International Journal of Structural Stability and Dynamics

A three-dimensional (3D) method of analysis is presented for determining the natural frequencies of shallow spherical domes with non-uniform thickness. Unlike conventional shell theories, which are mathematically two dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components $u_{\varphi }$, $u_{\theta }$, and $u_z$ in the meridional, circumferential, and normal directions, respectively, are taken to be periodic in $\theta$ and in time, and algebraic polynomials in the $\varphi$ and z directions. Potential (strain) and kinetic energies of the shallow spherical domes with non-uniform thickness are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies. Natural frequencies are presented for different boundary conditions. The frequencies from the present 3D method are compared with those from a 2D exact method, a 2D thick shell theory, and a 3D finite element method by previous researchers.

During the operation stage, parallel bridges may become nonparallel as a result of unequal load distribution between two parallel bridges and other special conditions. Aerodynamic performance could change significantly under nonparallel positions and become different from that under parallel positions. In this paper, the stationary aerodynamic performance of two parallel bridges under various nonparallel positions during operation stage is studied through a series of wind tunnel tests. This includes the investigation of two horizontal gap distances (HGDs), five relative vertical displacements (RVD) and five relative torsional displacements (RTD). First, sectional models of two closed box girders were tested in smooth flow for stationary aerodynamic force coefficients. An optimum iteration method was then used to calculate the structural displacements and torsional divergence critical wind velocities ($U_{\mathrm{\text{cr}}}$) of two assumed suspension bridges under stationary aerodynamic force. The research outcomes demonstrated that the changes of stationary aerodynamic force coefficients are dependent on the relative displacements of two girders and wind attack angles. In addition, it was revealed that interference effects are detrimental to stationary aerodynamic instability of two bridges with a larger gap-width ratio (i.e. D/B $=$ 1), which is related to the aerodynamic shape of girders and bridge structures. Further, the $U_{\mathrm{\text{cr}}}$ of the leeward bridge significantly decline when the vertical position of the leeward bridge become higher that of the windward bridge. Most importantly, it showed that the combination of RVD and RTD (e.g. RVD $=-20$mm and RTD $=-2^{\circ }$) could potentially lead to the worst stationary aerodynamic performance by decreasing $U_{\mathrm{\text{cr}}}$ of the windward and leeward bridge with 12.03% and 7.89%, respectively.

In this paper, the energy exponent is used to study the instability of parametrically excited systems governed by the damped Mathieu equation. Through the numerical tests, an energy-growth exponent (EGE) is adopted to evaluate the instability intensity and instability boundary of the system. The EGE can be expressed as a product of the modal frequency and a dimensionless coefficient, defined as the energy-growth coefficient (EGC). Based on the Floquet theory, the relationship between the EGE, Floquet exponent and Lyapunov exponent are derived. An energy criterion of parametric instability is proposed by using the EGE. Using a simple pendulum as an example, the geometric characteristics of the EGC are investigated, and approximate analytical formulae of the EGC/EGE for three different unstable patterns are developed. The EGC/EGE formulae are applicable to the parametrically excited systems governed by the damped Mathieu equation. The unstable behaviors and properties of parametric vibrations are analyzed and discussed in details with EGE/EGC for three systems including a triple pendulum, two-dimensional sloshing fluid, and a two-span continuous beam. The stability boundaries established by using EGE/EGC agree well with those by the conventional theory and experiment. As a practical tool, the EGE/EGC formulae can be easily applied to analyzing the unstable intensities and boundaries of the parametrically excited systems.

When studying the vibration of a bridge–vehicle coupled system, most researchers mainly focus on the intact or original bridge structures. Nonetheless, a large number of bridges were built long ago, and most of them have suffered serious deterioration or damage due to the increasing traffic loads, environmental effect, material aging, and inadequate maintenance. Therefore, the effect of damage of bridges, such as cracks, on the vibration of vehicle–bridge coupled system should be studied. The objective of this study is to develop a new method for considering the effect of cracks and road surface roughness on the bridge response. Two vehicle models were introduced: a single-degree-of-freedom (SDOF) vehicle model and a full-scale vehicle model with seven degrees of freedom (DOFs). Three typical bridges were investigated herein, namely, a single-span uniform beam, a three-span stepped beam, and a non-uniform three-span continuous bridge. The massless rotational spring was adopted to describe the local flexibility induced by a crack on the bridge. The coupled equations for the bridge and vehicle were established by combining the equations of motion for both the bridge and vehicles using the displacement relationship and interaction force relationship at the contact points. The numerical results show that the proposed method can rationally simulate the vibrations of the bridge with cracks under moving vehicular loads.

This paper applies the Chebyshev collocation method to finding accurate solutions of natural frequencies for circular cylindrical shells. The shells with different boundary conditions are considered in the parametric study. By using the method to solve the coupled differential equations of motion governing the vibration of the shell, numerical results are obtained from the algebraic eigenvalue equation using the Chebyshev differentiation matrices. And the results satisfy both the geometric and force boundary conditions. Based on the numerical examples, the proposed method shows its capacity and reliability in predicting accurate frequency results for circular cylindrical shells with various boundary conditions as compared to some exact solutions available in the literature.

Since gas explosion is the most frequent accidental event occurring in the oil and gas industry, all safety-related critical elements on the topside of offshore platforms should retain their integrity against extreme pressure demands. Although considerable effort has been devoted to develop blast-resistant design methods for offshore structures, there remain several issues that require further investigation. The duration of the triangular-shaped blast design pressure curve with a completely positive side is usually determined by the absolute area of each measured transient pressure response, using the flame acceleration simulator (FLACS). The negative phase pressure in a general gas explosion, however, is often quite crucial, unlike gaseous detonation or TNT explosion. The objective of this study is to thoroughly examine the effect of the negative phase pressure on structural behavior. A blast wall for a specific floating production, storage, and offloading (FPSO) topside is considered as an exemplar structure for blast-resistant design to focus only on overpressure because there is no drag pressure in this type of obstacle. Gas dispersion and explosion simulations were carried out using FLACS, while LS-DYNA was used in the nonlinear transient finite element structural analysis.

This paper presents an identification technique for damage assessment of structures where only the information about the changes of measured natural frequencies can be directly utilized. The structural damage is characterized by a local decrease in the stiffness as represented by a scalar reduction of the material modulus. The objective of this study is to investigate the feasibility of using such a technique for identifying the structural damage in a real steel girder bridge. Numerical examples involving damaged reinforced concrete beams are first used to demonstrate the capability of the proposed computational technique, based on the nonlinear perturbation theory, to predict the exact location and severity of the damage. To experimentally validate the theory, laboratory damage detection experiments were performed on a simply supported reinforced concrete beam with various damage scenarios as the example. The results of the damage identification procedure based on the measurement of structure’s frequencies before and after occurrence of the damage show that this method can accurately locate the damage and predict the extent of damage. The method performs well even for a structure with a very serious damage as demonstrated by application of the proposed direct iteration technique to a six-span steel girder bridge. Using a limited number of measured natural frequencies, significant reduction in the stiffness of the bridge at multi-sites is detected.

Prestressed concrete bridges with corrugated steel webs have emerged as a new form of steel-concrete composite bridges with remarkable advantages compared with the traditional ones. However, the assumption that plane sections remain plane may no longer be valid for such bridges due to the different behavior of the constituents. The sandwich beam theory is extended to predict the flexural vibration behavior of this type of bridges considering the presence of diaphragms, external prestressing tendons and interaction between the web shear deformation and flange local bending. To this end, a $C^1$ beam finite element is formulated. The proposed theory and finite element model are verified both numerically and experimentally. A comparison between the analyses based on the sandwich beam model and on the classical Euler–Bernoulli and Timoshenko models reveals the following findings. First of all, the extended sandwich beam model is applicable to the flexural vibration analysis of the bridges considered. By letting $\alpha$ denote the square root of the ratio of equivalent shear rigidity to the flange local flexural rigidity, and L the span length, the combined parameter $\alpha L$ appears to be more suitable for considering the diaphragm effect and the interaction between the shear deformation and flange local bending. The diaphragms have significant effect on the flexural natural frequencies and mode shapes only when the $\alpha L$ value of the bridge falls below a certain limit. For a bridge with an $\alpha L$ value over a certain limit, the flexural natural frequencies and mode shapes obtained from the sandwich beam model and the classical Euler–Bernoulli and Timoshenko models tend to be the same. In such cases, either of the classical beam theories may be used.

A time collocation finite element approach is employed to develop one- and two-step time integration schemes with algorithmic dissipation control capability. The newly developed time integration schemes are combined to obtain a new family of time integration algorithms using the concept employed by Baig and Bathe. The newly developed algorithm can effectively control the algorithmic dissipation by relating the collocation parameters with the spectral radius in the high frequency limit. The new algorithm provides better accuracy compared with the generalized-$\alpha$ method for highly dissipative cases and includes the Baig and Bathe method within its family as a special case.

In this paper, the effects of vertical irregularity of masonry-infill wall arrangements on the seismic performance and lateral stability of reinforced concrete (RC) frames have been investigated using nonlinear response history analysis. Discrete finite element models, which are endowed with a damage-based cohesive crack modeling, were developed for six prototype structures with different arrangements of infill panels. The analysis of failure modes and lateral force transfer mechanisms of infilled frames shows that the arrangement of infill panels can critically affect the dynamic properties and structural stability under seismic excitations. Diagonal continuity, infill ratios, and eccentricity of infill walls play essential roles in the lateral-load and displacement capacities of the structures. The hysteresis behavior, failure modes, and force transfer mechanisms of RC frames with concentric and eccentric arrangements of infill panels are compared and their implications on the seismic resistant design are discussed.

Existing structures can be retrofitted against earthquakes with tuned sloshing water dampers (TSWD). These dampers can be incorporated in the structure as displacement response reduction devices for avoiding failure of masonry panels while ensuring their structural function as diagonal struts. The proposal of retrofitting for an existing four story building with TSWDs has been examined through simulated experiments on a reduced scale model of the structure mounted with actual size TSWD. The effectiveness of the single frequency TSWD systems, optimally designed for response control of accurately assessed structures, against well-defined excitations, has been substantiated. Experiments have been conducted with multi-frequency TSWD systems for approximately assessed structures against broadband excitations. The multi-frequency sloshing water damper system exhibited a comparatively robust performance against broadband excitations for a reasonable range of structural frequencies. A retrofitting scheme for the structure has been proposed with multi-frequency TSWD systems.

Application of the piezoelectric patch to mitigate the train wheel squeal is presented in this paper. A complete model for the wheel, rail and foundation is employed in the frequency domain. The wheel squeal model with the shunted piezoelectric element is presented and the consequent added damping is calculated for the critical frequencies. Two different shunt circuits including the resistor ($R)$ and resistor–inductor (RL) are applied and the consequent performances in the noise mitigation are evaluated for different frequencies. The effect of contact point lateral displacement on occurrence of the wheel squeal is investigated. In the parametric study, the effects of shunting circuit and its parameters, size, position and number of piezoelectric elements on the control performance are evaluated. It is found that the resistance shunt circuit has optimal performance when the added damping over a broadband frequency range is implemented. In addition, both the added damping and added damping per piezoelectric volume become saturated by increasing the number of piezoelectric patches further over a specific limiting value.

The main objective of this study is to evaluate inelastic response spectra conditioned on constant displacement ductility demand for a single degree of freedom system, which has positive post-yield stiffness. To develop this analysis, the nonlinear Bouc–Wen model is used and it is subject to a seismic action modeled by a nonstationary stochastic process. The study utilises stochastic linearisation technique and peak theory to obtain inelastic response spectra. More in detail, inelastic acceleration spectra, response modification factor spectra, strength reduction factor spectra, yield strength spectra, and inelastic displacement ratio spectra are obtained for constant displacement ductility demand. The novelty of the present study with respect to the previous ones in this field is to obtain inelastic response spectra in stochastic terms, starting from a stochastic model of the seismic motion. Results suggest that the effect of post-yield stiffness must be considered when determining inelastic response.