Direct and inverse problems on free vibration analysis of cracked non-uniform beams carrying spring-mass systems by finite element method

This paper presents an analytical approach to investigate the free vibration analysis of cracked non-uniform beam carrying spring-mass systems by finite element method and illustrates a valid and reliable damage identification method which using hybrid neural genetic technique. Firstly, based on the finite element method, the dynamic characteristics of non-uniform cracked beam carrying spring-mass systems are obtained. Then, the first five frequencies are used as input parameters by combining genetic algorithm with neural network to identify the damage. Finally, Numerical simulations of direct and inverse problems of non-uniform cracked beams carrying a spring-mass system are carried out

Free vibration analysis of a cracked simply supported bridge considering bridge-vehicle interaction

This paper presents an analytical approach to investigate the free vibration of simply supported bridge with cracks under arbitrary number of vehicles. Calculation methods for natural frequencies and mode shapes are proposed based on Euler-Bernoulli beam theory, transfer matrix method and numerical assembly method. The vehicle is modeled as a half-car planar model. Equations of motion and displacement functions for bridge and vehicle are derived, respectively. The undermined coefficient matrices for wheels, vehicles and boundary conditions are obtained based on equilibrium and continuity conditions. Numerical assembly technique is adopted to construct the overall matrix of coefficients for bridge-vehicle vibration system. And natural frequencies and corresponding mode shapes are determined based on iterative method and overall matrix solution. Numerical simulation is presented to verify the effectiveness of the proposed method. The results reveal that solutions of the proposed method have favorable reliability. Natural frequencies and associate modal shapes of simply supported multi-girder bridge under the effects of crack and vehicle are investigated. The influences of crack and vehicle parameters on dynamic characteristics are also demonstrated. Meanwhile, a practical simply supported box-girder bridge model is analyzed by the proposed method and an effective crack identification algorithm is proposed

Flexural free vibrations of . . .

This paper presents an exact approach to investigate the flexural free vibrations of multistep nonuniform beams. Firstly, one-step beam with moment of inertia and mass per unit length varying as ( ) = 1 (1 + ) +4 and ( ) = 2 (1 + ) was studied. By using appropriate transformations, the differential equation for flexural free vibration of one-step beam with variable cross section is reduced to a four-order differential equation with constant coefficients. According to different types of roots for the characteristic equation of four-order differential equation with constant coefficients, two kinds of modal shape functions are obtained, and the general solutions for flexural free vibration of one-step beam with variable cross section are presented. An exact approach to solve the natural frequencies and modal shapes of multistep beam with variable cross section is presented by using transfer matrix method, the exact general solutions of one-step beam, and iterative method. Numerical examples reveal that the calculated frequencies and modal shapes are in good agreement with the finite element method (FEM), which demonstrates the solutions of present method are exact ones

Determination method of limit vehicle bump height in dynamic load test of simply supported bridge

The bump height is one of the key factors which affects the vehicle bump test. If the adopted value of bump height is too small, the test couldn’t get obvious excitation effect for bridge structures. On the other hand, it will cause additional structural damage when the value is rather large. Aiming at this point, the theoretical calculation method to determine limit bump height is proposed in this paper. The vehicle bump test is decomposed into three stages, i.e., the period before rear wheels contacting with bridge, the moment at rear wheels contacting with bridge, the period after rear wheels contacting with bridge. In stage I, the total momentum generated by vehicle rotating around front wheels is calculated. Then, the initial conditions for stage III are derived using the principle of momentum conservation in stage II. Finally, combining with vehicle-bridge coupling equations, the free-decay response of bridge could be calculated to determine the limit bump height in stage III. In this paper, the reliability of the proposed method is validated by finite element method (FEM), and numerical simulations on an actual simply supported hollow slab bridge are used to calculate the dynamic response of bridge considering various transverse positions of vehicle bump and determine the limit bump height

Laboratory Study on Properties of Diatomite and Basalt Fiber Compound Modified Asphalt Mastic

In order to improve the performance of asphalt mastic, some researchers have added diatomite or basalt fiber as a modifier to the asphalt mastic, and the results show that some properties of the asphalt mastic were improved. For the simultaneous addition of diatomite and basalt fiber, two kinds of modifier, compound modified asphalt mastic had not been reported; in this paper, thirteen groups of diatomite and basalt fiber (DBFCMAM) compound modified asphalt mastic with different content were prepared to study the performance. Softening point, cone penetration, viscosity, and DSR tests were conducted, for the high temperature performance evaluation of DBFCMAM, whereas force ductility and BBR tests were used in the low temperature performance study of the DBFCMAM. The results demonstrated that the high temperature performance of DBFCMAM was increased; moreover, the low temperature performance of DBFCMAM improved by diatomite and basalt fiber according to the results of the force ductility test; however, the conclusion of the BBR test data was inconsistent with the force ductility test. In summary, the high temperature and low temperature properties of DBFCMAM had been improved

Master Curve Establishment and Complex Modulus Evaluation of SBS-Modified Asphalt Mixture Reinforced with Basalt Fiber Based on Generalized Sigmoidal Model

Basalt fiber has been proved to be a good modified material for asphalt mixture. The performance of basalt fiber modified asphalt mixture has been widely investigated by extensive researches. However, most studies focused on ordinary static load tests, and less attention was paid to the dynamic mechanical response of asphalt mixture incorporating with basalt fiber. This paper aims to establish the master curve of complex modulus of asphalt mixture incorporating of styrene-butadiene-styrene (SBS) polymer and basalt fiber using the generalized Sigmoidal model. Both loading frequency and temperature were investigated for dynamic mechanical response of asphalt mixture with basalt fiber. In addition, based on the time-temperature superposition principle, the master curves of complex modulus were constructed to reflect the dynamic mechanical response at an extended reduced frequency range at an arbitrary temperature. Results indicated that the generalized Sigmoidal model in this paper could better reflect the dynamic mechanical response accurately with correlation coefficients above 0.97, which is utilized to predict the dynamic mechanical performances accurately. Simultaneously, the modulus values exhibit an increasing trend with loading frequency and decrease versus temperature. However, the phase angle values showed different trends with frequency and temperature

Flexural Free Vibrations of Multistep Nonuniform Beams

This paper presents an exact approach to investigate the flexural free vibrations of multistep nonuniform beams. Firstly, one-step beam with moment of inertia and mass per unit length varying as I(x)=α11+βxr+4 and m(x)=α21+βxr was studied. By using appropriate transformations, the differential equation for flexural free vibration of one-step beam with variable cross section is reduced to a four-order differential equation with constant coefficients. According to different types of roots for the characteristic equation of four-order differential equation with constant coefficients, two kinds of modal shape functions are obtained, and the general solutions for flexural free vibration of one-step beam with variable cross section are presented. An exact approach to solve the natural frequencies and modal shapes of multistep beam with variable cross section is presented by using transfer matrix method, the exact general solutions of one-step beam, and iterative method. Numerical examples reveal that the calculated frequencies and modal shapes are in good agreement with the finite element method (FEM), which demonstrates the solutions of present method are exact ones

Design Optimization of SBS-Modified Asphalt Mixture Reinforced with Eco-Friendly Basalt Fiber Based on Response Surface Methodology

This paper investigates the effects of basalt fiber content, length and asphalt-aggregate ratio on the volumetric and strength properties of styrene-butadiene-styrene (SBS)-modified asphalt mixture reinforced with eco-friendly basalt fiber. An experimental scheme was designed to optimize three preparation parameters for the Marshall test indices based on response surface methodology (RSM). The results showed that basalt fiber content presents a more significant effect on air voids, voids in mineral aggregates and voids filled with asphalt. Basalt fiber length is more related to Marshall stability, and flow value exhibits a significant variation trend with asphalt-aggregate ratio. The optimization of preparation parameters is determined as follows: basalt fiber content is 0.34%, length is 6 mm, asphalt-aggregate ratio is 6.57%, which possesses favorable and reliable accuracy compared with experimental results. Furthermore, basalt fiber reinforced asphalt binder and mixture were also studied, and it was found that basalt fiber can enhance the performance of asphalt binder and mixture in terms of cone penetration, softening point, force ductility, as well as pavement performance tests

Assessing High- and Low-Temperature Properties of Asphalt Pavements Incorporating Waste Oil Shale as an Alternative Material in Jilin Province, China

This study investigates the feasibility of recycling waste oil shale as an alternative material into asphalt pavements in Jilin province, China. The high- and low-temperature properties of asphalt materials play important roles for asphalt pavements in seasonal frozen regions. Laboratory experiments were conducted to analyze the high- and low-temperature properties of asphalt mastics and mixtures. Results indicated that adding oil shale ash (OSA) may lead asphalt to a softer consistency and less temperature susceptibility. Also, OSA could improve high-temperature stability and enhance rutting resistance of asphalt materials, whereas the effect of OSA on low-temperature properties is insignificant by comparison. Moreover, the high- and low-temperature performances of asphalt mixtures were evaluated based on testing roads through rutting depth index, riding quality index, and indirect tensile strength test. It can be proved that the sustainable asphalt materials have better high-temperature stability and rutting resistance and also fulfill the requirements of low-temperature cracking resistance