Dynamic Stability Analysis of Size-Dependent Viscoelastic/Piezoelectric Nano-beam

This paper analyzes the dynamic stability of an isotropic viscoelastic Euler–Bernoulli nano-beam using piezoelectric materials. For this purpose, the size-dependent theory was used in the framework of the modified couple stress theory (MCST) for piezoelectric materials. In order to capture the geometrical nonlinearity, the von Karman strain displacement relation was applied. Hamilton’s principle was also employed to obtain the governing equations. Furthermore, the Galerkin method was used in order to convert the governing partial differential equations (PDEs) to a nonlinear second-order ordinary differential one. Dynamic stability analysis was performed and the effects of such parameters as viscoelastic coefficients, size effect, and piezoelectric coefficient were investigated. The results showed that in this system, saddle points, central points, Hopf bifurcation points, and fork bifurcation points could be created, and the phase portraits connecting these equilibrium points exhibit periodic orbits, heteroclinic orbits, and homoclinic orbits.

Global Buckling Behavior of CFST Columns with Assembling Errors

Concrete-filled steel tubular (CFST) column has been widely used in engineering practice. In the process of assembling two columns to form a slender member, assembling errors (AE) are inevitably produced at the section of connection. When the AE are too large, the global buckling resistance of slender column would be significantly affected. Therefore, it is necessary to investigate the influence of AE on the stability performance of slender CFST columns. In this study, an axial compressive test involving three CFST columns with AE (AE-CFST columns) was conducted. A refined finite element (FE) model is established for further parametric analysis. Based on a simplified analytical model by analyzing the isolated steel connecting plate, a theoretical formula is proposed for predicting the critical thickness [Formula: see text] of the connecting plate. When the thickness [Formula: see text] of the connecting plate meets its requirement, the failure at the section of connection caused by AE could be effectively prevented. Stability design curves considering the influence of AE ratio (the ratio between assembling error and sectional depth of column) are proposed based on numerous FE examples. It is found that the proposed design curves are reliable for the design of AE-CFST columns with different AE ratios.

Cable Force Determination Using Phase-Based Video Motion Magnification and Digital Image Correlation

The mode shape-aided method provides a simple and effective way for cable force determination, which, however, requires accurate parameter identification of the cable structure. This paper proposes a phase-based video motion magnification to process the image sequences of a cable. Digital image correlations were engaged to measure the dynamic displacement–time history, through tracking the surface characteristic features of the cable. Thereafter, a frequency–domain decomposition technique was applied to extract the natural frequency and mode shape of the cable from the displacement–time history measurements. The identified cable mode shapes, along with a tensioned pinned-pinned cable model, were used to estimate the cable force. The accuracy of the proposed methodology was subsequently verified through laboratory testing on an inclined cable model and field testing on a typical hanger cable of a real-world arch bridge. Overall, the study results indicated that the proposed methodology could expediently and cost-effectively estimate the tension forces of a cable with reasonably acceptable identification accuracy.

Flutter Analysis of a 3D Box-Wing Aircraft Configuration

The aim of this paper is to present a flutter analysis of a 3D Box-Wing Aircraft (BWA) configuration. The box wing structure is considered as consisting of two wings (front and rear wings) connected with a winglet. Plunge and pitch motions are considered for each wing and the winglet is modeled by a longitudinal spring. In order to exert the effect of the wing-joint interactions (bending and torsion coupling), two ends of the spring are located on the gravity centers of the wings tip sections. Wagner unsteady model is used to simulate the aerodynamic force and moment on the wing. The governing equations are extracted via Hamilton’s variational principle. To transform the resulting partial integro-differential governing equations into a set of ordinary differential equations, the assumed modes method is utilized. In order to confirm the aerodynamic model, the flutter results of a clean wing are compared and validated with the previously published results. Also, for the validation, the 3D box wing aircraft configuration flutter results are compared with MSC NASTRAN software and good agreement is observed. The effects of design parameters such as the winglet tension stiffness, the wing sweep and dihedral angles, and the aircraft altitude on the flutter velocity and frequency are investigated. The results reveal that physical and geometrical properties of the front and rear wings and also the winglet design have a significant influence on BWA aeroelastic stability boundary.

Non-linear Dynamic Analysis on a Continuum Suspension Bridge Model with Spatial Layout of Main Cables

This study proposes an approach to set up a continuum full bridge model with spatially inclined cables based on the Hamilton principle. The dynamic governing functions, considering the geometric non-linearities of cables and deck, represent simultaneously the vertical motion of deck and vertical–horizontal motion of cable. With the comparison of the modal properties obtained from the model to those from the accurate model, results show that the proposed model is capable of accurately simulating the modal properties. The primary resonance responses and corresponding frequency-response curves are obtained through the multiple-scale-method. A finite element (FE) model is established, and the corresponding non-linear dynamic analysis in time domain is conducted. Comparing the results from two models, it can be checked that the proposed model is reliable. According to the results of the proposed model, it is found that the second-order shape functions (SOSFs) play a significant role in the system response. Once the non-linear vibration of the bridge becomes significant only considering the excited mode with using the classical Galerkin decomposition cannot correctly predict the structure response. The SOSFs can be classified into stationary and vibrating components. The vibrating component can deviate the time-series of response from the harmonic wave, and the stationary component directly determines the mean value of the time-series.

Analytical Solution for Vibrations of a Modified Timoshenko Beam on Visco-Pasternak Foundation Under Arbitrary Excitations

An analytical solution is derived for dynamic response of a modified Timoshenko beam with an infinite length resting on visco-Pasternak foundation subjected to arbitrary excitations. The modified Timoshenko beam model is employed to further consider the rotary inertia caused by the shear deformation of a beam, which is usually neglected by the traditional Timoshenko beam model. By using Fourier and Laplace transforms, the governing equations of motion are transformed from partial differential forms into algebraic forms in the Laplace domain. The analytical solution is then converted into the time domain by applying inverse transforms and convolution theorem. Some widely used loading cases, including moving line loads for nondestructive testing, travelling loads for seismic wave passage, and impulsive load for impact vibration, are also discussed in this paper. The proposed generic solutions are verified by comparing their degraded results to the known solutions in other literature. Several examples are performed to further investigate the differences of the beam responses obtained from the modified and the traditional Timoshenko beam models. Results show that the modified Timoshenko beam simulates the beam responses more accurately than the traditional model, especially under the dynamic loads with a high frequency. The analytical solutions proposed in this paper can be conveniently used for design and applied as an effective tool for practitioners.

Lateral Impact Response of Elliptical Hollow and Partially Concrete-Filled Cold-Formed Steel Columns Under Static Axial Compression Load

In recent years, the use of partially concrete-filled steel tubular (PCFST) columns has been considered due to their cost-effectiveness and reduction of structural weight in bridge piers and building columns. One of the critical discussions about these columns is their impact resistance. In this article, the dynamic response of hollow and PCFST columns with elliptical cross-section under simultaneous loading of static axial compressive load and lateral impact load is presented using finite element modeling in ABAQUS software (FEA). To ensure the accuracy of the numerical modeling, the analysis results are compared with the results of previous works. The effects of different parameters such as impact velocity, the height of the impact location, the impact direction, the impact block mass, the size and shape of the impact block are investigated in this paper. The results of the numerical analysis showed that the partially filled specimens had better performance than the hollow specimens. The changes in impact direction and impact block mass parameters have a significant effect on the failure of the columns, especially when they are under high impact velocity. Changing the impact velocity significantly affects the impact resistance of specimens. However, the size and shape of the impact block did not have a significant effect on the displacement of the column against the impact loading.

Torsional Vibration of a Pile in Transversely Isotropic Saturated Soil Considering Its Construction Disturbance Effect

The torsional dynamic response of a pile embedded in transversely isotropic saturated soil is investigated while allowing for the construction of disturbance effect. The dynamic governing equations of soil are established based on Biot’s poroelastic theory. By virtue of the continuous conditions of stress and displacement of adjacent disturbance circle and the boundary conditions of pile-soil coupling system, the circumferential displacement of soil and the shear stress on pile-soil contact surface are derived. Subsequently, a closed-form solution for the torsional dynamic response of a pile is derived in the frequency domain. By using inverse Fourier transform and the convolution theorem, a quasi-analytical solution for the velocity response of the pile head subjected to a semi-sine excitation torque is derived in the time domain. The proposed analytical solution is verified by comparing with the two existing solutions available in literature. Following the present solution, a parameter study is undertaken to portray the influence on the complex impedance, twist angle and torque of pile.

Stochastic Substructural Response Reconstruction and Reliability Analysis of High-Dimensional Systems

Existing stochastic dynamic response analysis requires the probability distributions of all variables in the system. Some of them are difficult or even impossible to obtain, and assumed probability density functions are often adopted which may lead to potential unrealistic estimation. This error may accumulate with the dimension of the structural system. This paper proposed a strategy to address this problem in the response analysis of a high-dimensional stochastic system. Partial measurement and finite element model of the target substructure of the system are required. The stochastic responses at several unmeasured locations are reconstructed from the measured responses. Only the variability of the substructure is considered. Other parameters outside the substructure are represented by their mean values contributing to the measured responses. The proposed strategy is illustrated with the analysis of a seven-storey plane frame structure using the probability density evolution method integrated with the response reconstruction technique. Measurement noise is noted to have a large influence on stochastic dynamic responses as different from that in a deterministic analysis. The proposed stochastic substructural response analysis strategy is found more computational efficient than traditional approach and with more realistic information of the structure from the measured responses.

Dynamic Analysis of a Rotating Double-Tapered FGM Beam with Various Shear Models Using a Constrained Variational Method

A constrained variation modeling method for free vibration analysis of rotating double tapered functionally graded beams with different shear deformation beam theories is proposed in this paper. The material properties of the beam are supposed to continuously vary in the width direction with power-law exponent for different indexes. The mathematical formulation is developed based on the geometrically exact beam theory for each beam segment, the admissible functions denoting motion quantities are then expressed by a series of Chebyshev orthogonal polynomials. The governing equations are eventually derived using the constrained variational method to involve the continuity conditions of adjacent segments. Different shear deformation beam theories have been incorporated in the formulations, and the nonlinear effect of bending–stretching coupling vibration together with the Coriolis effect is taken into account. Comparison of dimensionless natural frequencies is performed with the existing literature to ensure the accuracy and reliability of the proposed method. Comparative discussions are performed on the vibration behaviors of the double tapered rotating functionally graded beam with first-order shear deformation beam theory and other higher-order shear deformation beam theories. The effect of material property graduation, power-law index, rotation speed, hub radius, slenderness ratio, and taper ratios is scrutinized via parametric studies, respectively.