Bending Vibration Responses Research Articles

The dynamic bending analysis of plates under thermal load using an efficient wave-based method

Abstract The efficient Wave-Based Method (WBM) is extended to predict the bending vibration response of thin-walled rectangular plates under thermal load. Governing equations of dynamic plate bending problems considering thermal effects are first introduced. The general solution and particular solution of governing equation are derived by the separate variable method and residue theorem, respectively. Then novel wave functions and particular solution function are selected to establish the wave-based model of dynamic plate bending problems under thermal load. The accuracy of WBM is verified by finite element method (FEM) for a simply supported plate and a clamped plate. Then the influence of thermal load on the dynamic bending responses of a clamped plate is investigated. Simulation results prove that WBM achieves higher convergence rate than FEM. The thermal load significantly changes the structural dynamic behaviors. When both the temperature-dependent material properties and thermal stresses are considered, the increase of environment temperature leads to the resonant peak of displacement response shifts toward lower frequency.

Analysis of Coupling Bending Vibration Characteristics of Shafting and Hull under Propeller Excitation

Affected by some difficult factors such as bearing stiffness and lubricant film stiffness and so on, the calculation of the lateral vibration response of the ship shafting is difficult to guarantee high calculation accuracy. A mathematical model of the propulsion system-submarine hull coupling bending vibration was established by mathematical physics, and the bearing excitation of the propeller was calculated. A mathematical model of the bending vibration response of the propulsion shaft system and the transmission of vibrational power to the hull was established to calculate the transmitted power flow. The vibration response and bending vibration power flow of the shafting under the lateral excitation of the propeller were solved. Through MATLAB simulation calculation and analysis, the influence of system parameter variation on the bending vibration flow transmission of each node in the power flow transmission path was obtained.

Coupled torsion–bending dynamic analysis of gear-rotor-bearing system with eccentricity fluctuation

• A new nonlinear dynamic model of a gear-rotor-bearing system is established. • The model describes torsional and bending vibration properties of the system. • The simulation focuses on the nonlinear responses of the system. • The eccentricity has greater effects on vibration responses. This study performs a coupled torsion–bending vibration responses of a gear-rotor-bearing system, which has taken time varying mesh stiffness, nonlinear bearing force and gear eccentricity into account. A 16 DOF nonlinear dynamic model of gear-rotor-rolling bearing transmission system with bending–torsion coupling is established to obtain the dynamic response to the changes of different parameters. Based on the Runge–Kutta numerical method, the dynamics of the system is investigated, which describes torsional and bending vibration properties of the system more comprehensively. The vibration responses of the gear-rotor-bearing system are discussed, and the effects of gear eccentricity and rotational speed on the system are investigated in detail. The results show that gear eccentricity and rotational speed have influences on the meshing state of gear teeth, the vibration amplitudes, the frequency multiplication and random frequency components. When the system is in a lower rotational speed, the eccentricity has greater effects on the vibration response. The proposed model and numerical results provide a useful source of reference for engineers in designing and vibration controlling such systems.

Vibration analysis of coupled bending-torsional rotor-bearing system for hydraulic generating set with rub-impact under electromagnetic excitation

Based on Jeffcott rotor model, the coupled bending-torsional rotor-bearing system with rub-impact under electromagnetic excitation for hydraulic generating set is established and the corresponding equation is given. The influence of excitation current, mass eccentricity and electromagnetic torque in the system is investigated by taking use of numerical method. The simulation results show that eccentricity is the crucial factor causing the changes of system dynamic characteristics, compared to the effect of torsional degree of freedom. And the larger the eccentricity is, the more obviously it affects the system responses. While the complicated dynamic behavior of bending vibration response can be restrained, due to the introduction of torsion motion, which has the property to suppress complex dynamic response of system, particularly, the inhibited and improved effect is more evident, as the eccentricity turns to be smaller. In addition, the unstable jumping phenomena of torsional response can be motivated by electromagnetic torque, which has to be taken seriously during the process of model establishment and dynamic analysis of system. From the global view of electromechanical coupling characteristics, the coupled bending-torsional vibration model with rub-impact under electromagnetic excitation can supply a more comprehensive reflection about the dynamic characteristics of system and provide useful reference with system state recognition and fault diagnosis.

20901 Bergeron法によるはりの曲げ振動の瞬時応答解析手法の検討

This paper describes a new computational method for instantaneous bending vibration response based on the Bergeron method is the analysis method in electric and acoustic fields. The formulation of the Bergeron method for the bending vibration analysis is newly derived from the mobility analogy and the continuity of the state variable. Important parameters of the Bergeron method is the propagation property which has the attenuation factor and structural propagation delay. The structural propagation delay is dependent on the frequency though that is constant in electric field. Then we introduce the arbitrary correction to the attenuation factor for keeping the constant of the propagation delay. The result shows that instantaneous bending vibration analysis using Bergeron method is developed application to compared with the FEM result by less time consuming.

Analytical and experimental study on bending vibration of internal combustion engines shafting system based on wave equations

This paper proposes a new analytical approach to study the bending vibration of N step shafting system. Changes of the shaft step properties under rotary condition are governed by two-dimensional wave equations. The source of the bending vibration is first analysed. Then strain and stress equations of the spinning shaft are established. After Hamilton principle is applied, a two-dimensional wave equation is established. After that, the calculation formula of one dimensional bending vibration response is obtained where a sinusoidal excitation force is applied on an arbitrary concentrated mass. By using this formula, the total dynamic response can be obtained based on the principle of the linear superposition. The calculated results were compared with measured results. It was found they agree with each other in the vertical direction but not in the horizontal direction. At the end of paper, the reason of difference is analysed.

The bending vibration response and approximate calculation of elastic cylindrical shell

Useful structure characteristics of elastic cylindrical shells have led them to being widely applied in virtual projects, so it is important to conduct vibration research on the shells and find it’s a simpler corresponding compact calculation method. Utilising the input and transfer point mobility of a thin plate structure, a theoretical expression of the cylindrical shell's bending vibration responsewas deduced and numerical simulations were done to simplify the theoretical expression within an acceptable error margin, greatly reducing the amount of computations. Furthermore, whole vibration response distributions of the cylindrical shell were analyzed. It was found thathe vibration energy propagates in helical form under mono-frequency excitation, while under bandwidth frequency excitation, it attenuates around in term of fluctuation. The axial attenuation rate of the vibration energy is larger than the circumferential attenuation rate.