Radial integration BEM for vibration analysis of two- and three-dimensional elasticity structures

Mathematical Problems in Engineering

et al. 2018

The structural vibration of the main beam of a crane causes fatigue damage and discomfort to the driver. The swing of the payload has an effect on positioning precision, especially for a ladle crane, and this directly affects production safety. To study the influence of system parameters on the vibration of a crane's main beam and the angle of the payload, a system consisting of the main beam, trolley, payload, and cabin was constructed. A rigid-flexible coupling dynamic model of a moving trolley with a hanging payload that moves on the flexible main beam with a concentrated cabin mass is established, and the direct integration method is used to solve the nonlinear differential equations of system vibration, which are obtained through Lagrange's equation. Then, the time domain responses of the flexible main beam, payload angle, and cabin vibration are obtained. The influences of the trolley running speed, quality of the payload, and quality and position of the cabin on the vibration of the main beam and payload angle are analyzed. The results indicate that the amplitude of the main beam is directly proportional to the quality of the trolley, payload, and cab; the position of the cabin is closer to the mid-span; the amplitude of the main beam is larger; the structural damping has some influence on the vibration of the main beam; and the swing angle of the payload is related to the maximum running speed of the trolley, acceleration time, and length of the wire rope. In order to reduce the vibration of the main beam and cabin, the connection stiffness of the cabin should be ensured during installation.

Section: Solving Methods Of Dynamic Responsementioning

confidence: 99%

Section: Procedures Of Solutionmentioning

confidence: 99%

Nonlinear Vibration of Ladle Crane due to a Moving Trolley

Mathematical Problems in Engineering

et al. 2018

“…The time-domain response of the dynamic system can be obtained using the direct integration method for a linear dynamic system with constant coefficients. Newmark method [45][46][47] is a typical implicit solution approach to structural dynamics problems that has the advantages of good convergence, precision, and stability. Not only is the method condition stable but its stability condition is easily satisfied.…”

Section: Numerical Resultsmentioning

confidence: 99%

Dynamic Optimization Design of Cranes Based on Human–Crane–Rail System Dynamics and Annoyance Rate

2017

Shock and Vibration

The operators of overhead traveling cranes experience discomfort as a result of the vibrations of crane structures. These vibrations are produced by defects in the rails on which the cranes move. To improve the comfort of operators, a nine-degree-of-freedom (nine-DOF) mathematical model of a “human–crane–rail” system was constructed. Based on the theoretical guidance provided in ISO 2631-1, an annoyance rate model was established, and quantization results were determined. A dynamic optimization design method for overhead traveling cranes is proposed. A particle swarm optimization (PSO) algorithm was used to optimize the crane structural design, with the structure parameters as the basic variables, the annoyance rate model as the objective function, and the acceleration amplitude and displacement amplitude of the crane as the constraint conditions. The proposed model and method were used to optimize the design of a double-girder 100 t–28.5 m casting crane, and the optimal parameters are obtained. The results show that optimization decreases the human annoyance rate from 28.3% to 9.8% and the root mean square of the weighted acceleration of human vibration from 0.59 m/s2to 0.38 m/s2. These results demonstrate the effectiveness and practical applicability of the models and method proposed in this paper.

“…Formula (16) constitutes a two-dimensional system of second-order nonlinear time-varying differential equations. e direct integration method is effective for second-order nonlinear vibration systems, which has been verified in many studies [36,37]. In this study, the Newmark direct integration method is used to approximate the vibration response of the system.…”

Section: Procedures and Reliability Analysis Of The Solutionmentioning

confidence: 89%

“…Because temperature has a large in uence on the elastic modulus and mechanical properties of metal structures, and the casting crane operates under high temperature, it is necessary to analyze the dynamic characteristics of the main girder under the action of temperature. According to the literature [26], the elastic modulus of the main beam decreases substantially at temperatures above Reference [35] Reference [36] Figure 8: Calculation results of central displacement position de ection compared to references [38,39]. 300°C, so the midspan displacement of the main beam is signi cantly increased.…”

Section: Main Beam Dynamic Response To Temperaturementioning

confidence: 91%

Dynamic Response of a Casting Crane Rigid‐Flexible Coupling System to High Temperature

Advances in Civil Engineering

Dong

et al. 2020

To determine the influence of temperature on the mechanical properties of crane metal structures, three Q355 alloy steel samples were processed and their elastic moduli were tested at different temperatures using a metal tension test bed. The constitutive equation for the elastic modulus of Q355 alloy steel at different temperatures was predicted using test data and a neural network algorithm. Based on crane structural characteristics and the principle of system dynamics, a coupling vibration model was established that included the crane flexible girder, cabin, trolley, crane, and temperature. System motion equations were established according to the Lagrange equation, and the approximate solution of nonlinear system vibration was solved by the direct integration method (the Newmark method). The dynamic characteristics of the main beam and cabin were analyzed at different temperatures, as well as safety during service. The results show that, with increasing temperature, the maximum midspan displacement of the main beam increases gradually, by 14.3%, 21.4%, and 57.1% at temperatures of 300°C, 400°C, and 600°C, respectively. The cabin vibration displacement increases with temperature, by up to 32.5% at 600°C, but the influence of temperature on cabin vibration acceleration is not obvious. It was concluded that the influence of temperature on the dynamic characteristics of the main beam must be considered during the design stage of cranes. The proposed model and analysis method provide a theoretical basis for the design of casting cranes according to temperature.