Abstract: Summary Large deformations and discontinuous problems can be calculated using the discontinuous deformation analysis (DDA) method by solving time steps, and this method is suitable for simulating the seismic dynamic response of engineering rock mass structures. However, the boundary setting must be carefully analyzed. In this paper, four boundary settings for the DDA method are investigated. First, the contributions to the DDA equations for nonreflecting boundaries (including the viscous boundary and the viscoelastic boundary) are deduced based on the Newmark method. Second, a free-field boundary is introduced in the DDA method with boundary grid generation and coupling calculation algorithms to accurately simulate external source wave motion, such as earthquakes. Third, seismic input boundary treatments are intensively examined, and the force input method is introduced based on nonreflecting boundaries. Finally, the static-dynamic unified boundary is implemented to ensure consistent boundary transformation. The boundary setting method in the DDA method is discussed, and the suggested treatments are used to analyze the seismic dynamic response of underground caverns. Copyright © 2015 John Wiley & Sons, Ltd.

Abstract: Accepted 18 November 2015 This study presents a new approach to control the nonlinear dynamics of an adaptive absorber using shape memory alloy (SMA) element. Shape memory alloys are classified as smart materials that can remember their original shape after deformation. Stress and temperature-induced phase transformations are two typical behaviors of shape memory alloys. Changing the stiffness associated with phase transformations causes these properties of SMA. A thermo-mechanical model (based on the transformation strain which is a measure of strain indicating the phase transformation) is used to constrain the general thermo-mechanical features of the SMA. Here, the one-dimensional SMA model is adopted to calculate both the pseudo-elastic response and the shape memory effects. The dynamic behavior of shape memory alloys is then investigated, and a Newmark method is adopted to analyze the nonlinear dynamic equations. Results demonstrate that the vibration of an initial system can be tuned using the SMA absorber in a wide range of frequencies. Therefore, SMAs as adaptive tuned vibration absorbers provide an excellent performance to control vibrations. Keyw ord s:

Abstract: This paper presents a finite element procedure for dynamic analysis of non-uniform Timoshenko beams made of axially Functionally Graded Material (FGM) under multiple moving point loads. The material properties are assumed to vary continuously in the longitudinal direction according to a predefined power law equation. A beam element, taking the effects of shear deformation and cross-sectional variation into account, is formulated by using exact polynomials derived from the governing differential equations of a uniform homogenous Timoshenko beam element. The dynamic responses of the beams are computed by using the implicit Newmark method. The numerical results show that the dynamic characteristics of the beams are greatly influenced by the number of moving point loads. The effects of the distance between the loads, material non-homogeneity, section profiles as well as aspect ratio on the dynamic responses of the beams are also investigated in detail and highlighted.

Abstract: This paper represents the radial vibrations of simply supported pseudoelastic shape memory alloy cylindrical shells under time-dependant internal pressure based on Donnell-type classical shell theory. The material behavior is simulated via the Boyd–Lagoudas model. The Hamilton’s principle, Differential Quadrature, and Newmark method are employed to obtain and solve the equations of motion. The phase transformation effects are studied on the time and frequency responses of the shell. Results show that the frequency response peak points have a shift to the left with respect to the natural frequencies of the linear system (pure austenitic phase) due to the phase transformation.

Abstract: Discontinuous deformation analysis (DDA) is a numerical method for analyzing the deformation of block system. It employs unified dynamic formulation for both static and dynamic analysis, in which the so-called kinetic damping is adopted for absorbing dynamic energy. The DDA dynamic equations are integrated directly by the constant acceleration algorithm of Newmark family integrators. In order to have an insight into the DDA time integration scheme, the performance of Newmark time integration scheme for dynamic equations with kinetic damping is systematically investigated, formulae of stability, bifurcation, spectral radius, critical kinetic damping and algorithmic damping are presented. Combining with numerical examples, recognition and suggestions of Newmark integration scheme application in the DDA static and dynamic analysis are proposed.

Abstract: The dams are huge structures storing a large amount of water and failures of them cause especially irreparable loss of lives during the earthquakes. They are named as a group of structures subjected to fluid-structure interaction. So, the response of the fluid and its hydrodynamic pressures on the dam should be reflected more accurately in the structural analyses to determine the real behavior as soon as possible. Different mathematical and analytical modelling approaches can be used to calculate the water hydrodynamic pressure effect on the dam body. In this paper, it is aimed to determine the dynamic response of concrete gravity dams using different water modelling approaches such as Westergaard, Lagrange and Euler. For this purpose, Sariyar concrete gravity dam located on the Sakarya River, which is 120km to the northeast of Ankara, is selected as a case study. Firstly, the main principals and basic formulation of all approaches are given. After, the finite element models of the dam are constituted considering dam-reservoir-foundation interaction using ANSYS software. To determine the structural response of the dam, the linear transient analyses are performed using 1992 Erzincan earthquake ground motion record. In the analyses, element matrices are computed using the Gauss numerical integration technique. The Newmark method is used in the solution of the equation of motions. Rayleigh damping is considered. At the end of the analyses, dynamic characteristics, maximum displacements, maximum-minimum principal stresses and maximum-minimum principal strains are attained and compared with each other for Westergaard, Lagrange and Euler approaches.

Abstract: Visco-elastic material models with fractional characteristics have been used for several decades. This paper provides a simple methodology for Finite-Element-based dynamic analysis of structural systems with viscosity characterized by fractional derivatives of the strains. In particular, a re-formulation of the well-known Newmark method taking into account fractional derivatives discretized via the Grunwald–Letnikov summation allows the analysis of structural systems using standard Finite Element technology.

Abstract: Based on von Karman non-linear strain-displacement relationships and classical thin plate theory, a list of non-linear dynamic equilibrium equations for a thin narrow composite strip with transverse matrix cracking under thermal and mechanic loads are established and solved by the finite difference method, Newmark method, Newton-Cotes method and iterative method synthetically. Numerical examples show effect of the mechanical parameters, thermal environment, damage evolution and geometric parameters for thermoviscoelastic dynamic behavior of the thin narrow composite strip.

Abstract: The stability of numerical time integrators, and of the physical systems to which they are applied, are normally studied independently. This conceals a very interesting phenomenon, here termed inconsistent stability, wherein a numerical time marching scheme predicts a stable response about an equilibrium configuration that is, in fact, unstable. In this paper, time integrator parameters leading to possible inconsistent stability are first found analytically for conservative systems (symmetric tangent stiffness matrices), then several structural arches with increasing complexity are used as numerical case studies. The intention of this work is to highlight the potential for this unexpected, and mostly unknown, behavior to researchers studying complex dynamical systems, especially through time marching of finite element models. To allow for direct interpretation of our results, the work is focused on the Newmark time integrator, which is commonly used in structural dynamics.

Abstract: A time-domain numerical modeling of brass instruments is proposed. On one hand, outgoing and incoming waves in the resonator are described by the Menguy-Gilbert model, which incorporates three key issues: nonlinear wave propagation, viscothermal losses, and a variable section. The non-linear propagation is simulated by a TVD scheme well-suited to non-smooth waves. The fractional derivatives induced by the viscothermal losses are replaced by a set of local-in-time memory variables. A splitting strategy is followed to couple optimally these dedicated methods. On the other hand, the exciter is described by a one-mass model for the lips. The Newmark method is used to integrate the nonlinear ordinary differential equation so-obtained. At each time step, a coupling is performed between the pressure in the tube and the displacement of the lips. Finally, an extensive set of validation tests is successfully completed. In particular, self-sustained oscillations of the lips are simulated by taking into account the nonlinear wave propagation in the tube. Simulations clearly indicate that the nonlinear wave propagation has a major influence on the timbre of the sound, as expected. Moreover, simulations also highlight an influence on playing frequencies, time envelopes and on the playability of the low frequencies in the case of a variable lips tension.

Abstract: The novel transient dynamic vibration model of pump-turbine’s shaft system considers nonlinear seal fluid forces, in addition to the coupled effects of unbalanced magnetic pull (UMP), guide bearing force, unbalanced mass force and hydraulic force. The calculations are based on the finite element method (FEM) and Lagrange equation. Node automation division method (NADM) is developed in-house for quick and accurate node division. The differential equations of motion and the dynamic response of the unit are resolved by implicit Newmark method. The nonlinear dynamic characteristics of crown seal force and UMP are researched. The transient and steady lateral vibrations of three bearings are also analyzed using the periodic response diagrams, steady axis orbits and waterfall diagrams. The calculated results demonstrate that the mounted eccentricity, crown seal channel clearance and air-gap length have significant effects on the dynamic vibration of the shaft system. When the mounted eccentricity is 0mm, clearance of crown seal is 3mm, air-gap length is 35mm, the stability of the system is the highest. Both quantitative and qualitative results are relevant for engineering use in pump-turbine’s shaft system design.

Abstract: The radial integral BEM (RIBEM) with a step-by-step integration method is presented for solving non-Fourier heat conduction problems in this paper. First, the system of second-order ordinary differential equations is obtained by using the RIBEM to discretize the space domain. Then, the Newmark method and the central difference method are adopted to solve the system of ordinary differential equations with respect to time. Finally, several numerical examples with laser heat sources are performed to demonstrate the performance of the present method. The results show that the present approach can obtain accurate and stable numerical results.

Abstract: The thermoelastoplastic behavior of a high strength low alloy (HSLA) steel plate subjected to low-velocity impact is investigated in this paper. A yield criterion related to the spherical tensor of stress is proposed to describe the mixed hardening of the orthotropic material. Based on the classical nonlinear thin plate theory, the incremental nonlinear motion equations are obtained, and are solved by the combination of finite difference method and Newmark method with iterations. To explain the contact process, a thermoelastoplastic contact criterion is developed, of which the validity has been proved. Numerical results show that the radius of the impactor, initial impact velocity, environment temperature, and the thickness of the HSLA steel plate all have great influences on the thermoelastoplastic behavior of the HSLA steel plate subjected to low-velocity impact.

Abstract: In this study, the dynamic response of the laminated composite beam with arbitrary lay-ups has been investigated within the framework of the third-order shear deformation theory using the finite element method. A new three-nodded finite element compliant with the theory is introduced next. To deal with the dynamic contact between the delaminated segments, unilateral contact constraints are employed in conjunction with Lagrange multiplier method. Furthermore, the Poisson’s effect is incorporated in the formulation of the beam constitutive equation. Also, the higher-order inertia effects and material couplings (flexure–tensile, flexure–twist and tensile–twist couplings) are considered in the formulation. Results are extracted based on two methods namely the Eigen-value techniques for frequencies and the Newmark method to calculate the transient response. Then, the obtained results have been verified with the other results available in the literature and very good agreements have been observed. Furthermore, ...

Abstract: This work is concerned with the development of two boundary element method (BEM) formulations for the solution of one-dimensional scalar wave propagation problems. The first formulation is called TD-BEM, TD meaning time-domain, as it employs a time-dependent fundamental solution. The second formulation is called D-BEM, D meaning domain, and employs the fundamental solution from the static problem. The Houbolt and the Newmark methods are employed for the time-marching in the D-BEM approach. Two examples, constituted of five analyses, are included.

Abstract: In this article, thermoviscoelastic dynamic behavior of a double-layered cylinder with a thermal barrier coating under radially symmetric mechanic and thermal loadings is investigated. The double-layered hollow cylinder is constructed of a viscoelastic layer and a homogenous layer, and the cylinder is subjected to thermal shocking. The material parameters of the cylinder are assumed to be temperature-dependent. The governing equation of the motion of the double-layered hollow cylinder under both dynamic mechanical and thermal loads is obtained based on the plane-stain theory, meanwhile, the transient heat transfer problems are solved by the finite difference method (FDM), Newmark method (NM), and iterative method. Numerical results show that mechanical load, boundary conditions, temperature field and whether considering the viscoelasticity of the inner layer each have a great influence on the dynamic behavior of the double-layered hollow cylinder.

Abstract: In this paper, transient response analysis of a circular sandwich plate with a functionally graded material (FGM) central disk and two piezoelectric layers is presented. Material properties of the FGM central disk for the circular sandwich plate are assumed to vary through the structural thickness according to a power law and the Poisson’s ratio is assumed as the same constant. Based on the first-order shear deformation theory and geometric nonlinear relationship, the nonlinear motion equations of the circular sandwich plate are formulated by using the Hamilton’s variational principle, then combining with the boundary and initial conditions, the whole problem is solved by adopting the finite difference method, Newmark method and iterative method. Numerical results are presented to illustrate that the volume fraction index, geometric parameters, mechanical and electrical loads have a great influence on transient response of the circular sandwich plate.

Abstract: This paper makes a survey of several popular time integration methods, including the backward Euler, central difference, Crank–Nicolson, Newmark, weighted residual finite element, and time-discontinuous Galerkin methods, and comparisons are made by applying some of the methods to the vibration analysis of a stator-housing structure as well as to the transient response analysis of an electromagnet. The comparison of vibration analysis shows that with an acceptably small step-size, the Newmark method gives result as accurate as the Euler method does, with half the cost. In the transient analysis of the electromagnet, however, it was observed that applying the Euler method to the magnetic equation performs much better compared with the Crank–Nicolson method even though the theoretical accuracy of the latter is higher.

Abstract: This paper aims to present an alternative analytical method for transient vibration analysis of doubly-curved laminated shells subjected to dynamic loads. In the method proposed, the governing differential equations of laminated shell are derived using the dynamic version of the principle of virtual displacements. The governing equations of first order shear deformation laminated shell are obtained by Navier solution procedure. Time-dependent equations are transformed to the Laplace domain and then Laplace parameter dependent equations are solved numerically. The results obtained in the Laplace domain are transformed to the time domain with the help of modified Durbin's numerical inverse Laplace transform method. Verification of the presented method is carried out by comparing the results with those obtained by Newmark method and ANSYS finite element software. Also effects of number of laminates, different material properties and shell geometries are discussed. The numerical results have proved that the presented procedure is a highly accurate and efficient solution method.

Abstract: The nonlinear dynamic response and damage evolution of functionally graded shallow spherical shell under low-velocity impact are investigated in this work. Basing on continuum damage theory, a damage constitutive relation is established for functionally graded material and the Kachanov damage evolution law is adopted to predict the damage propagation in the structure. A modified contact model suitable for non-homogenous material (functionally graded material) is applied to model the contact force in impacting process. The laminated modeling method is adopted to model the functionally graded shell with varying material constants along the thickness by dividing the shell to N plies with the constant material properties for each ply. With the established damage constitutive relations and nonlinear geometric relations of FGM shallow spherical shell with elastic modulus varying as a power-law function, the nonlinear motion equations of FGM shallow spherical under low-velocity impact have been obtained in the term of displacement functions. The problems are solved by using the orthogonal collocation point method, the Newmark method and the iterative method synthetically. Some numerical examples are carried out to validate present impacting model and the calculating methods, and parametrical analysis are presented to discuss the effects of the material properties, the geometrical size and impacting velocity on damage state and dynamic response of the structure when under low-velocity impact.

Abstract: The assessment of thermoelastic attenuation is crucial in designing surface acoustic wave (SAW) devices. As irregular structures are more and more involved in modern applications for which efficient numerical tools are required, a multi-physics finite-element model is proposed in this paper, where thermoelastic damping in piezoelectric materials can be accounted for in both coated and uncoated conditions. The coupled equations are solved iteratively in time domain, using the Newmark method. The mechanical, electrical, and thermal degrees of freedom are calculated simultaneously at each time step. An application of the model is presented through the investigation of thermoelastic loss in a lithium niobate SAW device.

Abstract: A dynamic model of offset press gear transmission system made up of gears, cylinders and bearings is proposed in this study. The model based on finite element method (FEM) includes some nonlinearity such as time-varying meshing stiffness, backlash, static transmission error and contact nonlinearity, which lead to complex nonlinear coupling. The Darren Bell principle and Lagrangian approach are applied to derive the motion equations of system, then the Newmark method is used to solve the equations for meshing force, acceleration, shoulder iron and rubber contact force. Eigenvalue solution is used to predict the critical speed, moreover, the influence of the radial and axial stiffness on the first-order critical speed is discussed. Considering the importance of acceleration and meshing force, the RMS value of acceleration and dynamic factor are also studied in this paper. The dynamic orbits of system are observed from the phase diagram, power spectrum, Lyapunov exponent and Poincare map. The figures clearly indicate that there are various forms of periodic and chaotic motions in different conditions. The simulation results show that with the increase of rotating speed, dynamic orbits transfer from periodic motion to chaotic motion in the cylinder discrete state.