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In this study, effects of the presence of vacancy defects in a hexagonal nanosheet on Young's modulus, effective Poisson's ratio, buckling loads and buckling modes, regardless of its constituent atoms, have been studied. Explicit expressions are proposed in order to define these characteristics considering a defect distribution term as a modifying parameter. Molecular structural mechanics concepts and FEM simulation are utilized in order to obtain these expressions and results. Different sizes and shapes of defects as well as random distribution of vacancies have been considered. The results for perfect Boron Nitride, Silicon Carbide and graphene nanosheet as well as defected Boron Nitride nanosheets are in a good agreement with those available in literature. Linear degradation behavior of Young's modulus and linear increase of effective Poisson's ratio in terms of defects distribution are observed in obtained results. A second order behavior is also observed in decreasing buckling load in terms of increasing vacancy distribution. Moreover, buckling mode characteristics due to the percentage of defects distribution has been investigated. [ABSTRACT FROM AUTHOR]

Arteries can become tortuous in response to abnormal growth stimuli, genetic defects and aging. It is suggested that a buckling instability is a mechanism that might lead to artery tortuosity. Here, the buckling instability in arteries is studied by examining asymmetric modes of bifurcation of two-layer cylindrical structures that are residually stressed. These structures are loaded by an axial force, internal pressure and have nonlinear, anisotropic, hyperelastic responses to stresses. Strain-softening and reduced opening angle are shown to lower the critical internal pressure leading to buckling. In addition, the ratio of the media thickness to the adventitia thickness is shown to have a dramatic impact on arterial instability. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an investigation on the buckling and postbuckling of microtubules (MTs) subjected to a uniform external radial pressure in thermal environments. The microtubule is modeled as a nonlocal shear deformable cylindrical shell which contains small scale effects. The governing equations are based on higher order shear deformation shell theory with a von Kármán–Donnell-type of kinematic nonlinearity and include the extension-twist and flexural-twist couplings. The thermal effects are also included and the material properties are assumed to be temperature-dependent. A singular perturbation technique is employed to determine the buckling pressure and postbuckling equilibrium paths. The small scale parameter e 0 a is estimated by matching the buckling pressure of MTs measured from the experiments with the numerical results obtained from the nonlocal shear deformable shell model. The numerical results show that buckling pressure and postbuckling behavior of MTs are very sensitive to the small scale parameter e 0 a. The results reveal that the 13_3 microtubule has a stable postbuckling path, whereas the 13_2 microtubule has an unstable postbuckling behavior due to the presence of skew angles. [Copyright &y& Elsevier]

On the basis of the Bernoulli–Euler beam theory, the properties of free transverse vibration and buckling of a double-beam system under compressive axial loading are investigated in this paper. It is assumed that the two beams of the system are simply supported and continuously joined by a Winkler elastic layer. Explicit expressions are derived for the natural frequencies and the associated amplitude ratios of the two beams, and the analytical solution of the critical buckling load is obtained. The influences of the compressive axial loading on the responses of the double-beam system are discussed. It is shown that the critical buckling load of the system is related to the axial compression ratio of the two beams and the Winkler elastic layer, and the properties of free transverse vibration of the system greatly depend on the axial compressions. [Copyright &y& Elsevier]

Abstract: The free vibration and buckling of partial interaction composite beams are investigated using the state-space method based on the two-dimensional theory of elasticity. The analytical solutions of a beam with two simply supported ends are obtained as well as semi-analytical solutions are obtained for other end conditions using the differential quadrature method coupled with the state-space method. The frequencies and buckling loads are tabulated and compared with those available in the literature. Because the plane section assumption of the classical beam theory is not used, the presented method is applicable not only to slender beams, but also to thick beams. Consequently, the presented method can be a benchmark for other approximate methods based on one-dimensional beam theories. [Copyright &y& Elsevier]

Abstract: Buckling and vibrational behavior of polar orthotropic circular plates of linearly varying thickness is presented on the basis of classical plate theory. The plate is resting on Winkler-type foundation. An approximate solution has been obtained by Ritz method, which employs basis functions based upon static deflection of polar orthotropic plates. The effect of elastic foundation and that of orthotropy on the natural frequency of plate has been illustrated for different values of taper parameter, flexibility parameter, in-plane force and nodal diameter. The critical buckling load for clamped and simply supported plates have been obtained. A comparison of results with those available in literature has been presented. [Copyright &y& Elsevier]

A buckled beam with immovable pinned ends is considered. Attached to the beam are either one concentrated mass, two concentrated masses, a spring–mass system (that could model a human, robot, or passive vibration absorber), or a horizontal rigid bar with two vertical end springs (a “bounce–pitch” system that could model an animal or a vehicle). In the theoretical analysis, the beam is modeled as an inextensible elastica. Equilibrium configurations are determined first. Then small free vibrations about equilibrium are examined, and the lowest frequencies and corresponding modes are computed. The effects of various parameters are investigated, such as the ratio of the span to the total arc length of the beam, the locations and weights of the attached masses and systems, and the stiffnesses of the springs. For the case of a single attached mass, experiments are conducted and the results are compared to the theoretical ones. [ABSTRACT FROM AUTHOR]

Abstract Modal shifting and jumping in thermally buckled plates has been investigated previously using computational models; however, relatively few experimental explorations have been reported. In this study, the modal shifts and jumps in a simple rectangular plate or panel were investigated using digital image correlation to obtain detailed mode shapes. One face of the planar panel, which was 219 × 146 mm, was speckled and viewed with a stereoscopic digital image correlation system using pulsed-laser illumination and with a laser vibrometer at a single point. The other face was heated using a set of 1 kW quartz lamps to produce a non-uniform temperature distribution which progressively increased from room temperature to around 760 K. An infra-red camera recorded the time-varying temperature distribution on the panel while it was excited with an electrodynamic shaker. A waterfall plot, or time-frequency spectrogram, showing natural frequencies as a function of time was generated, which highlighted the shifting response of the panel with temperature. The heating sequence was repeated and the panel excited at the natural frequencies identified in the waterfall plot, which permitted the corresponding mode shapes to be measured. These data showed that mode shifting and jumping was present with asymmetric heating, but not with spatially uniform heating, and was associated with thermally-induced buckling. [ABSTRACT FROM AUTHOR]

Abstract: A general procedure for the determination of the natural frequencies and buckling load for a set of beam system under compressive axial loading is investigated using Timoshenko and high-order shear deformation theory. It is assumed that the set beams of the system are simply supported and continuously joined by a Winkler elastic layer. The model of beam includes the effects of axial loading, shear deformation and rotary inertia. In the special case of identical beams, explicit expressions for the natural frequencies and the critical buckling load are determined using a trigonometric method. The influences of the compressive axial loading and the number of beams in the system on the natural frequencies and the critical buckling load are discussed. These results are of considerable practical interest and have wide application in engineering practice of frameworks. [Copyright &y& Elsevier]

Abstract: Based on the nonlocal elastic theory, small scale effects are considered in the investigation of the mechanical properties of protein microtubules. A new prediction formula for the persistence lengths of microtubules with the consideration of the small scale effect is presented. Subsequently, the buckling of microtubules is studied based on a nonlocal elastic beam model. The predicted results of our model indicate that the length-dependence of persistence length is related not only to the shear terms, but also to the small scale effect. The Eular beam model, which is always considered unable to explain the length-dependence of microtubules, can capture the length-dependence of the persistence length of microtubules with the consideration of the small scale effect. The elastic buckling behaviors of microtubules in viscoelastic surrounding cytoplasm are also considered using the nonlocal Timoshenko beam model in this paper, and the results indicate that the small scale effect of microtubules also plays an important role in the buckling of microtubules. [Copyright &y& Elsevier]

Microtubules including tubulin heterodimers arranging in a parallel shape of cylindrical hollow plays an important role in the mechanical stiffness of a living cell. In the present study, the nonlocal strain gradient theory of elasticity including simultaneously the both nonlocality and strain gradient size dependency is put to use within the framework of a refined orthotropic shell theory with hyperbolic distribution of shear deformation to analyze the size-dependent buckling and postbuckling characteristics of microtubules embedded in cytoplasm under axial compressive load. The non-classical governing differential equations are deduced via boundary layer theory of shell buckling incorporating the nonlinear prebuckling deformation and microtubule-cytoplasm interaction in the living cell environment. Finally, with the aid of a two-stepped perturbation solution methodology, the explicit analytical expressions for nonlocal strain gradient stability paths of axially loaded microtubules are achieved. It is illustrated that by taking the nonlocal size effect into consideration, the critical buckling load of microtubule and its maximum deflection associated with the minimum postbuckling load decreases, while the strain gradient size dependency causes to increase them. [ABSTRACT FROM AUTHOR]

Abstract: Physical phenomena are usually described by nonlinear differential equations. If some of the physical parameters are unknown then adding appropriate constraints may transform a nonlinear problem to a nonlinear eigenvalue problem. This principle is illustrated by a variety of problems associated with deflections of a flexible rod. The basic problem studied is the problem formed by the natural extension of the linear buckling problem of a flexible rod when large deflections are taken into account. The unknown parameter in these problems is the load, and the constraint is the predetermined distance between the rod's ends. The problem of finding large deflections of the strongest column is also addressed. A simple numerical method for solving these problems is given. The paper gives insight into the problem of forming a non-linear eigenvalue problem. It highlights the relations between the mathematical formulation and the governing physical laws, and demonstrates the similarity between the linear and the nonlinear solutions. [Copyright &y& Elsevier]

Abstract: In this paper, the vibration and stability of orthotropic conical shells with non-homogeneous material properties under a hydrostatic pressure are studied. At first, the basic relations have been obtained for orthotropic truncated conical shells, Young''s moduli and density of which vary continuously in the thickness direction. By applying the Galerkin method to the foregoing equations, the buckling pressure and frequency parameter of truncated conical shells are obtained from these equations. Finally, carrying out some computations, the effects of the variations of conical shell characteristics, the effects of the non-homogeneity and the orthotropy on the critical dimensionless hydrostatic pressure and lowest dimensionless frequency parameter have been studied, when Young''s moduli and density vary together and separately. The results are presented in tables, figures and compared with other works. [Copyright &y& Elsevier]

The present work deals with the active vibration control of composite beam under thermal environment using finite element method. The effect of fiber orientation and temperature on natural frequency and damping of the system are investigated for different boundary conditions. The temperature-dependent properties of viscoelastic core are considered. Results are presented for frequencies and loss factor with different core material and core thickness. Characteristics of loss factor and frequency near the buckling temperature are discussed, and the effect of core thickness on buckling temperature is also investigated. [Copyright &y& Elsevier]

Abstract: The static and dynamic stability of an elastically restrained Beck column with an attached end mass subjected simultaneously to gravity and follower axial forces is presented. The analytical solution takes into account the simultaneous effects of: (1) translational and rotational elastic restraints at the base support; (2) the uniform mass per unit length of the column (including any additional uniformly distributed mass) and rotary inertia of the column; (3) the rotary and translational inertias of the attached end mass; (4) the distance from the centroid of the attached end mass to the column free end; and (5) the shear deformation. The analytical eigenvalue solution can be used to study these effects on the static and dynamic stability of the Beck column. The analytical method and eigenvalue equation capture the static buckling (or divergence) as well as the dynamic (flutter) instability of cantilever columns elastically restrained at the base and subjected to any combinations of gravity and follower compressive axial forces applied at the free end. A parametric study is carried out on the effects of the translational and rotational inertias of the end mass, the distance from the centroid of the attached end mass to the column free end, and the rotational restraint on the static and dynamic stability of a perfectly clamped Beck column. Four comprehensive examples are presented to show the simplicity and effectiveness of the analytical method, and the obtained results compared with those obtained analytically and experimentally by others researchers. [Copyright &y& Elsevier]