International Journal of Structural Stability and Dynamics

This paper deals with dynamic optimal arches, built with a constant volume of arch material, that have the largest fundamental natural frequencies. The cross-section of each arch is a solid regular polygon with its depth varying in a functional fashion. Three shapes of arch (circular, parabolic, and sinusoidal) and three kinds of taper type (linear, parabolic, and sinusoidal) are considered. Differential equations governing free vibrations of such tapered arches are derived, in which the effect of rotatory inertia is included; these equations are numerically solved to calculate the natural frequencies. The numerical results are presented in tables and figures that relate the frequency curves to arch parameters. Typical examples of obtaining the geometry of the dynamic optimal arch are presented. Laboratory scale experiments were conducted to measure the natural frequencies.

We investigate the buckling behaviors of short multi-walled carbon nanotubes (MWCNTs) under axial compression by using molecular mechanics (MM) simulations. The effects of the number of walls, length and chiral angle of MWCNTs on the buckling behaviors are examined. The results show that the buckling behaviors of short MWCNTs are rather different from single walled carbon nanotubes (SWCNTs) and slender MWCNTs. Moreover, it is observed that the buckling strains of short MWCNTs vary inversely proportional to the number of nanotube walls. For slender MWCNTs, the buckling strains fluctuate as the number of walls increase. It increases for beam-like buckling mode, decreases for shell-like buckling mode and is approximately constant for the shell-beam-like buckling mode. The increase in the length of MWCNT has also led to a significant decrease of the buckling strain for short MWCNTs. However, chirality does not have a significant effect on the buckling strain of MWCNTs nor alter the buckling mode of short MWCNTs.

Based on the second-order inelastic analysis, this paper presents a practical method of design for steel–concrete composite beam-columns that satisfies code performance requirements. The concept of second-order inelastic analysis for structures is to consider both geometric and material nonlinearities and their imperfections so that the real structural behavior can be captured and the assumption for effective lengths is not required. The refined plastic hinge approach proposed herein traces the gradual material yielding and simulates full plasticity of a cross-section. The definitions of the initial and full yield surfaces (which are used to initiate the yielding and to indicate the full plastic stage) for steel–concrete composite cross-sections, based on the cross-section analysis, are presented. The proposed method is verified in examples of isolated composite columns and frames.

Chaotic vibrations of functionally graded doubly curved shells subjected to concentrated harmonic load are investigated. It is assumed that the shell is simply supported and the edges can move freely in in-plane directions. Donnell's nonlinear shallow shell theory is used and the governing partial differential equations are obtained in terms of shell's transverse displacement and Airy's stress function. By using Galerkin's procedure, the equations of motion are reduced to a set of infinite nonlinear ordinary differential equations with cubic and quadratic nonlinearities. A bifurcation analysis is carried out and the discretized equations are integrated at (i) fixed excitation frequencies and variable excitation amplitudes and (ii) fixed excitation amplitudes and variable excitation frequencies. In particular, Gear's backward differentiation formula (BDF) is used to obtain bifurcation diagrams, Poincaré maps and time histories. Furthermore, maximum Lyapunov exponent and Lyapunov spectrum are obtained to classify the rich dynamics. It is revealed that the shell may exhibit complex behavior including sub-harmonic, quasi-periodic and chaotic response when subjected to large harmonic excitations.

A Timoshenko beam element for large displacement analysis of planar beam and frame structures is formulated in the context of the co-rotational method. The shallow arch expression is adopted for the local strain, and cubic and quadratic polynomials obtained from the field consistence approach are respectively employed to interpolate the transversal displacement and rotation. The numerical examples show that the proposed element is capable of furnishing accurate results with a smaller number of elements as compared to the elements previously used in the examples. It has also shown that the nonlinear term in the expression of the local strain plays an important role in the accuracy of the element in the large displacement analysis of beam and frame structures.

In this paper, multibody dynamic modeling and flutter analysis of a flexible slender vehicle are investigated. The method is a comprehensive procedure based on the hybrid equations of motion in terms of quasi-coordinates. The equations consist of ordinary differential equations for the rigid body motions of the vehicle and partial differential equations for the elastic deformations of the flexible components of the vehicle. These equations are naturally nonlinear, but to avoid high nonlinearity of equations the elastic displacements are assumed to be small so that the equations of motion can be linearized. For the aeroelastic analysis a perturbation approach is used, by which the problem is divided into a nonlinear flight dynamics problem for quasi-rigid flight vehicle and a linear extended aeroelasticity problem for the elastic deformations and perturbations in the rigid body motions. In this manner, the trim values that are obtained from the first problem are used as an input to the second problem. The body of the vehicle is modeled with a uniform free–free beam and the aeroelastic forces are derived from the strip theory. The effect of some crucial geometric and physical parameters and the acting forces on the flutter speed and frequency of the vehicle are investigated.

This paper deals with the geometrically nonlinear dynamic analysis of smart laminated composite plates integrated with the patches of active constrained layer damping (ACLD) treatment. The constraining layer of the ACLD treatment is made of active fiber composite (AFC) materials. The Von Kármán type nonlinear strain–displacement relations and the first-order shear deformation theory (FSDT) are adopted in deriving the coupled electromechanical nonlinear finite element (FE) model. The Golla–Hughes–McTavish (GHM) method is implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. Symmetric/antisymmetric cross-ply and antisymmetric angle-ply laminated substrate plates are considered in the numerical analyses. The results indicate that the ACLD patches significantly improve the damping characteristics of the plates for suppressing the geometrically nonlinear transient vibrations of the plates. The effects of variation of piezoelectric fiber orientation in the AFC constraining layer on the control authority of the ACLD patches have also been investigated.

An efficient time-integration algorithm for nonlinear dynamic analysis of structures is presented. By adopting the temporal discretization for time finite element approximation, very large time steps can be used by the algorithm. With an accuracy of fourth order, this technique requires only displacements and velocities to be made available at the start of the current time step for integration in state space. Using the weighted momentum principle, the problem of discontinuity caused by impulsive loads is resolved after time-integration of the applied load in external momentum. Since no knowledge is required of acceleration at the current time step, the errors caused by estimation of acceleration by previous finite-difference methods are circumvented. Moreover, an iterative procedure is included for each time step, involving the three phases of predictor, corrector, and error-checking. The effectiveness and robustness of the proposed algorithm in solving nonlinear dynamic problems is demonstrated in the numerical examples.

A huge number of data can be obtained continuously from a number of sensors in long-term structural health monitoring (SHM). Different sets of data measured at different times may lead to inconsistent monitoring results. In addition, structural responses vary with the changing environmental conditions, particularly temperature. The variation in structural responses caused by temperature changes may mask the variation caused by structural damages. Integration and interpretation of various types of data are critical to the effective use of SHM systems for structural condition assessment and damage detection. A data fusion-based damage detection approach under varying temperature conditions is presented. The Bayesian-based damage detection technique, in which both temperature and structural parameters are the variables of the modal properties (frequencies and mode shapes), is developed. Accordingly, the probability density functions of the modal data are derived for damage detection. The damage detection results from each set of modal data and temperature data may be inconsistent because of uncertainties. The Dempster–Shafer (D–S) evidence theory is then employed to integrate the individual damage detection results from the different data sets at different times to obtain a consistent decision. An experiment on a two-story portal frame is conducted to demonstrate the effectiveness of the proposed method, with consideration on model uncertainty, measurement noise, and temperature effect. The damage detection results obtained by combining the damage basic probability assignments from each set of test data are more accurate than those obtained from each test data separately. Eliminating the temperature effect on the vibration properties can improve the damage detection accuracy. In particular, the proposed technique can detect even the slightest damage that is not detected by common damage detection methods in which the temperature effect is not eliminated.

This paper introduces the use of a two-degree-of-freedom (2DOF) model which comprises two spring-connected lumped masses for analyzing the response behavior of a plate structure to a low velocity impact of a flying solid object. We propose a novel method for calculating the value of the equivalent lumped mass and that of the spring constant which characterizes the 2DOF model. This is an important contribution given that existing calculation methods that are based on results from modal analysis would only be suitable for modeling the impact actions of wind or blast. Analysis involving the use of a 2DOF model is inexpensive and convenient to operate whilst achieving very good accuracies as demonstrated herein. By contrast, modeling impact response behavior by finite element analyses can be very time consuming and labour intensive because of the need to model in detail the impactor in contact with the target.

Some types of rigid origami possess specific geometric properties. They have a single degree of freedom, and can experience large configuration changes without cut or being stretched. This study presents a numerical analysis and finite element simulation on the folding behavior of deployable origami structures. Equivalent pin-jointed structures were established, and a Jacobian matrix was formed to constrain the internal mechanisms in each rigid plane. A nonlinear iterative algorithm was formulated for predicting the folding behavior. The augmented compatibility matrix was updated at each step for correcting the incompatible strains. Subsequently, finite element simulations on the deployable origami structures were carried out. Specifically, two types of generalized deployable origami structures combined by basic parts were studied, with some key parameters considered. It is concluded that, compared with the theoretical values, both the solutions obtained by the nonlinear algorithm and finite element analysis are in good agreement, the proposed method can well predict the folding behavior of the origami structures, and the error of the numerical results increases with the increase of the primary angle.

It is illustrated in this paper that a nonlinearly elastic column, depending upon the values of different material parameters involved, exhibits several stability characteristics and types of buckling which are generally observed separately in distinctively different structural systems. By introducing finite disturbances it is shown that the column may buckle well before the bifurcation buckling load is reached. The proposed approach can be useful in engineering practice since it can be utilized to study the stability of uniaxial structural elements made from rubber or any other material which obeys the modified Ludwick's constitutive model.