Yih-Hwang Lin

Finite element analysis of elastic beams subjected to moving dynamic loads

Abstract A method for the dynamic analysis of elastic beams subjected to dynamic loads induced by the arbitrary movement of a spring-mass-damper system is presented. The governing equations for the interaction between the beam and the moving dynamic system are derived, based on a finite element formulation. This set of equations is a system of second order differential equations with time dependent coefficients. The governing equations are solved with a Runge-Kutta integration scheme to obtain the dynamic response for both the support beam and the moving system. The method is capable of handling any time dependent dynamic system motion profile with complex boundary conditions in a computationally efficient fashion. Comparison of results with several simplified test conditions previously reported shows excellent agreement. The analysis is applied to a high-speed machining operation to demonstrate the unique capabilities and characteristics of the method.

Discretization considerations in moving load finite element beam models

Abstract This paper investigates continuum discretization for finite element models analyzing a moving load on an elastic beam. Moving load analysis is shown to require accurate evaluation of beam deformations over the entire length of an element, and not only the nodes. Model accuracy is shown to be related to element interpolation which in turn directly affects three aspects of the moving load finite element model; (1) calculation of equivalent nodal reactions for the moving load; (2) calculation of transmitted forces from a moving sprung mass, and; (3) system responses for a moving load initially positioned within the support beam span. The analysis indicates that the model accuracy can be maintained at an acceptable level provided that, in general, the number of elements used to discretize the support structure continuum is at least two to eight times greater than the number used in static analysis.

Nonlinear vibrations of Timoshenko pipes conveying fluid

This paper presents a finite element approach for nonlinear vibration analysis of Timoshenko pipes conveying fluid. An approach using the concept of fictitious loads to account for the kinematic corrections was applied to establish the finite element model, without the need to establish the nonlinear equations of motion. Computation of system responses was carried out by iteratively updating the nodal coordinates until convergence was reached. The formulation and implementation of the approach were verified first by comparing the analysis results with those available in the literature for the case of both slender and short beams undergoing static large deformations and the case of flow induced vibration of a slender cantilever pipe with supercritical flow speeds. Limit cycle and its associated vibration amplitude for the flow induced vibration problem were discussed. Further analysis was conducted for assessment of the effects of flow speed and fluid/pipe mass ratio on the limit cycle vibration amplitude. The influence of slenderness ratio on the limit cycle amplitude was also reported.

Automated condition classification of a reciprocating compressor using time–frequency analysis and an artificial neural network

The purpose of this study is to develop an automated system for condition classification of a reciprocating compressor. Various time–frequency analysis techniques will be examined for decomposition of the vibration signals. Because a time–frequency distribution is a 3D data map, data reduction is indispensable for subsequent analysis. The extraction of the system characteristics using three indices, namely the time index, frequency index, and amplitude index, will be presented and examined for their applicability. The probability neural network is applied for automated condition classification using a combination of the three indices. The study reveals that a proper choice of the index combination and the time–frequency band can provide excellent classification accuracy for the machinery conditions examined in this work.

Optimal modal vibration suppression of a fluid-conveying pipe with a divergent mode

This study deals with the divergence characteristics of pipes conveying fluid and explores the applicability of active modal vibration control for suppressing the associated excessive structural vibration. The Timoshenko beam theory is used to establish the system equation of motion. The analysis is based on the finite element method. Active modal control technique is developed in this work for pipes conveying fluid with a flow speed exceeding the critical one. Optimal independent modal space control (IMSC) is applied for the design. For pipes conveying super-critical flow speed, as considered in this work, the systems eigenvalues have both real and complex roots, which must be dealt with in a different way from what has been established in the literature. A weighting matrix with finite weights is applied for the control of complex modes, whereas a weighting matrix with an infinite weight is used for controlling the divergent mode, with roots being real. From this study, it is demonstrated that the control approach proposed in this work can ensure closed loop stability. The mode switching scheme of directing control to the mode which has higher modal response is found to be beneficial in reducing the overall structural vibration of the fluid-conveying pipe.

Automated valve condition classification of a reciprocating compressor with seeded faults: experimentation and validation of classification strategy

This paper deals with automatic valve condition classification of a reciprocating processor with seeded faults. The seeded faults are considered based on observation of valve faults in practice. They include the misplacement of valve and spring plates, incorrect tightness of the bolts for valve cover or valve seat, softening of the spring plate, and cracked or broken spring plate or valve plate. The seeded faults represent various stages of machine health condition and it is crucial to be able to correctly classify the conditions so that preventative maintenance can be performed before catastrophic breakdown of the compressor occurs. Considering the non-stationary characteristics of the system, time–frequency analysis techniques are applied to obtain the vibration spectrum as time develops. A data reduction algorithm is subsequently employed to extract the fault features from the formidable amount of time–frequency data and finally the probabilistic neural network is utilized to automate the classification process without the intervention of human experts. This study shows that the use of modification indices, as opposed to the original indices, greatly reduces the classification error, from about 80% down to about 20% misclassification for the 15 fault cases. Correct condition classification can be further enhanced if the use of similar fault cases is avoided. It is shown that 6.67% classification error is achievable when using the short-time Fourier transform and the mean variation method for the case of seven seeded faults with 10 training samples used. A stunning 100% correct classification can even be realized when the neural network is well trained with 30 training samples being used.

Optimal Vibration Suppression in Modal Space for Flexible Beams Subjected to Moving Loads

Optimal independent modal space control for vibration suppression of beam structures traversed by a moving concentrated force was examined. Two control methodologies, optimal linear quadratic tracking and an optimal linear quadratic regulator, were utilized, with the former approach taking into account the disturbance due to the moving load and the latter one simply ignoring that disturbance. One single actuator placed at the beam center was found to be sufficient to suppress excessive vibration of a beam traversed by the moving load with a reasonable amount of control input. This study shows that excessive vibration of the beam structure induced by the moving load can be more effectively suppressed using the tracking control approach than using the regulator design, even with ±50% variation of the moving load magnitude or speed from that designed for the tracking control system.

Finite Element Analysis of Fluid-Conveying Timoshenko Pipes

A general finite element formulation using cubic Hermitian interpolation for dynamic analysis of pipes conveying fluid is presented. Both the effects of shearing deformations and rotary inertia are considered. The development retains the use of the classical four degrees-of-freedom for a two-node element. The effect of moving fluid is treated as external distributed forces on the support pipe and the fluid finite element matrices are derived from the virtual work done due to the fluid inertia forces. Finite element matrices for both the support pipe and moving fluid are derived and given explicitly. A numerical example is given to demonstrate the validity of the model.

Active modal control of timoshenko pipes conveying fluid

Abstract This paper deals with vibration control of Timoshenko pipes conveying fluid. Excessive vibration in this flow induced vibration problem is suppressed via an active feedback control scheme. The strategy of the active vibration suppression technique will be presented and system dynamics formulated. Optimal independent modal space control technique is applied for best obtainable system performance. The computation consideration, implementation of control strategy, and the effectiveness of the control scheme are addressed. A finite element method is used for both the vibration and control analyses of the problem considered. Classical analysis by solving the partial differential equation is only applicable to systems with simple boundary conditions, such as simply supported pipes. When a more complex situation occurs, a closed form expression becomes very difficult, if not impossible, to obtain. The use of a finite element approach alleviates such deficiencies and is readily applicable to pipes with intermediate supports, nonuniform cross sections, and flexible supports. The problem of a large model size for the control system due to the use of the finite element approach is avoided by using the control technique presented. It is demonstrated in this work that a critical damping design can be achieved for the targeted mode controlled disregarding how large the model size is.

A Novel Signal Processing Approach for Valve Health Condition Classification of a Reciprocating Compressor with Seeded Faults Considering Time-Frequency Partitions

This study deals with a novel signal processing approach for automated valve condition classification of a reciprocating compressor with seeded faults. The classification system consists of a front end time-frequency analysis platform for the vibration signal measured, fault feature vectors for making the formidable amount of time-frequency data manageable, and a probabilistic neural network for automatic classification without the intervention of human experts. Rather than representing each time-frequency data set with one single feature vector comprising three indices, namely time, frequency, and amplitude, the time-frequency plane is further partitioned into an appropriate number of sub-regions to enhance the characteristics representation of the time-frequency data. This study shows that a flawless classification can be realized by using the proposed approach with appropriate selections of index modification method and number of time-frequency sub-regions without resorting to the removal of similar fault cases.