique and determines the required receptance of the absorber at the excitation frequency. Moreover, a procedure is developed to suppress the vibration amplitude of two arbitrary points on a linear structure subjected to harmonic excitations by attaching two sprung mass absorbers. A cantilever beam is considered for the numerical case study, and the sprung masses are designed to suppress the vibration amplitude of the beam at the selected arbitrary points. A U-shape plate was considered for the experimental validation of the method for imposing a node using one absorber. Also, a beam was tested to demonstrate the effectiveness of method for imposing two nodes on the structures. The experimental results show that the designed absorbers can considerably suppress the vibration amplitude at the selected points on the structure.

Yeast cells can be regarded as micron-sized and liquid-filled cylindrical shells. Owing to the rigid cell walls, yeast cells can bear compressive forces produced during the biotechnological process chain. However, when the compressive forces applied on the yeast go beyond a critical value, mechanical buckling will occur. Since the buckling of the yeast can change the networks in its cellular control, the experimental research of the buckling of the yeast has received considerable attention recently. In this paper, we apply a viscoelastic shell model to study the buckling of the yeast. Meanwhile, the turgor pressure in the yeast due to the internal liquid is taken into account as well. The governing equations are based on the first-order shear deformation theory. The critical axial compressive force in the phase space is obtained by the Laplace transformation, and the Bellman numerical inversion method is then applied to the analytical result to obtain the corresponding numerical results in the physical phase. The concepts of instantaneous critical buckling force, durable critical buckling force, and delay buckling are set up in this paper. And the effects of the transverse shear deformation and the turgor pressure on the buckling phenomena are also given. The numerical results show that the transverse shearing effect will decrease the instantaneous critical buckling force and the durable critical buckling force, while the turgor pressure will increase both of them.