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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.

This paper is concerned with the flexural vibration analysis of rotating Timoshenko beams by using the variational iteration method (VIM). Accurate natural frequencies and mode shapes of rotating Timoshenko beams under various rotation speeds and rotary inertia are obtained. The VIM solutions are verified by comparing with some existing results in the literature as well as validated from a comparison study with experimentally measured ones. High accuracy and efficiency of VIM are demonstrated by the use of only a small number of iteration steps required for convergence of the first to the tenth mode frequencies of rotating Timoshenko beam.

This paper presents an accurate analysis of the natural frequency and mode shape of carbon fiber-reinforced steel–concrete composite beam with double-slip surfaces. To study the flexural vibration of the composite beam, a governing differential equation considering the shear-slip effects of two interfaces is formulated. Based on this formulation, the natural frequency and mode shape of carbon fiber-reinforced composite beams are calculated. For comparison purpose, numerical simulations of the composite beams are conducted using the ANSYS in order to verify the present results. High consistency in the two calculation values is revealed. In addition, carbon fiber-reinforced composite beams are fabricated and tested. It is found that the experimental values agreed well with the theoretical results. The findings from this study may provide the benchmark reference for engineering analysis and design of carbon fiber-reinforced steel–concrete composite beams.

In this study, the modified first-order shear deformable theory (FSDT) is applied to analyze the resonant characteristics of piezoelectric (PZT) moderately thick plate vibrators with different thicknesses. A simple and straightforward simplification method between mechanical and electrical functions is also proposed based on the modified FSDT. The natural frequencies and associated mode shapes of piezoelectric plates with completely free boundary are analyzed. The displacement fields of the flexural modes are presented based on the superposition method. This analytical method provides a strong-form novel solution for the flexural-dominated motion’s out-of-plane and in-plane coupling displacement fields. The solutions of displacement functions, which are obtained from the superposition method, show excellent convergence for numerical calculation. To verify the validity of the theoretical solution, the resonant frequencies and the corresponding mode shapes are compared with that obtained by the finite element method (FEM) and experimental measurements using the amplitude-fluctuation electronic speckle pattern interferometer (AF-ESPI) technique. According to the electromechanical formula and the derived theoretical solution, four types of electrode are designed to excite the moderately thick PZT specimen for examining the application feasibility of the proposed method. It is shown in this study that the theoretical analysis, numerical calculation, and experimental measurement are fully compared, and excellent agreements of the piezoelectric moderately thick plate are also obtained.

The rotary inertia defined by Timoshenko to account for the angular velocity effect in flexural vibration of beams has been questioned by some researchers in recent years, and it caused some confusions. This paper discusses the appropriate rotary inertia in Timoshenko beam theory (TBT) and evaluates the influence of the two forms of the rotary inertia on the prediction of the higher-mode frequencies of transversely vibrating beams. Based on the theory of elasticity and variational principle, this work shows that the rotary inertia in the original TBT, defined in terms of the rotation of beam cross-section induced by bending deformation, is variational consistent and is capable of yielding good results of the phase velocities of transversely vibrating beams even in the case where the wavelength of vibrating beams approaches the beam height. On the other hand, the so-called corrected TBT, in which the rotary inertia is defined in terms of the slope of beam deflection, is neither variational consistent nor accurate when the wavelength of vibrating beams approaches the beam height. Therefore, the rotary inertia in TBT defined by Timoshenko is correct and should be used in the dynamic analysis of beams.