Papers by Keyword: Harmonic Balance Method

Abstract: The correct computation of the Stress Intensity Factor (SIF) in ultrasonic Very-High-Cycle Fatigue (VHCF) loading conditions is a key issue when investigating the crack growth rate curve with pre-cracked specimens or when evaluating critical SIF values from fracture surfaces of failed specimens. Dynamic conditions related to the resonance of the vibrating specimen, contact nonlinearity between crack faces and stress singularity at the crack tip make the SIF computation difficult and cumbersome. Generally, numerical computation through Finite Element Models (FEMs) under non-linear dynamic conditions makes use of direct integration methods (implicit or explicit). However, in the high frequency regime of ultrasonic VHCF tests, the procedure may lead to an unacceptable computational time. In order to reduce the computational time, a hybrid procedure based on the Harmonic Balance Method (HBM) and on the Virtual Crack Closure Technique (VCCT) is originally presented and applied in this paper. The dynamic field parameters calculated with the HBM are used as input data for the computation of the SIF through the VCCT.

Abstract: Unsteady aerodynamics research is the foundation of aeroelastic analysis. How to effectively improve the aeroelastic computational efficiency,it is the key of current research on aeroelasticity now.Reduced order models are proposed as a powerful tool to solve this problem. Analyzed the three reduced-order models for Volterra ,Proper Orthogonal Decomposition and Harmonic Balance method ,their advantages and disadvantages were pointed out. The direction of the reduced order model in the future was Proposed and some suggest was given out for its application.

Abstract: The nonlinear governing equations of motion for the rotating composite thin-walled beam are derived using Hamilton’s energy principle and variational-asymptotical method (VAM) on the basis of von Karman’s assumption. The nonlinear vibration of the beam is studied using Galerkin method and harmonic balance method. The large amplitude free vibration of the beam can be expressed as a nonlinear eigenvalue problem and solved using an iterative solution procedure. Numerical results are obtained for Circumferentially Uniform Stiffness (CUS )laminated composite configuration thin-walled beam. The study exhibit the effect of the fiber orientation and rotating speed on nonlinear natural frequency vs. amplitude curves. The developed model can be capable of describing nonlinear free vibration behaviors of rotating composite thin-walled beam with large deformations.

Abstract: The paper presents a multi-dimensional harmonic balance analysis utilized to study the vibration responses of the cracked rotor subject to gravity, unbalance and an additional lateral harmonic force generated by an active magnetic bearing. The nonlinear terms resulting from the shaft crack are included via an alternating frequency/time domain (AFT) method. The example addressed in this paper is a simple rotor modeled by using the rigid finite element (RFE) approach. Combination frequencies are recognized as evident symptoms of the shaft crack.

Abstract: This paper aims at to study the damping ratio and nonlinear stiffness property of rubber isolator effect on vibration response under different excitation level and temperature. By the means of experiment, the curves of amplitude-frequency of rubber isolator were obtained. Based on the experimental results, the damping ratio was ascertained by the method of half power point. A single freedom mechanics model that describes the isolated system was built, and the equation of frequency response deduced and solved by harmonic balance method. Furthermore, the effects of nonlinear factor of stiffness effect on vibration response were analyzed. The precision of the approximation that solved by harmonic balance method was validated using Runge-Kutta method. It is indicated that the equation of frequency-response can be used to describe the property of frequency-response of rubber isolator.

Abstract: The paper proposes a new variable friction system, of which the friction force can increase linearly with the displacement of system. This new system can be used in TMD to avoid the disadvantage of Coulomb friction TMD. Using first order harmonic balance method, the equivalent damping ratio and frequency of SDOF variable friction system is deduced and analyzed. The frequency response characteristics of SDOF variable friction system is discussed. The control effectiveness of variable friction TMD under harmonic excitation is analyzed theoretically. The results demonstrate that the frequency response curves of variable friction TMD and classically damped TMD are similar and both can effectively reduce structural response under harmonic excitation.

Abstract: A harmonic balance approach has been developed to compute nonlinear viscous unsteady flows around oscillating blades. The computed results using two orders harmonic balance method are compared with those by conventional dual-time stepping method. Results obtained with the present method agree well with those from dual-time stepping method, which demonstrate the ability of the present analysis method to model accurately the unsteady flow. Furthermore，the present method is highly efficient. It is about 36 times fast than conventional dual-time stepping method in the present computation. Then the effects of oscillation amplitude and reduced frequency on unsteadiness of flows are studied. The analysis exploits the fact that, (1) the hysteresis effect of unsteady flow is hardly affected by oscillation amplitude, but the first harmonic unsteady pressure across the blade is proportional to oscillation amplitude; (2) the higher the reduced frequency, the wider the range of unsteady aerodynamic forces, the more intense the hysteresis effect.