Newmark Integration Method Research Articles

Dynamic instability and nonlinear response analysis of nanocomposite sandwich arches with viscoelastic cores

This paper presents a comprehensive study of the nonlinear dynamic behavior and snap-through phenomena in sandwich arch structures with viscoelastic cores and carbon nanotube-reinforced nanocomposite face sheets. Subjected to uniform time-dependent pressure shocks, these arches exhibit complex snap-through behavior critical for practical engineering applications. Utilizing third-order shear deformation theory, the study accurately captures nonlinear behaviors. The viscoelastic core, modeled with the Kelvin-Voigt law, enhances damping and reduces vibration amplitudes. Numerical solutions are obtained using a Chebyshev-based Ritz method, Newmark integration, and Newton-Raphson method. The Budiansky-Ruth criterion evaluates dynamic buckling loads. Key findings include significant instability near buckling loads, increased buckling loads and vibration damping due to viscoelastic effects, reduced buckling loads with foam cores, improved performance with CNTs, and more pronounced CNT effects with greater deflections. Additional conclusions highlight the sensitivity of dynamic snap-through to geometric parameters and the superior accuracy of the proposed approach compared to traditional models. This research advances the understanding and design strategies for nonlinear sandwich arch structures, enhancing predictive capabilities in complex structural systems.

Active vibration control of piezoelectric multilayers FG‐CNTRC and FG‐GPLRC plates

AbstractThis study investigates the active vibration control of multilayer Functionally Graded Carbon NanoTube Reinforced polymer Composite (FG‐CNTRC) plates and multilayer functionally graded graphene platelets reinforced polymer composite (FG‐GPLRC) plates covered with a piezoelectric layer (PZTG1195N) serve as both actuators and sensors. The plate's heart is supposed to be reinforced nonlinearly using both types of reinforcement. Active vibration control of plates under uniform load was achieved by utilizing a velocity feedback control algorithm with a specific gain value. The finite element method is employed to analyze both the static and dynamic behavior of a square plate discretized into 9‐node quadratic finite elements with 5 ° of freedom per node. The material properties are assumed to change across the thickness direction following a power law distribution, exhibiting various patterns: Uniform Distribution (UD), as well as Functionally Graded types X, O, and A (FG‐X, FG‐O, and FG‐A). The geometrical nonlinear equations are solved by the Newmark integration method. This work begins by validating the natural frequencies of a Functionally Graded (FG) composite plate reinforced with four different distributions of Nano‐filler and then aims to show the effect of the nonlinear distribution of nanofillers on the plate's stiffness. The Results obtained after the execution of a developed code highlight the significance of employing a nonlinear distribution of nanofillers to attenuate vibrations.Highlights FG composite and sandwich plates reinforced with GPLs and CNTs. Effect of nonlinear nanofillers distribution of reinforcement on free and forced vibration. The ability of the nonlinear distribution of nanofillers to attenuate forced vibrations.

Coupling vibration analysis of heat exchanger tube bundles under different stiffness conditions

A two-dimensional tube bundles fluid–structure coupling model was developed using the CFD approach, with a rigid body motion equation and the Newmark integral method. The numerical simulations were performed to determine the vibration coupling properties between various tube bundles of stiffness. Take the corner square tube bundles with a pitch ratio of 1.28 as the research object. The influence of adjacent tubes with different stiffness on the vibration of the central target tube was analyzed. The research results show that the vibration characteristic of tube bundles is affected by the flow field dominant frequency and the inherent frequency of tube bundles. The vibration of adjacent tube bundles significantly impacts the amplitude and frequency of the central target tube. The equal stiffness and large stiffness tubes upstream or downstream inhibit the vibration displacement of the target tube to some extent. The low-stiffness tubes upstream or downstream significantly enhanced the amplitude of the target tube. The findings can be used to provide a basis for reasonable design and vibration suppression of shell-and-tube heat exchangers.

Rocking sensitivity of a dual‐block stack ‐ Numerical simulation and experimental evidence

AbstractHistoric monuments, drywall structures, and graphite blocks in AGR nuclear power plants are block‐like structures that have to withstand rocking when subject to seismic excitation of their base, which can lead to overturning of some of their components and results in the collapse of the whole structure. We revisit the known nonlinear equations of motion for a dual‐block stack and present the conditions for transition between the eight possible rocking configurations (due to initiation of rocking, opening of new contacts, and collisions between blocks). An algorithm for the numerical simulation of rocking of the dual‐block stack is developed using the Newmark integration method, the Newton‐Raphson iteration method, and a novel contact detection and resolution procedure. The algorithm is used to evaluate rocking stability of five dual‐block stacks, one of which is compared to the results available in the literature. In parallel, a novel experimental program is designed and implemented, to validate the numerically obtained results using a shaking table. While most of the excitation conditions leading to stable rocking and limit values leading to overturning have been successfully validated, some discrepancies between the numerically and experimentally obtained results still exist and point to the need for improvement of the algorithm used, possibly through a more realistic energy‐loss mechanism. Most importantly, we have confirmed the known theoretical prediction that splitting a single block into two half‐size blocks benefits its rocking stability.

Dynamic characteristics analysis of a dual-rotor system with bolted-disk joint

This article presents a nonlinear vibration characteristics study of a bolted joint dual-rotor system. The motion equations are derived through the lumped mass modeling method and a two-node bolted joint element. Nonlinear time-varying bending stiffness at the joint interface is considered in the numerical integration. Qualitative analysis of the effect of preload on system responses is conducted through changing the value of the transition point of bending stiffness of the bolted joint. Moreover, the transfer path of vibration in the dual-rotor system through inner-shaft bearing was discussed in the present work. The nonlinear differential equations are solved using the Newmark integration method to predict the dynamic characteristics of the dual-rotor system. The results show that the maximum vibration displacement of LP rotor is positively correlated with that of HP rotor as preload changes. Moreover, the maximum amplitude of the time-domain responses of the HP rotor will decrease and the minimum amplitude will increase with the increase of preload. The difference between the maximum and minimum values of the time-domain response will decrease with the increase of preload. This can be explained by the “stiffness hardening” phenomenon of the bolted joint. The research results can help understanding the dynamic properties of the bolted joint dual-rotor system and the vibration transfer path of the rotor system through inner-shaft bearing.

Dynamic stability evaluation of subsea wellhead based on fully coupled model

The subsea wellhead is a key equipment for offshore oil and gas development. Traditional research focuses on static stability of subsea wellhead system in which the dynamic effect is neglected. In this paper, a drilling platform/riser/wellhead/conductor fully coupled dynamic model is established to evaluate the dynamic stability of subsea wellhead system. An algorithm for solving the fully coupled dynamic model is proposed based on finite element method and Newmark integral method. A fully coupled analysis program is also developed in MATLAB to conduct the dynamic stability evaluation of subsea wellhead system based on the proposed fully coupled model and solving algorithm. Simulation results show that the maximum dynamic response of subsea wellhead system is obviously larger than static response. That is, the subsea wellhead system is likely to be unstable with dynamic loads. The depth of wellhead dynamic displacement and bending moment induced by dynamic loads reaches 32 m and 45 m under mudline, respectively. The dynamic response value appears an inflection point at a certain depth under the mud line. The subsea wellhead system vibrates in the opposite direction before and after the inflection point.

Dynamic Fracture Modeling of Impact Test Specimens by the Polygon Scaled Boundary Finite Element Method

In the polygon scaled boundary finite element method, the modeling of crack can be simplified and the stress intensity factors are extracted from the semi-analytical solution directly. These salient features are applied to develop an efficient method to model the impact test specimens, one of which occurs without crack propagation, the other with crack propagation. The notched bend specimens are discretized by polygon elements with no local refinement around the crack tip. The mass and stiffness matrix of polygon elements are derived based on the SBFEM, and then the elastodynamic equations of the global system are established. The Newmark integration method is applied to obtain the dynamic responses of the specimens. For the case with crack propagation, an efficient local remeshing algorithm is used to track the crack tip and model the crack propagation. The dynamic stress intensity factors are computed directly from the instantaneous displacement field and crack velocity. The numerical results of the two specimens correspond well with the experimental data and other numerical results reported in the literature. The effects of the time step, mesh density and damping coefficient are also investigated. Moreover, the displacement and stress contours are extracted from the dynamic solution, which is helpful for the interpretation of the experimental observations.

Topology optimization of bi‐material curved shell structures for minimizing time‐domain sound radiation

AbstractSo far, the research on topology optimization against noise has mainly addressed frequency‐domain problems, while time‐domain analysis is also widely used in practical engineering. Nonetheless, the topology optimization work on the latter was rarely reported due to its complexity. This article presents a new topology optimization scheme of bi‐material curved shell structure to reduce the time‐domain noise generated by transient vibration. A finite element formulation for an eight‐node curved shell element is presented. The Newmark integral method is employed to calculate transient responses, and the obtained results are input into the time‐domain boundary element method to predict transient sound pressure. In the optimization model, the volumetric densities of material in a bi‐material interpolation model constructed by the solid isotropic material with penalization model are chosen as the design variables; the time integral of the squared sound pressure on structural surfaces or prescribed reference points in acoustic medium over a specified time interval of interest is taken as the objective function; and the constraint on material volume is considered. A volume‐preserving Heaviside penalization is introduced to suppress gray elements. Furthermore, the calculation of time‐domain sound radiation sensitivity is transformed into the following two processes: (a) the derivation of transient response based on the Newmark integral method; (b) the derivation of transient sound pressure based on the discrete time‐domain boundary integral equation. Numerical examples demonstrate the validity of the approach proposed in this article. The influences of volume‐preserving Heaviside penalization, volume constraint, loading position and form, and selection of objective function on the optimal design are discussed.

A single-step recursive representation of foundation flexibility functions to soil-structure interaction using first-order IIR filters

The rational approximation of the dynamic impedance function of the foundation plays a vital role in the soil-structure interaction (SSI) analysis in the time domain. The filter representation of the rational approximation proposed by Safak provides a multi-step recursive parameter model facilitating incorporation into the time history analysis. However, it encounters both the uncertainty of the parameter identification and numerical instability. According to the linear time-invariant system theory in signal processing, this paper presents an improved single-step recursive representation of the foundation flexibility function using first-order infinite impulse response (IIR) filters. Based on the discrete responses of the foundation to the triangular unit impulse, the well-developed technologies of the digital filter can efficiently identify the stable filter parameters. It is easy to incorporate the filters into the motion equations of the structure in the forms of additional stiffness and single-step recursive variables. A computational scheme founded on the Newmark integration method is proposed to obtain the structural responses. According to the spectral radius theory, combining the filters with the Newmark integration method produces only a single operation matrix, thus effectively making the numerical stability guaranteed. Finally, a multi-degree-of-freedom model subjected to earthquake ground motion is employed to approve the proposed scheme.

Dynamics of an offshore drilling tube system with pipe-in-pipe structure based on drift element model

Controllable dynamic behavior of an offshore drilling tube system is significant to secure the operation safety for deep water drilling. In the present work, a dynamic model of a drilling riser system is developed based on Hamilton's principle; and the corresponding finite element model is obtained via introducing the Hermite cubic interpolation function of a curved beam element. In order to consider the effect of the vibration of drill string on the dynamics of drilling riser, a new drift element model is proposed to describe the interaction between the riser and the drill string, and thus a coupled finite element model for the drilling tube system with pipe-in-pipe structure is developed according to the virtual work principle. The Newmark integral method is used to solve the mathematical model numerically; moreover, the obtained dynamic response of the pipe-in-pipe system is further verified and modified according to different collision states. The system dynamics are analyzed in both the frequency domain and the time domain, the vibration of the drill string is demonstrated to restrict the lateral deflection of the riser system; hence, for an actual offshore drilling tube system with pipe-in-pipe structure, it has stronger capacity of maintaining stability and reliability to overcome heavy ocean environmental loads. In addition, in order to effectively control the lateral deflection of the drilling riser, the strategy with high top tension and low buoyancy coefficient is suggested.

Analysis of shock calculation based on Newmark integral method

In this paper, the time domain method for the calculation of impact resistance is studied. Firstly, the central difference method and the Newmark integration method based on the analysis of the linear equations and the solution of the nonlinear equations are educed. Then, the advantages and disadvantages of these two methods are compared and analyzed, and the conclusion is that the Newmark integral method is suitable for the calculation of the non dynamic equation.

Effect of the inlet oil temperature on vibration characteristics of the high-speed turbocharger rotor system

The inlet oil temperature of the rotor system with high-speed and light-load turbocharger will change during operation, which will change the vibration characteristics of the rotor system and even cause vibration accidents. Taking a certain type of high-speed and light-load turbocharger rotor system as the research object, the changes in oil film viscosity, friction power consumption, oil film temperature rise, and ring speed ratio with the inlet oil temperature of floating ring bearings are analyzed. A dynamic finite-element model of the turbocharger rotor–floating-ring-bearing system is constructed, and the finite-element model is verified through the critical speed and colormap spectrogram. The Newmark integral method is used to analyze the nonlinear transient response of the rotor system, and the influence of the inlet oil temperature on the vibration response characteristics of the rotor system is studied. The results show that an increase in the inlet oil temperature leads to a decrease in the internal and external oil film viscosities, frictional power consumption, temperature rise, and an increase in the ring speed ratio. When the inlet oil temperature increases from 50 °C to 130 °C, the amplitude of the inner oil film oscillation will gradually decrease, but the amplitude of the outer oil film vortex will gradually increase, and the journal speed point where the inner oil film oscillation and the outer oil film vortex will appear about 30% in advance. In summary, the rotor vibration is better when the inlet oil temperature is about 90 °C. The conclusion of this paper can provide a theoretical reference for selecting the operating parameters of the rotor system with the least vibration for high-speed light-load turbochargers.

Dynamic response of buried fluid-conveying pipelines subjected to blast loading using shell theory

In this study, the dynamic response of buried fluid-conveying pipelines subjected to blast loading using the Love shell theory has been investigated. The fluid is considered as ideal fluid, and the velocity potential is used to describe the fluid pressure acting on the pipeline. The governing equations of the buried fluid-conveying pipelines are derived through Hamilton’s principle. The modal superposition method and the Newmark integral method are used to analyze the dynamic response of the pipelines under blast loading. Results show that the displacement amplitudes of the pipelines are larger in the soil with a higher acoustic impedance. The Winkler foundation can enhance the stiffness of the pipelines. Moreover, the increase in the scaled distance leads to the decrease in the displacement amplitudes of the pipelines. The increase in the fluid velocity results in the rise of the displacement amplitudes of the pipelines. In addition, the maximum displacement increases first and then decreases with the increase in length-to-radius ratio of the pipelines. With the increase in thickness-to-radius ratio, the maximum displacement of the pipelines tends to decrease.

Integrated design optimization of actuator layout and structural ply parameters for the dynamic shape control of piezoelectric laminated curved shell structures

Compared with static shape control, dynamic shape control is more difficult due to its time-varying nature. To improve the control precision and reduce the number of actuators needed, an integrated design optimization model of structure and control is proposed. The following three sets of design variables are considered to minimize the time domain variance between the controlled and desired dynamic shapes: the time-varying actuator voltages, the actuator layout and the structural ply parameters. To satisfy the engineering performance requirements to the greatest extent possible, constraints on the structural mass, the energy, the maximum transient voltage and the number of actuators are considered. Because the control voltages are varying in time, a two-level optimization strategy is adopted. In the inner optimization problem, the Newmark integral method is applied to derive discrete time domain expressions for the shape control equations, and then, the Kuhn-Tucker condition is introduced to calculate the optimal time-varying voltage distribution. To solve the outer optimization problem, because of the coexistence of discrete variables and continuous variables, a simulated annealing algorithm is used. To address the shape control of complicated curved shells, a finite element formulation for an eight-node laminated curved shell element with piezoelectric actuators is derived. Numerical examples show that the proposed integrated design optimization method can significantly improve the control effect and that the optimization of the structural ply parameters plays an important role. Moreover, the control system can be simplified by taking the minimum number of actuators as the objective function when the control accuracy allows.

The Influence of Ring‐Speed Ratio Dynamic Change on Nonlinear Vibration Response of High‐Speed Turbocharger Rotor System

The ring‐speed ratio is a comprehensive dynamic index of floating ring bearing structure and operating parameters, which directly affects the dynamic behavior of the turbocharger rotor system. The cross stiffness of ring‐speed ratio and floating ring bearing and the work of oil film force are analyzed. The influence of dynamic ring‐speed ratio change on the vibration response of floating ring bearing was studied. The finite element model of the rotor‐floating ring bearing system is constructed; its model parameters are verified through the measured critical rotor speed. Newmark integral method is used to analyze the nonlinear transient response. The results show that when the ring‐speed ratio is between 0.18 and 0.24, the rotor is in a good operating state; when it increases from 0.24 to 0.36, the rotor vibration is dominated by frequency division, and the system will be less stable. The square of the ring‐speed ratio is inversely proportional to the rotational speed of the journal where the subfrequency vibration occurs. It helps to know the nonlinear vibration by judging the journal speed when the rotor vibration occurs in subfrequency. The conclusion provides a reference for the mechanical dynamics design and intelligent management and maintenance of this kind of turbine rotors.

Nonlinear Inelastic Earthquake Analysis of 2D Steel Frames

In this work, a new method for nonlinear time-history earthquake analysis of 2D steel frames by a fiber plastic hinge method is presented. The beam-column element based on the displacement-based finite element method is established and formulated in detail using a fiber plastic hinge approach and stability functions. Geometric nonlinearities are taken into accounting by stability functions and the geometric stiffness matrix. A nonlinear dynamic algorithm is established based on the combination of the Newmark integration method and the Newton-Raphson iterative algorithm for solving dynamic equations. The proposed program predicts the nonlinear inelastic responses of 2D steel frames subjected to earthquakes as efficiently and accurately as commercial software. This study also shows that the initial residual stresses of steel should be considered in nonlinear inelastic time-history earthquake analysis of 2D steel frames while SAP2000 does not consider the effects of residual stresses.

Moving Element Analysis of High-Speed Train-Slab Track System Considering Discrete Rail Pads

This paper presents a study of the dynamic behavior of a coupled train-slab track system considering discrete rail pads. The slab track is modeled as a three-layer Timoshenko beam. The study is carried out using the moving element method (MEM). By introducing a convected coordinate system moving at the same speed as the vehicle, the governing equations of motion of the slab track are formulated in a moving frame-of-reference. By adopting Galerkin’s method, the element stiffness, mass and damping matrices of a truncated slab track in the moving coordinate system are derived. The vehicle is modeled as a multi-body with 10 degrees of freedom. The nonlinear Hertz contact model is used to account for the wheel–rail interaction. The Newmark integration method, in conjunction with a global Newton–Raphson iteration algorithm, is employed to solve the nonlinear dynamic equations of motion of the vehicle–track coupled system. The proposed MEM model of the system is validated through comparison with available results in the literature. Further study is then made to investigate the vehicle–track system accounting for track irregularities modeled as short harmonic wave forms. Results showed that irregularities with short wavelengths have a significant effect on wheel–rail contact force and rail acceleration, and the dynamic response of the track structure does not increase monotonously with the increase of the vehicle speed.

An efficient three-dimensional dynamic contact model for cylindrical gear pairs with distributed tooth flank errors

Coupled loaded tooth contact analysis (LTCA) model and lumped-parameters model, an efficient three-dimensional dynamic contact model for cylindrical gear pairs with distributed tooth flank errors is established. The solution scheme of the proposed model is constructed using a combination of the loaded tooth contact algorithm and the Newmark integration method. The dynamic load distributions at different input speeds can be determined, and the dynamic time-dependent mesh stiffness and dynamic composite mesh error are proposed and calculated. The proposed model is validated by comparing the obtained numerical results with the experimental results from the published works, and has much higher efficiency compared with three-dimensional dynamic contact finite element method. The effects of helix angle, mesh damping, distributed tooth flank errors and output torque on the vibration behaviors and dynamic load distributions of cylindrical gear pairs under different working conditions are investigated and discussed. The proposed model can also be used to predict the vibration behaviors and the instantaneous three-dimensional dynamic contact state of cylindrical gear pairs with different distribution forms of tooth flank errors and various tooth surface modifications.

An efficient refracted salp swarm algorithm and its application in structural parameter identification

Efficient and accurate structural parameter identification is critical for the practical application of structural health monitoring. In this paper, a novel algorithm named refracted salp swarm algorithm (RSSA) is proposed and applied to identify structural parameters. Firstly, the basic salp swarm algorithm is improved by refracted opposition-based learning strategy, multi-leader mechanism and adaptive conversion parameter strategy. The superiority of the proposed algorithm is verified by experiments of eight benchmark functions of various types and dimensions. Secondly, a new type of structural parameter identification (SPI) model is established by combining RSSA and the Newmark integration method, which is mainly used to solve the optimization problem based on structural acceleration, thereby identifying structural parameters such as stiffness, mass and damping ratio. Numerical simulation test of seven-floor frame proves that the new proposed RSSA could be successfully applied in the SPI model. Compared with other heuristic algorithms, RSSA can obtain more accurate recognition results under the circumstances incomplete measurement data and low signal-to-noise ratio.

An Improved Computational Method for Vibration Response and Radiation Noise Analysis of Two-Stage Gearbox

In this work, an improved computational method for the prediction of the vibration and noise of a gearbox that considers the flexibility of the shaft is developed. Based on the finite element method (FEM), a coupled dynamic model of a spur gear-shaft-bearing system is established, and the time-varying mesh stiffness (TVMS), the time-varying bearing stiffness (TVBS), and the flexibility of the shaft are considered. The Newmark integration method (NIM) is utilized to obtain the dynamic load of the bearing. Furthermore, the proposed model is validated by experiments. The bearing load is then considered to be the excitation of the housing, and the radiated noise is calculated via the finite element method/boundary element method (FEM/BEM). The effects of the shaft flexibility on the bearing response and radiated noise are discussed based on the proposed method. The results demonstrate that, when the shaft flexibility is considered, the system undergoes the bending vibration of the shaft, and the vibration amplitude and excitation frequency components of the bearing load decrease significantly. Additionally, the main resonance mode of the gearbox is changed, and the radiated noise is enhanced. The effects of the input speed and shaft stiffness on the bearing response and radiated noise are also investigated. The results provide a theoretical basis for the further development of the vibration and noise reduction of gearboxes.