Y. Y. Lee

Dynamic stability of a curved beam under sinusoidal loading

Abstract This paper is a study of snap-through properties of a non-linear dynamic buckling response to sinusoidal excitation of a clamped—clamped buckled beam. Using a simple formula, the highly non-linear motion of snap-through and its effects on the overall vibration response have been studied. The non-linear governing equation obtained here is solved using the Runge—Kutta (RK-4) numerical integration method. Critical parameters at the onset of the snap-through motion, which vary with different damping coefficients and linear circular frequencies of a flat beam, are studied and given in terms of the excitation level and response displacement. The relationships between static and dynamic responses at the start of the snap-through motion are also predicted. The analysis brings out various characteristic features of the phenomenon, i.e. (a) small oscillations about the buckled position, (b) chaotic motion of intermittent snap-through and (c) large oscillations of continuous snap-through motion crossing the two buckled positions. The non-linear dynamic instability behaviour of the beam, changing from the softening spring type to the hardening type, is due to the snap-through motion.

Structural-acoustic coupling effect on the nonlinear natural frequency of a rectangular box with one flexible plate

Abstract The nonlinear natural frequency of a rectangular box, which consists of one flexible plate and five rigid plates, is studied in this paper. The flexible plate is assumed to vibrate like a simple piston. The behavior of the structural-acoustic coupling between the flexible plate and the air cavity is analyzed by using the proposed finite element modal method. The system finite element equation is reduced and expressed in terms of the modal coordinates with small degrees of freedom by using the proposed reduction method. The system nonlinear stiffness matrix representing the large amplitude vibration can be transformed to be a constant modal matrix. The natural frequencies are determined by using the harmonic balance method to solve the eigenvalue equations of the structural-acoustic system. The effect of the cavity depth on the natural frequencies and convergence studies are discussed in detail.

Application of a noisy data classification technique to determine the occurrence of flashover in compartment fires

This paper presents a hybrid Artificial Neural Network (ANN) model that is developed for noisy data classification. The model, named GRNNFA, is a fusion of the Fuzzy Adaptive Resonance Theory (FA) model and the General Regression Neural Network (GRNN) model. The GRNNFA model not only retains the important features of the parent models, which include stable learning, fast training, and an incremental growth network structure, but also facilitates the removal of noise that is embedded in training samples. The robustness of the GRNNFA model is demonstrated by the Noisy Two Intertwined Spirals problem and other benchmarking problems. The model is then applied to Fishers Iris Data, which is a real-world classification problem. The results show that the percentage of correct predictions is statistically higher than in variant models of the adaptive resonance theory. The GRNNFA is further employed in a new application area of soft computing-fire dynamics, which is highly non-linear in nature. Flashover is the most dangerous scenrio in the development of a compartment fire, during which, any unburned combustible material, including the unburned soot particles inside the compartment, is ignited spontaneously and all combustible material is then simultaneously involved in the burning process. The GRNNFA model is applied to predict the occurrence of the flashover in compartment fires based on the fire size and the geometry of the fire compartment. The performance of the GRNNFA is compared with other published results, and it is shown to be statistically superior to other ANN models.

Chaotic responses of curved plate under sinusoidal loading

In the present investigation, the nonlinear dynamic buckling of a curved plate subjected to sinusoidal loading is examined. By the theoretical analyses, a highly nonlinear snap-through motion of a clampedfreeclampedfree plate and its effect on the overall vibration response are investigated. The problem is reduced to that of a single degree of freedom system with the Rayleigh-Ritz procedure. The resulting nonlinear governing equation is solved using Runge-Kutta (RK.-4) numerical integration method. The snap-through boundaries, which vary with different damping coefficient and linear circular frequency of the flat plate are studied and given in terms of force and displacement. The relationships between static and dynamic responses at the start of a snap-through motion are also predicted. The analysis brings out various characteristic features of the phenomenon, i.e. l) small oscillation about the buckled position-softening spring type motion, 2) chaotic motion of intermittent snap-through, and 3) large oscillation of continuous snap-through motion crossing the two buckled positions-hardening spring type. The responses of buckled plate were found to be greatly affected by the snap-through motion. Therefore, better understanding of the snap-through motion is needed to predict the full dynamic response of a curved plate.

FLOW ANGLE, TEMPERATURE AND AERODYNAMIC DAMPING ON SUPERSONIC PANEL FLUTTER STABILITY BOUNDARY

The effects of flow yaw angle, temperature, and aerodynamic damping on supersonic flutter of plates are investigated. Quasisteady, first-order piston theory is employed for formulation of aerodynamic forces. The von Karman large-deflection plate theory is adapted for the aerothermal deflection. Two types of thermal effects are considered: 1) plate expansion by uniform temperature and 2) thermal moment induced by temperature gradient across the plate thickness. A finite element modal formulation and a two-step procedure are presented for the predictions of stability boundaries and nonlinear aerothermal deflection and shown to be efficient in solution. Results have shown that flow angle has lesser effect on stability boundaries as compared with temperature for isotropic square plates. However, both flow angle and temperature have a large influence on stability boundaries for rectangular isotropic and laminated composite plates. The presence of the ripple characteristics of stability boundaries for composite plates caused by the frequency coalescence of higher modes and the smaller effect of aerodynamic damping is investigated. The stabilization effects on panel motions induced by variations of flow angle, temperature, and aerodynamic damping are discussed.

Supersonic Nonlinear Panel Flutter Suppression Using Shape Memory Alloys

An efficient finite element procedure is developed to predict large-amplitude nonlinear flutter response of shape memory alloy hybrid composite plates at an arbitrary supersonic yawed angle and an elevated temperature. The temperature-dependent material properties of shape memory alloy and traditional composites, as well as the von Karman large deflections, are considered in the formulation. Finite element system equations of motion are transferred to aeroelastic modal coordinates to reduce the large number of structural-node degrees of freedom. Time-domain numerical integration is employed to analyze flutter behaviors of the shape memory alloy hybrid composite panel under thermal loads. The flutter stability regions under the combined aerodynamic and thermal loads are studied. All of the possible behaviors, including the two types of static behavior and four types of dynamic motion of flutter, can be predicted for shape memory alloy hybrid composite plates. The static behaviors are 1) flat and stable and 2) aerothermally buckled but dynamically stable. The four types of dynamic motion are nearly simple harmonic limit-cycle oscillation, periodic limit-cycle oscillation, quasi-periodic oscillation, and chaotic oscillation. The flutter response of shape memory alloy hybrid composite plates are compared with those of traditional composite plates without a shape memory alloy. Results show that the desired flat and stable region can be greatly enlarged by using a shape memory alloy.

Thermal Buckling Suppression of Supersonic Vehicle Surface Panels Using Shape Memory Alloy

An efficient finite element method for the prediction of critical temperature, postbuckling deflection, and vibration characteristics is presented for traditional composite plates embedded with prestrained shape memory alloy (SMA) wires. The temperature-dependent material properties of SMA and composites and the large deflections are considered in the formulation. An iterative eigensolution is presented to determine the critical temperature, the Newton-Raphson method is employed to obtain postbuckling large deflection, and the eigensolver is used to predict free vibration frequencies about the thermally buckled equilibrium positions. Results show that the critical buckling temperature can be raised high enough and that the postbuckling deflection can be completely suppressed for surface panels of supersonic vehicle applications by the proper selection of SMA volume fraction, prestrain, and alloy composition. Weight savings based on critical temperature in the use of SMA as compared with the traditional composite and titanium plates are demonstrated.

Structural Vibration Suppression Using the Piezoelectric Sensors and Actuators

An experimental study for the active vibration control of structures subject to external excitations using piezoelectric sensors and actuators is presented. A simply supported plate and a curved panel are used as the controlled structures in two experiments, respectively. The Independent Modal Space Control (IMSC) approach is employed for the controller design. In order to increase the adaptability, the time-domain modal identification technique is incorporated into the controller to real-time update the system parameters. The adaptive effectiveness of the time-domain modal identification technique is tested by fixing an additional mass on the simply supported plate to change its structural properties. The vibration suppression performances of the controller are 5.7 dB and 10.8 dB for the simply-supported plate with/without the mass subject to a chirp sine excitation, respectively. For the experiment of the curved panel subject to a sinusoidal excitation, the vibration attenuation of the control scheme is 5.0 dB even the control circuit is subject to some noise generated by electrical and magnetic interferences.

Nonlinear random response of internally hinged beams

Nonlinear responses of beams with an internal hinge under stationary, ergodic, Gaussian and zero mean uniform random pressure are studied. Two types of support condition: clamped-clamped and clamped-simply supported are considered. The equivalent linearization method is employed on the basis of finite element modal formulation to assess the influence of hinge location on root mean square (RMS) maximum deflection and RMS maximum micro-strain. The internal hinge is modeled with two transition elements that proved to be effective and convenient. Internal hinge location is optimized based upon lowest RMS maximum deflection and/or micro-strain. Numerical simulation results are obtained and compared with results from equivalent linearization to show the good agreement between the two methods.

Numerical simulation model of vibration responses of rectangular plates embedded with piezoelectric actuators

A numerical simulation model for random large amplitude vibration control of composite plate using piezoelectric material is presented. The H∞ control design is employed to suppress the large amplitude vibrations of composites plates under random loading. The numerical simulation model is developed and based on the finite element method. The finite element governing equation includes fully coupled structural and electrical nodal degrees of freedom, and consider the von Karman large amplitude vibration. The modal reduction method using the structural modes is adopted to reduce the finite element equations into a set of modal equations with fewer degrees of freedom. The modal equations are then employed for controller design and time domain simulation. In the simulations without control, the value of the linear mode to the nonlinear deflection is quantified; and the minimum number of linear modes needed for accurate model is obtained. In the simulations with control, it is shown that the truncated modes, which are neglected in the control design, deteriorate the controller performance. Generally, the vibration reduction level is not monotonically increasing with the size of the piezoelectric actuator. The optimal piezoelectric actuator size depends on the excitation level. For higher excitation level, optimal actuator size is larger. The H∞ controller based on the linear finite element formulation gives better vibration reduction for small amplitude vibration, but it still gives reasonable performance for large amplitude vibration provided that the piezoelectric actuator is big and powerful enough.