Dimensionless wave numbers evolution of a three spans simply supported beam when the intermediate supports are moving along the whole beam

Continuous beams simply supported with several intermediate supports are very common in engineering achievements everywhere. The paper shows the evolution of the dimensionless wave number in 3D format, respectively of the eigenfrequencies for a continuous beam with three openings when the intermediate supports take any position inside the beam. The frequency equation for calculating the dimensionless wave number is presented and the modal function is given with an example for the case where the eigenfrequency has the maximum value at fist vibration mode.

Damage severity for cracked simply supported beams

This paper investigated the static and dynamic behaviors of isotropic cracked simply supported beam using finite element analysis (FEA), ANSYS software. Modal and harmonic vibration analysis of intact and damaged beam were performed in order to extract mode shapes of bending vibration, natural frequencies and obtain frequency response diagram. Static finite element analysis of undamaged and damaged simply supported beam was carried out to determine zero frequency deflection, then stiffness of intact and cracked beam was computed using conventional formula. Crack damage severity of damaged beam was calculated and it is noticed that as crack position is increased from left hand support of beam up to central point and crack depth is increased, then crack damage severity increases. The effect of mode shape pattern is investigated and it is found that the amount of decreasing of natural frequency is proportional to the normalized mode shape at position of crack. The exhibited correlation between results for damaged beam revealed that crack damage severity is proportional to zero frequency deflection and inversely proportional to first mode frequency.

Multi-level residue harmonic balance method for nonlinear vibration of the beam

This study presents the nonlinear vibration and chaotic response of a beam subjected to harmonic excitation. The multi-level residue harmonic balance method is applied to solve the geometrically cubic nonlinear vibration of the simply supported beam. The obtained results agree well with those of the numerical integration method. The amplitude frequency response curves are presented to illustrate the nonlinear dynamic system response both for a damping and without damping model. Also, the chaotic response is examined for a simply supported beam with a nonlinear dynamic system.

The Influence of Trains on the Seismic Response of Simply-Supported Beam Bridges with Different Pier Heights Expressed through a Safety Factor

With the extension of high-speed railways to high-intensity earthquake regions, it is impossible to avoid structural vibrations due to the joint action of trains and earthquakes. Therefore, it is of great significance to study the influence trains on bridge structures exposed to earthquakes. In this paper, a coupled finite element analysis model of a high-speed railway vehicle-bridge was established by considering a simply-supported beam bridge with the China Railway Track System (CRTS) II plate and the CRH2C high-speed train. The correctness of the model was experimentally verified. By considering the ground motion randomness, the influence of the train on the response of the bridge structure exposed to an earthquake was analyzed. Also, the influence level of the running train on the seismic response of bridge structures with different pier heights was studied. The results revealed that the train dynamic effect significantly reduced seismic responses of piers and supports, and that the effect itself decreased with the pier height increase. Furthermore, the dynamic effect of the train increased the seismic response of the track structure, while the bridge pier height had little influence on the dynamic efficiency of the track structure. For different pier heights, the probability distribution model of the train dynamic effect for the track-bridge system seismic response was considered as the normal distribution. This indicated that the seismic response of the track-bridge system under vehicle condition could be simplified as the product of the seismic response and safety factor under no vehicle condition.

A Seismic Data Acquisition System Based on Wireless Network Transmission

A seismic data acquisition system based on wireless network transmission is designed to improve the low-frequency response and low sensitivity of the existing acquisition system. The system comprises of a piezoelectric transducer, a high-resolution data acquisition system, and a wireless communication module. A seismic piezoelectric transducer based on a piezoelectric simply supported beam using PMN-PT is proposed. High sensitivity is obtained by using a new piezoelectric material PMN-PT, and a simply supported beam matching with the PMN-PT wafer is designed, which can provide a good low-frequency response. The data acquisition system includes an electronic circuit for charge conversion, filtering, and amplification, an FPGA, and a 24-bit analog-to-digital converter (ADC). The wireless communication was based on the ZigBee modules and the WiFi modules. The experimental results show that the application of the piezoelectric simply supported beam based on PMN-PT can effectively improve the sensitivity of the piezoelectric accelerometer by more than 190%, compared with the traditional PZT material. At low frequencies, the fidelity of the PMN-PT piezoelectric simply supported beam is better than that of a traditional central compressed model, which is an effective expansion of the bandwidth to the low-frequency region. The charge conversion, filtering, amplification, and digitization of the output signal of the piezoelectric transducer are processed and, finally, are wirelessly transmitted to the monitoring centre, achieving the design of a seismic data acquisition system based on wireless transmission.

The The Effect of Continuous Suspension Constraint on the Free Vibration and Buckling of a Beam

In this paper, the free vibration and the buckling of a continuously suspended simply-supported beam are analyzed. A semi-analytical approach is used to calculate the natural circular frequencies and the critical forces of the beam. The length of the suspension is used as a parameter, and the natural circular frequencies and the critical forces are presented in a frequency map or a buckling map. The maps are analyzed in view of the trivial solutions, and the frequency map is compared to the map of discrete cable-stayed beams. Finally, for the validation of the results a numerical, finite element analysis is performed.