International Journal of Structural Stability and Dynamics

This technical note presents a static–dynamic relationship for the flexural free vibration analysis of beams in tension with some specific boundary conditions. It is shown to be possible that a free vibration system can be solved via a static analysis approach to determine the natural frequencies of the beam with tension forces. The key idea of this study is to substitute the real natural frequency parameters with zero or negative elastic foundation stiffness, thereby allowing one to obtain the natural frequencies by analyzing the case with negative foundation elastic constant. This static approach for vibration problems can be extended for more complicated engineering structural systems.

This paper presents a three-dimensional (3D) analysis for the natural frequencies of completely free, toroidal shells of revolution with hollow circular cross-sections by the Ritz method. The displacement components $u_r$, $u_{\theta }$, and $u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in $\theta$, and of the ordinary algebraic simple polynomials in the $r$ and $z$ directions. The potential (strain) and kinetic energies of the torus are formulated, and the upper bound values of the frequencies are obtained by a minimization procedure. As the degree of the polynomials increases, the frequencies computed converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the torus. Comparisons are made between the frequencies from the present 3D method, a 3D finite element method, experimental methods, and thin and thick ring theories.

The importance of soil–structure interaction analysis has been proven by many researchers. It is obvious that soil media should be considered as an infinite domain to represent the radiation of waves into infinity. Perfectly matched discrete layer (PMDL) is one of the most promising methods to describe properly the infinite domain in soil media in frequency and time domains. In this research, a modified version of PMDLs that has a different strategy to determine their parameters is proposed. The method is named perfectly matched discrete layers with analytical wavelengths (AW-PMDLs). For verification of the proposed method, the dynamic compliances of strip foundations are analyzed and validated in the frequency domain. In the analyses, frequency-dependent system properties and hysteretic (material) damping are considered. The results show that the proposed procedure, AW-PMDL method, is effective for soil–structure interaction analysis in the frequency domain.

This study investigates the behaviors of simply supported reinforced concrete (RC) beams subjected to impact loads. A numerical model of RC beams has been calibrated and a total of 18 RC beams with varying longitudinal reinforcement, transverse shear reinforcement, span and effective depth are investigated, subjected to different input impact energy. It is found that inertia force plays an important role in resisting an impact load at the starting time. The slenderness of the beam can cause increased downward reaction force and also amplifies the upward reaction force. Based on the numerical results, recommendations are made for designing RC beams under low velocity impact load. A formula is derived to predict the maximum mid-span deflection under low velocity impact load with respect to the kinetic energy and static bending capacity. The maximum spacing and the diameter of stirrups are also recommended so as to avoid the brittle failure under impact load.

Based on the classical thin plate theory, this paper proposes new sets of enriched basis functions for in-plane and out-of-plane displacements of square plates that can yield admissible functions for the Ritz method using the moving least-squares (MLS) approach. These admissible functions display the discontinuities of displacement and slope across a crack; give the correct singularity order for the stress resultants at the crack tips; and enhance the Ritz method’s ability to recognize the existence of an internal crack in a plate. To confirm the validity of the proposed approach, convergence studies were performed on the buckling loads and vibration frequencies of plates with central horizontal cracks, and the results obtained agree closely with the published ones as well as those generated by the commercial finite element software. To demonstrate the importance of including all the in-plane stress resultant components in the analysis, the effects of different in-plane stress resultant components on the buckling loads and vibration frequencies of simply supported center-cracked square plates under uniaxial uniform loading were investigated. The present approach was further employed to study the effects of cracks’ lengths, orientations, and locations on the buckling loads and frequencies of cracked square plates under different boundary conditions and in-plane loading conditions.

Low-cost robotic welding and wide availability of high strength steel plates of grades over 500MPa make the use of tapered members an economical alternative to conventional prismatic members for modern steel structures, as experienced by the authors in some practical projects in Hong Kong and Macau. This paper proposes a new and efficient numerical method for modal and elastic time-history analysis of the frames with tapered sections. A series of non-prismatic elements is derived on the basis of analytical expressions, and the exact consistent mass and tangent stiffness matrices are formulated. Five common types of tapered sections for practical applications, namely the circular solid, circular hollow, rectangular solid, rectangular hollow and doubly symmetric-I sections, are studied. Contrary to the conventional method using the approximate assumptions for the section properties along the member length, this research analytically expresses the flexural rigidity and cross-sectional area for the stiffness and mass matrices of an element. Further, the techniques for obtaining the dynamic performances, such as natural vibrations and time-history responses, of non-prismatic members are investigated. Finally, three examples are conducted for validating and verifying the accuracy of the proposed formulations. The present work can be used in the dynamic response analysis of frame structures with tapered sections in seismic zones.

A three-dimensional (3D) pedestrian–structure interaction (PSI) system based on the biomechanical bipedal model is presented for general applications. The pedestrian is modeled by a bipedal mobile system with one lump mass and two compliant legs, which comprise damping and spring elements. The continuous gaits of the pedestrian are maintained by a self-driven walking kinetic energy, which is a new driven mechanism for the mobile unit. This self-driven mechanism enables the pedestrian to operate at a varying total energy level, as an important component for further modeling of the crowd-structure dynamic interaction. Numerical studies show that the pedestrian walking on the structure leads to a reduction in the natural frequency, but an increase in the damping ratio of the structure. This model can also reproduce the reaction forces between the feet and structure, similar to those measured in the field. In addition, the proposed model can well describe the 3D pedestrian–structure dynamic interaction. It is recommended for use in further study of more complicated scenarios such as the dynamic interaction between a large scale kinetic crowd and slender footbridge.

The dynamic interaction of bridge-traffic system is dependent on the stochastic characteristics of various parameters that are random in nature, such as the surface roughness, traffic flow, and so on. It is necessary to include these uncertainties in the analysis. In this paper, the bridge-traffic coupled vibration system is studied considering the stochastic characteristics of traffic flows and surface roughness. The parameters, such as the extrapolation maximal displacement and mean value of the random process, are firstly presented in the probability analysis. Two vehicle models, one with 18 degrees of freedom (DOFs) and the other with 3 DOFs, were adopted in the vehicle simulation. A cellular automaton (CA) model is adopted to simulate the traffic flows and bridge surface roughness. The numerical investigation shows that: (1) the mean value distribution of the bridge vertical and lateral dynamic displacements generally remains stationary; (2) the dynamic responses at different time and under different traffic flows have negligible correlation; and (3) the extrapolation maximal value of the bridge displacement strictly and monotonically increases with the growth of design period.

Full-scale tests are conducted to investigate the load-bearing capacity and failure mechanism of power transmission towers subjected to various loading patterns (broken lines, wind and ice). Detailed finite element models of power transmission towers are established based on these experimental prototypes. To capture the member instability, the integral stability coefficients are obtained from different specifications and introduced into a user-defined material model. Subsequently, the failure analysis of power transmission towers is carried out using an explicit algorithm, and good agreement is found in comparison with experimental results. The results show that the proposed procedure is effective in simulating the power transmission tower failure process. The full-scale test and numerical simulation studies can provide a valuable database for the design of power transmission towers subjected to various loads.

This paper is concerned with the buckling and post-buckling behaviors of a simply supported symmetric functionally graded (FG) microplate lying on a nonlinear elastic foundation. The modified couple stress theory is used to capture the size effects of the FG microplate, and the Mindlin plate theory with von Karman’s geometric nonlinearity taken into account is adopted to describe its deflection behavior. Based on these assumptions and the principle of minimum potential energy, the equilibrium equations of the FG microplate and associated boundary conditions are derived. By applying the Galerkin method to the equilibrium equations, closed-form solutions for the critical buckling load and the load–displacement relation in the post-buckling stage are obtained. Furthermore, the effects of the power law index, the material length scale parameter to thickness ratio, the stiffness of the elastic foundation, and in-plane boundary conditions on the buckling and post-buckling behaviors of the FG microplate are discussed in detail.

This paper is concerned with the lateral and torsional coupled vibration of monosymmetric I-beams under moving loads. To this end, a train is modeled as two subsystems of eccentric wheel loads of constant intervals to account for the front and rear wheels. By assuming the lateral and torsional displacements to be restrained at the two ends of the beam, both the lateral and torsional displacements are approximated by a series of sine functions. The method of variation of constants is adopted to derive the closed-form solution. For the most severe condition when the last wheel load is acting on the beam, both the conditions of resonance and cancellation are identified. Once the condition of cancellation is enforced, the resonance response can always be suppressed, which represents the optimal design for the beam. Since the condition for suppressing the torsional resonance is exactly the same as that for the vertical resonance, this offers a great advantage in the design of monosymmetric I-beams, as no distinction needs to be made between the suppression of vertical or torsional resonance.

This paper investigates the free vibration and dynamic response of functionally graded sandwich beams resting on an elastic foundation under the action of a moving harmonic load. The governing equation of motion of the beam, which includes the effects of shear deformation and rotary inertia based on the Timoshenko beam theory, is derived from Lagrange’s equations. The Ritz and Newmark methods are employed to solve the equation of motion for the free and forced vibration responses of the beam with different boundary conditions. The results are presented in both tabular and graphical forms to show the effects of layer thickness ratios, boundary conditions, length to height ratios, spring constants, etc. on natural frequencies and dynamic deflections of the beam. It was found that increasing the spring constant of the elastic foundation leads to considerable increase in natural frequencies of the beam; while the same is not true for the dynamic deflection. Additionally, very large dynamic deflection occurs for the beam in resonance under the harmonic moving load.

For long-term simulation of dynamic problems, it is desirable for the integration method to capture higher-order accuracy, while maintaining zero numerical damping. To this end, this paper proposes an efficient four-parameter single-step method (FPSM), which only adds two vector operations per step compared with the Newmark method. For linear analysis, these four parameters can be uniquely determined and the generated optimal scheme possesses several desirable attributes, such as nondissipation for undamped systems, fourth-order accuracy and an enough stability interval. Compared with existing nondissipative methods, such as the central difference method and the trapezoidal rule, the present method is recommended for general use due to its high accuracy and efficiency. Finally, several numerical examples are prepared to validate these superiorities of the proposed method.

This paper focuses on the size dependency of lateral vibration of a micro overhung rotor-disk system subjected to an axial load based on the modified strain gradient theory. The governing equations of motions as well as the boundary conditions are derived from Hamilton’s principle. The assumed modes approach is employed to transform the governing partial differential equations into a set of infinite ordinary differential equations. The first two natural frequencies and associated instability rotational speeds of the system are analytically determined. The effects of variation in the parameters, such as the rotational speed, material length scale parameters, axial load and rotor length, on the natural frequencies and instability speeds are discussed and presented. The results obtained reveal that each of the material length scale parameters has a significant impact on the vibration response characteristics of the system.

Rain load acting on a transmission tower is large enough to receive attention according to previous studies and, therefore, a parametric analysis is necessary to understand its mechanism. In this paper, the effects of different raindrop size distributions on both rain pressure and tower response are studied. First, a theoretical method is proposed to estimate the shape parameters of the gamma raindrop size distribution based on the conservation of rain intensity. The influence of raindrop spectrum on rain pressure in free wind field is then investigated. The results reveal that raindrop spectrum has great effect on the rain pressure distribution and its time interval has a large impact on the total rain pressure. In addition, the time interval has greater influence than the spectrum when the rain intensity is constant. At last, six different raindrop spectra are employed to simulate the tower response induced by wind and rain loads, of which the results indicate that the raindrop spectrum has a significant effect on the tower response. The maximum increasing percentage of rain load relative to wind load can reach up to 13.7%, indicating that the influence of rain load is quite remarkable and should be considered in analyzing the response of transmission towers.