Dynamics of a Rigid Foundation on the Surface of an Elastic Half-Space

Advances in Structural Engineering

Lian

et al. 2019

To analyze the behavior of the vibrator–ground coupling vibration, a model containing equivalent dynamic stiffness and equivalent dynamic damping to describe the interaction between the vibrator and the ground is established based on half-space theory. According to load cell test, this model shows a good agreement with the experimental data. Dynamic responses of the structure are analyzed on displacement, velocity, acceleration, and ground force. Results show that the stroke and pump displacement are main constraints that limit the bandwidth of vibrator toward low frequency, and the stroke of conventional vibrator is not long enough to achieve lower frequency. Analysis of velocity response indicates that with the increase of frequency, a larger mass results in a lower velocity under external force. The influence of the ground acting on the baseplate is limited, and the acceleration of the baseplate is determined by its own mass beyond 80 Hz. Analysis of ground force shows that the response of the structure can be divided into three stages. The reaction mass, the baseplate, and the ground play different roles in dominating the ground force at different frequency bands.

Section: Modeling Of the Vibrator–groundmentioning

confidence: 99%

A model for the vibrator–ground coupling vibration and the dynamic responses under excitation of sweep signal

Advances in Structural Engineering

Lian

et al. 2019

“…The key to establish a vibrator-ground model is describing the interaction between the baseplate and the ground in consideration of frequency. In civil engineering, the half-space theory is widely used to solve the foundation-ground vibration problems at different frequencies (Hamidzadeh-Eraghi and Grootenhuis, 2010; Kausel, 2010; Lou et al, 2011). The baseplate vibrating on the ground is similar to the foundation vibrating on the ground, which provides a reference for the establishment of a vibrator-ground model.…”

Section: Establishment and Validation Of The Model Of Vibrator-groundmentioning

confidence: 99%

Modeling of energy transfer and parameter effects on it of a vibrator-ground system

Wen

Advances in Structural Engineering

et al. 2020

The amount of energy transferred to the ground truly represents the performance of the seismic vibrator. So, it is crucial to investigate the transfer of energy in the vibrator-ground system and how parameters affect it. For this purpose, a model of vibrator-ground system considering frequency change is developed based on half-space theory, and methods of calculating energy transfer is innovatively proposed. Results show that the total energy done by the hydraulic force on the vibrator-ground system in the frequency band of 3–200 Hz is 3.156×105 J, and 9.11% of the energy is transferred to the ground. In addition, effects of structural parameters and soil parameters on energy transfer are carried out. It is concluded that lightweight reaction mass can significantly increase the total energy, but heavier reaction mass generates more ground energy. Baseplate with small mass not only helps the vibrator to transmit energy uniformly but also generates more ground energy above 100 Hz. Larger baseplate area can improve the baseplate-ground interaction to transfer more energy to the ground. For the effects of soil on energy transfer, the ground energy in low-frequency band is mainly dominated by soil elastic modulus, and both elastic modulus and density of soil have great effects on energy transferred to ground at high frequencies.

“…According to the half-space theory, equivalent dynamic stiffness K z and equivalent dynamic damping C z are functions of dimensionless frequency a 0 , and the following relations exist: 29,30…”

Section: Establishment and Validation Of Vibrator-ground Coupling Vibration Modelmentioning

confidence: 99%

Modal characteristics and phase response of vibrator under excitation of sweep frequency

Wen

Advances in Mechanical Engineering

et al. 2020

To analyze the dynamic responses of vibrator, a vibrator-ground coupling vibration model considering sweep frequency is proposed based on half-space theory, and modal characteristics and phase response of the structure are investigated. Results show that the sweep frequency has a significant effect on the dynamic responses of the vibrator. The natural frequency of the vibrator changes with sweep frequency, and the resonance may occur at 2.071 Hz and 53.12 Hz. The vibrator has two mode shapes. The first-order mode shape is that the reaction mass and the baseplate move in the same direction and the structure is dominated by the reaction mass. At the second-order resonance, the reaction mass and the baseplate move in opposite directions and the baseplate dominates the system. The phase of the vibrator also changes with the frequency and varies greatly. The phases of reaction mass acceleration, baseplate acceleration and ground force suffer abrupt changes at about 2 Hz and 50 Hz. Especially, the phase of the baseplate acceleration experiences a 180° jumping at about 50 Hz. The abrupt change/jumping frequencies of the phase are basically the same as the natural frequencies, indicating that the resonance has significant effect on the vibrator output.