Differential quadrature element method for static analysis of Reissner–Mindlin polar plates

In this paper, a new numerical technique, the differential quadrature element method (DQEM) , has been developed for static analysis of the two-dimensional polar Reissner–Mindlin plate in the polar coordinate system by integrating the domain decomposition method (DDM) with the differential quadrature method (DQM) . The detailed formulations for the sectorial DQEM plate bending element and the compatibility conditions between each element are presented. The convergence properties and the accuracy of the DQEM for bending of thick polar plates are investigated through a number of numerical computations. Consequently, the DQEM has been successfully applied to analyze several annular sector plates with discontinuous loading and boundary conditions and cutouts to illustrate the simplicity and flexibility of this method for solving Reissner–Mindlin plates in polar coordinate system which are not solvable directly using the differential quadrature method. The numerical results are verified by the existing exact solutions or the FEM solutions obtained using the software package ANSYS (Version 5.3) .     

Analysis of nonlinear dynamic response and dynamic buckling for laminated shallow spherical thick shells with damage

Based on the nonlinear theory of shallow spherical thick shells and the damage mechanics, a set of nonlinear equations of motion for the laminated shallow spherical thick shells with damage subjected to a normal concentrated load on the top are established. According to Hertz law, the contact force acted upon the shells is determined due to the impact of a mass, and it is related to the mass and initial velocity of the striking object, the geometrical and physical character of the shell. By using the finite difference method and the time increment procedure, the nonlinear equations are resolved. In the numerical examples, the effects of the damage, the initial velocity, and mass of the striking object, the shells’ geometrical parameters on the dynamic responses and dynamic buckling of the laminated shallow spherical thick shells are discussed. Research of Y. Fu, Z. Gao and F. Zhu was supported by National Natural Science Foundation of China (No. 10572049).     

Estimation of stochastic nonlinear dynamic response of rock-fill dams with uncertain material parameters for non-stationary random seismic excitation

This research investigates the effect of uncertain material parameters on the stochastic, dynamic response of a rock-fill dam-foundation system subjected to non-stationary random excitation. The uncertain material parameter of particular interest is the shear modulus, developed from a lognormal distribution model. The stochastic seismic response model of the dam-foundation system, with uncertain material parameters and subjected to random loads is the result of a Monte Carlo simulation method. The nonlinear behavior model arises from an equivalent linear method, which considers the nonlinear variation of soil shear modulus and soil damping as a function of shear strain. Specification of the non-stationary stochastic process arises from a simulation method, which generates artificial earthquake accelerograms obtained from the product of a deterministic function of time and a stationary process. The artificial earthquake ground acceleration records reflect the characteristics of soft, medium and firm soil types. Comparison of the numerical results from these approaches provides stochasticity in earthquake seismic excitation and randomness in material parameter (shear modulus) cases. Further, the results indicate that both these cases generally influence the nonlinear dynamic response of rock-fill dams to a non-stationary seismic excitation.     

A multibody-based dynamic simulation method for electrostatic actuators

A numerical simulation method is developed to analyze the dynamic responses of electrostatic actuators, which are electromechanically-coupled systems. The developed method can be used to determine the dynamic responses of cantilever-type switches, which are an example of typical MEMS (Micro-Electro-Mechanical System) devices driven by an electrostatic force. We propose the approach that adopts a point charge to deal with electric field effects between electrodes. This approach may be considered as a lumped parameter model for the electrostatic interactions. An advantage of this model may be the easy incorporation of the electrostatic effects between electrodes into a multibody dynamics analysis algorithm. The resulting equations contain the variables for position, velocity, and electric charge to describe the motion of the masses and the charges on the electrodes in a system. By solving these equations simultaneously, the dynamic response of an electrostatically-driven system can be correctly simulated. In order to realize this approach, we implement the procedures into RecurDyn, the multibody dynamics software developed by the authors. The developed numerical simulation tool was evaluated by applying it to cantilever-type electrostatic switches in many different driving conditions. The results suggest that the developed tool may be useful for predicting behaviors of electrostatic actuators in testing as well as in design.     

Device for direct measurement of dynamic viscoelastic properties of solid-state materials at frequencies higher than 1 kHz

Viscoelastic (VE) materials are widely used in daily life. For the effective utilization of VE materials, it is necessary to know their viscoelasticity with accuracy over a wide range of frequencies, especially for high frequencies. Currently, the viscoelasticity of solid-state materials is directly measured only in the low-frequency range; for high frequencies, it is estimated based on the time-temperature superposition (TTS) principle. However, it is generally recognized that the TTS principle is suitable only for estimating the viscoelasticity of rheologically simple materials for temperatures within a limited range that is higher than the glass-transition temperature. In this paper, we propose a device that can directly measure the shear modulus and tan δ values of solid-state VE materials at high frequencies. We also propose a method for compensating for the shear deformation mode resonance of VE materials based on the mass of the moving part, to gain a more accurate understanding of viscoelasticity in the high-frequency range, and discuss the causes of errors in the compensation method. Finally, we report the VE properties of natural rubber (NR 65 IRHD) measured using the developed device and compensation method, and compare the measured results with those obtained using commercial VE measurement equipment.     

A method for analyzing on-line video images of crystallization at high-solid concentrations

Recent research has demonstrated that on-line video imaging is a very promising technique for monitoring crystallization processes. The bottleneck in applying the technique for real-time closed-loop control is considered as image analysis that needs to be robust, fast and able to handle varied image qualities due to temporal variations of operating conditions such as mixing and solid concentrations. Image analysis at high-solid concentrations turns out to be extremely challenging because crystals tend to overlap or attach to each other and the boundaries between the crystals are usually ambiguous. This paper presents an image segmentation algorithm that can effectively deal with images taken at high-solid concentrations. The method segments crystals attached to each other along the mostly related concave points on the contours of crystal blocks. The detailed procedure is introduced with application to crystallization of L-glutamic acid in a hot-stage reactor.     

A double-superposition global–local theory for vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates: a complex modulus approach

A higher-order global–local theory is proposed based on the double-superposition concept for free vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates subjected to thermomechanical loads. In contrast to all theories proposed so far for analysis of the viscoelastic plates, the continuity conditions of the transverse shear and normal stresses at the layer interfaces and the nonzero traction conditions at the top and bottom surfaces of the sandwich plates are satisfied. Another novelty is that these conditions may be satisfied for viscoelastic plates with temperature-dependent material properties and nonlinear behaviors subjected to thermomechanical loads. Furthermore, transverse flexibility is also taken into account. Some dynamic buckling/wrinkling analyses of the viscoelastic plates are performed in the present paper, for the first time. Comparisons made between results of the paper and results reported by well-known references confirm the accuracy and the efficiency of the proposed theory and the relevant solution algorithm.     

High order behavior of sandwich plates with free edges––edge effects

The edge effects of a sandwich plate with a “soft” core and free edges, i.e. the plate is supported only at the lower face-sheet, and the upper face-sheet and the core are free of stresses at their edges, using the high order approach (HSAPT), are presented. The two-dimensional analysis consists of a mathematical formulation that uses the classical thin plate theory for the face-sheets and a three-dimensional elasticity theory for the core. The governing equations and the required boundary conditions are derived explicitly through variational principals, yielding a system of eight partial differential equations. The non-homogeneous differential equations system is numerically solved using a modification of the extended Kantorovich method (MEKM). The model presented enables a two-dimensional solution of the stress and displacement fields when subjected to a general scheme of loads. It is applicable to any type of boundary conditions that can be applied separately on each face-sheet and on the core. A numerical study is presented, and it examines the behavior and the two-dimensional stress field of a sandwich plate with free edges, at the upper face-sheet and core, subjected to thermal and uniformly distributed loads, for various boundary conditions at the lower face-sheet. For completeness, the MEKM solution of the two-dimensional high order model is verified through comparison with a three-dimensional Finite Element model revealing good correlation. Furthermore, the problems involved in the construction of an appropriate three-dimensional FE model of a full scale sandwich plate that require large computer resources are discussed.The numerical study yields that the peeling (normal) stresses, which reach their maximum values at the edges of the sandwich plate, using a one-dimensional analysis, varies also in the transverse direction from a maximum value in the middle of the edge, descending towards the corners. Moreover, the nature of variation along the boundaries strongly depends on the type of loading and the transverse boundary conditions. The substantial variation of the stress field in the transverse direction clearly shows the necessity of a two-dimensional analysis and the inefficiencies of the one-dimensional model.     

Reliable impulsive lag synchronization for a class of nonlinear discrete chaotic systems

The problem of reliable impulsive lag synchronization for a class of nonlinear discrete chaotic systems is investigated in this paper. Firstly a reliable impulsive controller is designed by the impulsive control theory. Then, some sufficient conditions for reliable impulsive lag synchronization between the drive system and the response system are obtained. Numerical simulations are given to show the effectiveness of the proposed method.     

Development of testing systems for dynamic assessment of sheet metal specimens

The work presented herein regards the analysis of an experimental technique for the execution of dynamic tensile tests on structural material sheet specimens. Dynamic tensile testing of sheet is becoming more important due to the need for more optimized vehicle crashworthiness analysis in the automotive industry. Positive strain-rate sensitivity, i.e. the strength increases with strain-rate, offers a potential for improved energy absorption during a crash event. Tests have been carried out in the Reliability and Safety Laboratory of the 2^nd Engineering Faculty of the Politecnico di Torino. Different types of testing techniques have been used to generate data under dynamic conditions. However, no guidelines are available for the testing method, specimen dimensions, measurement devices, and other important issues which are critical for the quality of the results. Accurate signal processing and curve smoothing are often necessary to make the testing data usable.     

A new constitutive equation for solid propellant with the effects of aging and viscoelastic Poisson’s ratio

A new constitutive equation for solid propellant with the effects of aging and viscoelastic Poisson’s ratio is proposed. Effects of thermo-oxidative aging and viscoelastic Poisson’s ratio are considered in this comprehensive constitutive equation with two sets of reduced time system coping with the time and temperature dependence. In order to simulate the single and combined effects of aging and viscoelastic Poisson’s ratio, constitutive equation is rewritten into an incremental form and implemented in the user subroutine UMAT at the platform of finite element code ABAQUS. Detailed procedure for acquiring the parameters in constitutive equation is introduced and conducted for the subsequent applied analysis. Two typical loading cases during the service life of solid rocket motor and four sets of combined constitutive models are simulated. Von Mises strain and stress distribution and their changes versus time are utilized as the main analysis index. The results show that the effects of aging and viscoelastic Poisson’s ratio or their combinations will improve or decrease the level and change the distribution of Von Mises strain and stress in varying degrees.     

The method of the reciprocal theorem of forced vibration for the elastic thin rectangular plates (II)—Rectangular plates with two adjacent clamped edges

In this paper, applying the method of reciprocal theorem, we give the distributions of the amplitude of bending moments along clamped edges and the amplitude of deflections along free edges of rectangular plates with two adjacent clamped edges under harmonic distributed and concentrated loads.     

Determination of the global responses characteristics of a piecewise smooth dynamical system with contact

In this paper the global response characteristics of a piecewise smooth dynamical system with contact, which is specifically used to describe the rotor/stator rubbing systems, is studied analytically. A method to derive the global response characteristics of the model is proposed by studying each piece of the equations corresponding to different phases of the rotor motion, i.e., the phase without rubbing, the phase with rubbing and the phase of self-excited backward whirl. After solving the typical responses in each phase and deriving the corresponding existence boundaries in the parameter space, an overall picture of the global response characteristics of the model is obtained. As is shown, five types of the coexistences of the different rotor responses and deep insights into the interactive effect of parameters on the dynamic behavior of the model are gained.     

A predictor–corrector time integration algorithm for dynamic analysis of nonlinear systems

Nonlinear Dynamics - This paper presents a step-by-step time integration algorithm for efficiently solving second-order nonlinear dynamic problems. The method employs the rewriting of motion as two...     

A symbolic algorithm for the automatic computation of multitone-input harmonic balance equations for nonlinear systems

A symbolic algorithm is developed for the automatic generation of harmonic balance equations for multitone input for a class of nonlinear differential systems with polynomial nonlinearities. Generalized expressions are derived for the construction of balance equations for a defined multitone signal form. Procedures are described for determining combinations for a given output frequency from the desired set obtained from box truncated spectra and their permutations to automate symbolic algorithm. An application of method is demonstrated using the well-known Duffing–Van der Pol equation. Then the obtained analytical results are compared with numerical simulations to show the accuracy of the approach. The computation times for both the numerical solutions of equations versus the number of frequency components and the symbolic generation of the equations versus the power of nonlinearity are also investigated.     

Mathematic modeling and characteristic analysis for dynamic system with asymmetrical hysteresis in vibratory compaction

We investigate dynamic characteristics of vibratory compaction system with asymmetrical hysteresis. An asymmetrical model derived from Bouc-Wen differential equation is employed to describe hysteretic behavior of vibration engineering. A practical polynomial expression for hysteretic restoring force is deduced to be substituted into standard equation of the system, assuming that the non-linearity of the restoring force is weak. An asymptotic method, which combines Krylov-Bogolyubov-Mitropolsky (KBM) method with harmonic balance (HB) method, is applied to analyze steady-state responses of the asymmetrical hysteretic system subjected to harmonic excitation. Dynamic responses, such as the restoring force time histories and frequency responses of the system for the first order approximate, are obtained. Furthermore, numerical solution obtained using Runge-Kutta method as well as results of experiments (asphalt compaction on the Beijing-Fuzhou highway) are compared with the asymptotic solution. These results investigated that asymmetrical hysteretic model and the methods applied in this paper are quite appropriate for engineering applications.     

A nonlinear numerical simulation of a lab centrifuge with internal damping

This paper is about numerical simulations of dissipation processes in rotor shaft joints of rotor systems. Based on measurement results a nonlinear simulation model of a lab centrifuge is stated. The effects of internal damping in combination with nonlinear stiffness and friction in the rotor shaft joint of the lab centrifuge are worked out. It is shown that the nonlinearities cause the amplitudes to rest limited once increased amplitudes due to internal damping appear. One focus is the derivation of suitable force laws describing the mechanisms of the components within the connection.     

Adaptive fuzzy controller design of nonlinear systems with unknown gain sign

For a class of uncertain nonlinear non-affine systems, an adaptive fuzzy controller is proposed in this paper. Compared with the existing results, the proposed controller does not require a priori knowledge about the sign of the control gain coefficient. It can be shown that all the signals in the closed-loop system are bounded and the tracking error converges to a bounded compact sets by choosing design parameters appropriately. A simulation example is given to guarantee the effectiveness of the proposed controller.     

A numerical model for static and free vibration analysis of elastic composite beams with end shear restraint

The end shear restraint, which is an un-classical type of end support, has a significant effect on the behavior of elastic composite beams. The principal aim of this paper is to present a numerical model for studying the effect of end shear restraint on static and free vibration behavior of elastic composite beams with various end conditions. The elastic composite beam, considered in this study, is composed of an upper concrete slab and a lower steel beam, connected at the interface by shear transmitting studs. This type of beam is widely used in constructions especially for highway bridges. The three types of end conditions considered in this study are simple, fixed and free supports. The numerical model is based on the combination of transfer matrix and analog beam methods. The field transfer matrices for the element of the elastic composite beam are derived. The present model is applied to the beam systems with and without end shear restraint and the static response and natural frequencies are calculated. the effect of shear stiffness between the upper slab and lower beam is also demonstrated.     

Finite element analysis of functionally graded plates for coupling effect of extension and bending

In this paper, the coupling effect of extension and bending in functionally graded plate subjected to transverse loading for Kirchhoff-Love plate theory equations is studied. The material properties of the FG plates are assumed to vary continuously throughout the thickness direction of the layer according to sigmoid distribution of the volume fractions of constituents. The two plate functionals are used which are developed by Gateaux differential and potential operator concept. A layer wise, isoparametric, mixed finite element approach was used and results of two different quadrilateral elements, one considering the membrane forces and the other one not, were compared by an analytical study. Finally, for different composition profiles the effect of variations of the Young’s moduli and of variations volume fraction index to dimensionless displacement, strain and stress values are studied.