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This paper proposes a modified segmented rod method (MSRM) in order to facilitate the introduction of boundary conditions in the analysis of free vibrations and buckling of Euler–Bernoulli beams. First, the basic idea of proposed modifications is presented in the case of elementary length beam, and then the idea is generalized to the full-length beam. In addition to facilitating the introduction of boundary conditions, by comparing the results of MSRM with segmented rod method (SRM) and Hencky bar-chain method (HBM), a faster convergence of MSRM results to the exact ones was observed. Although the case of uniform beam is considered in this paper, proposed MSRM may contribute to greater use of segmented beam approach in solving of various static, free vibration or buckling problems of non-uniform beams. Also, it was shown that MSRM can be easily adapted for the analysis of beams that resting on partial elastic foundation. [ABSTRACT FROM AUTHOR]

In this paper, the free vibration and buckling behaviors of nanoscale beams with different boundary conditions are analyzed using the integral formulation of Eringen's nonlocal elasticity theory. To this end, both strain- and stress-driven nonlocal integral models are employed. The nanobeams are modeled according to the Euler–Bernoulli beam theory. Moreover, a novel numerical approach is proposed for solving the obtained governing equations. By this numerical method, which uses matrix differential and integral operators, the integral governing equation is directly solved and the difficulties related to converting the integral governing equation into the differential one are bypassed. Comparisons are made between the predictions of strain and stress-driven models about the vibration and buckling responses of nanobeams subject to various end conditions. The results indicate that based on the stress-driven model, the frequency and critical buckling load increase with increasing the nonlocal parameter, whereas they decrease when the strain-driven integral model is used. [ABSTRACT FROM AUTHOR]

We present a computational study that develops isogeometric analysis based on higher-order smooth NURBS basis functions for the analysis of in-plane laminated composites. Focusing on the stress, vibration and stability analysis of angle-ply and cross-ply 2D structures, we compare the convergence of the strain energy error and selected stress components, eigen-frequencies and buckling loads according to overkill solutions. Our results clearly demonstrate that for in-plane laminated composite structures, isogeometric analysis is able to provide the same accuracy at a significantly reduced number of degrees of freedom with respect to standard finite elements. In particular, we observe that the smoothness of spline basis functions enables high-quality stress solutions, which are superior to the ones obtained with conventional finite elements. [ABSTRACT FROM AUTHOR]

The objective of this study is to develop and validate similitude requirements and scaling laws for studying the real characteristics of structures easily and economically, especially for large structures. The generalized similitude requirements and the scaling law of orthogonally stiffened cylindrical panels and shells for buckling and free vibration are derived by applying the similitude transformation to the total energy of the structural system directly. In practice, due to either the difficulty of satisfying all of the similitude requirements simultaneously or to save experimental cost and time, distorted models with partial similarity are necessarily employed and approximate scaling laws are proposed. The partial similitude is mainly investigated first by using specific formulas of stiffness parameters and corresponding scaling laws are given. Also discussed herein are particular models with relaxations in the material properties of stiffeners, the materials of both the skin and the stiffeners and the material properties and geometry. The obtained results indicate that the distorted models are able to accurately predict the behavior of the prototype. [ABSTRACT FROM AUTHOR]

Quasi-three-dimensional (3D) stability and free vibration analyses of bi-axially loaded, simply-supported, sandwich piezoelectric plates with an embedded either a functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) core or a multilayered fiber-reinforced composite (FRC) one are presented. Three different distributions of carbon nanotubes (CNTs) through the thickness of the CNTRC core, i.e. uniformly distributed and FG V-, rhombus- and X-type variations, are considered, and the effective material properties of the CNTRC core are estimated using the rule of mixtures. The Pagano method, which is conventionally used for the analysis of multilayered FRC plates, is modified to be feasible for the study of sandwich hybrid CNTRC and piezoelectric ones, in which Reissner mixed variational theorem, the successive approximation and transfer matrix methods, and the transformed real-valued solutions of the system equations are used. The modified Pagano solutions for the stability and free vibration of multilayered hybrid FRC and piezoelectric plates are in excellent agreement with the exact 3D ones available in the literature, and those for sandwich hybrid CNTRC and piezoelectric plates may be used as the benchmark solutions to assess the ones obtained by using various 2D theories and numerical models. [ABSTRACT FROM AUTHOR]

This paper presents the Hencky bar-chain model (HBM) for buckling and vibration analyses of Euler-Bernoulli beams with elastic end restraints. The Hencky bar-chain comprises rigid beam segments (of length a = L/n where L is the total length of beam and n the number of beam segments) connected by frictionless hinges with elastic rotational springs of stiffness EI/a where EI is the flexural rigidity of the beam. The elasticity and the mass of the beam are concentrated at the hinges with rotational springs. The key contribution of this paper lies in the modeling of the elastic end restraints of the Hencky bar-chain that will simulate the same buckling and vibration results as that furnished by the first-order central finite difference beam model (FDM) which was earlier shown to be analogous to the HBM. The establishment of such a physical discrete beam model allows one to obtain solutions for beam-like structure with repetitive cells (or elements) as well as to calibrate the Eringen's coefficient e0 in the nonlocal beam theory that captures the small length scale effect. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the transverse vibration of a circular plate loaded by uniform pressure along its edge. The plate is supported by an elastic ring support being coaxial with the plate. At its edge the plate is clamped but the radial displacement is allowed. Apart from this problem, the heated plate clamped at its edge, but without the possibility of radial displacement, is also analyzed. The analytical solution of governing equation is obtained in the form of Bessel's functions. Using the analytical solution, the frequencies of transverse vibrations depending on loads, elastic ring stiffness and the location of ring are obtained. The results show that the lowest frequencies vibrations can be either symmetric or asymmetric having one or two nodal diameters. It is also shown that multiple vibration frequencies can occur for special values of load and ring stiffness. [ABSTRACT FROM AUTHOR]

Sandwich panels have been developed to either produce lighter structures capable of carrying prescribed loads or increase the load-carrying capacity subject to limitations on weight. In these panels, facings carry bending and in-plane loads while the core functions similarly to the web of a beam, mostly resisting transverse shear. Improvements in the load-carrying capacity of sandwich panels can be achieved through modifications in their geometry, boundary conditions, and material distribution. One of the methods recently considered by the authors is based on using facings with a step-wise variable thickness that increases at the critical region of the structure.1 It was illustrated that the strength of a sandwich panel can be considerably enhanced using such stepped facings, without a detrimental increase of the weight. The present paper expands the study of the feasibility of the stepped-facing sandwich panel concept concentrating on three structural problems, i.e. a possible improvement in stability, changes in the natural frequencies, and forced dynamic response to the explosive blast. It is illustrated that the stepped-facing design can improve stability of the panel and its response to blast loading. However, fundamental frequencies of stepped-facing panels decrease compared to those in their conventional equal-weight counterparts. Such decrease is detrimental in the majority of engineering applications representing a limitation of stepped-facing panels. Nevertheless, the usefulness of the stepped-facing design is proven in the problems of bending, stability, and blast loading. Numerous examples presented in the paper validate our suggestion that the combination of a relatively simple manufacturing process and an improved structural response of sandwich panels with stepped facings may present the designer with an attractive alternative to conventional sandwich structures. [ABSTRACT FROM AUTHOR]

Developed herein are the scaling laws for physical modeling of anti-symmetric cross-ply laminated circular cylindrical shells for buckling and free vibration experiments. In the absence of experimental data, the validity of the scaling laws is verified by numerical experiments. This is accomplished by calculating theoretically the buckling loads and fundamental frequencies of the model and substituting into the scaling laws to obtain the corresponding values of the prototype. The predicted values of the prototype from the scaling laws are then compared with existing closed-form solutions. Examples for the complete similitude cases with various stacking sequences, number of plies, and length-to-radius ratios show exact agreement. The derived relationships between the model and prototype will greatly facilitate and reduce the need for costly experiments. In reality, either due to the complexity of the scaling laws or to economize experimental cost and time, it may not be feasible to construct the model to fulfil the scaling laws completely. Thus, several possible models of partial similitude are investigated numerically. These include models with distortion in laminated material properties, stacking sequences and number of plies. Model with distortion in material properties yields a high percentage of discrepancy and is not recommended. [ABSTRACT FROM AUTHOR]

The present paper is concerned with the vibration, buckling and dynamic instability behavior of laminated composite, cross-ply, doubly-curved panels with a central circular hole subjected to in-plane static and periodic compressive loads. A generalized shear deformable Sanders' theory is used to model the curved panels, considering the effects of transverse shear deformation and rotary inertia. Bolotin's approach is used for studying the dynamic instability regions of doubly-curved panels. The effects of non-uniform edge loads, curvature with different cutout ratios, static and dynamic load factors, and lamination parameters on curved panels are investigated with the results discussed. [ABSTRACT FROM AUTHOR]

The similitude invariants and scaling laws for the buckling and free vibration of antisymmetric angle-ply laminated circular cylindrical shells were derived by directly applying the similitude transformation to the governing differential equations of the problem considered. The scaling laws relate the buckling load and natural frequency of a model to those of a prototype when the similarity requirements between the two systems are fulfilled. In the absence of experimental data, the validity of the scaling laws was verified by calculating theoretically the buckling loads and fundamental frequencies of vibration of the model and substituting them into the scaling laws to yield values for the prototype, which were then compared with those directly computed for the prototype. The numerical studies show that for the case of complete similitude with various stacking sequence, number of plies, and radius ratio, the solutions predicted by the similitude theory agree exactly with those obtained directly from the theory. Some typical partial similitude cases were also investigated. It was demonstrated that the partial similitude model with distortion in stacking sequence is reliable for predicting the behavior of the prototype. On the other hand, models with distortion in material properties are not recommended because of the existence of large discrepancies in the predicted results. [ABSTRACT FROM AUTHOR]