Newmark Average Acceleration Method Research Articles

Large Deformation Dynamic Characteristics of Cracked Laminated Panel and Improvement of Stiffness Using Shape Memory Alloy Fiber

Abstract This study explores the investigation of the nonlinear dynamic responses or time-dependent deflection analysis of a laminated composite shell panel integrated with a shape memory alloy (SMA), considering both undamaged and damaged set-ups. The primary focus of this research is to examine the impact of SMA incorporation on the structural behavior of the parent configuration, aimed at enhancing its structural stiffness. To ensure the validity of the proposed model, sensitivity analyses and numerical validations are presented. The mathematical framework employed in this study employs the higher-order shear deformation theory (HSDT), which offers enhanced accuracy in capturing the intricate behaviors of these shell panels. The dynamic responses are obtained using the Newmark average acceleration method. Numerical simulations are carried out using a dedicated MATLAB code developed in-house, allowing amplified correctness in outcomes and widespread analysis. The study thoroughly assesses a range of geometric parameters and those relevant to SMA for both intact and impaired shell panels. The outcomes of the investigation reveal affirmative findings, underscoring notable improvements in structural strength and enhanced nonlinear dynamic responses through the introduction of SMA reinforcement into the composite shell panel.

Moving Load Analysis of Laminated Porous Micro Beams Resting on Elastic Foundation

This research highlights dynamic displacements of laminated porous micro beams resting on elastic foundation under moving load. In the constituted equation of laminated micro scaled beam, the modified coupled stress theory is used in order to determine the size effect. Each layer is considered as identical and porosity distribution and assumed as uniform. Lagrange technique is applied in achieving governing equations, and Ritz method within algebraic polynomials is used for solution. For dynamic solution steps, Newmark average acceleration method is used within time domain. Influences of porosity coefficients, length scale parameter, foundation parameter, order of laminas, fiber orientation angles on dynamically deflections of laminated micro beam are investigated.

Vibration and wave propagation in functionally graded beams with inclined cracks

This paper proposes an FEA method to study the vibration and wave propagation in functionally graded material (FGM) beams with multiple inclined cracks by introducing the local flexibility matrix caused by the cracks. The bending and tensile stiffnesses of the inclined cracks and their interaction are taken into consideration. Two-node (three degrees of freedom per node) beam element is used. The inclined cracks are equivalent to transversal cracks to calculate the additional flexibility matrix of the inclined cracked FGM beam element. The material properties of the FGM beam are supposed to satisfy the exponential law along its thickness. The governing equations of motion for the FGM beam with multiple inclined cracks are deduced in the frame of Euler-Bernoulli theory and Lagrange function, and numerically solved by the Newmark average acceleration method. Both theoretical and numerical comparisons are presented to validate the present method for the inclined cracked FGM beam with varying boundary conditions, arbitrary inclined crack angles as well as varying inclined crack lengths. The effects of the location, length, inclined angle and number of the inclined cracks as well as material property ratio on the fundamental frequencies and wave propagation characteristics of the inclined cracked cantilever FGM beams are comprehensively investigated.

Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

AbstractIn this article, various non‐polynomial higher‐order shear deformation theories are applied for the first time to analyze the free vibration and transient responses of plates with functionally graded material (FGM) supported on an elastic foundation. The shear deformation theories account for the non‐linear variation of the transverse shear strains with various warping functions, namely trigonometric, inverse hyperbolic, and inverse trigonometric ones. These models also inherently satisfy the traction‐free boundary conditions of transverse shear stresses at the top and bottom surfaces of the plates and do not require any shear correction factor. A two‐parameter model, namely Winkler‐Pasternak's elastic foundation model, is utilized to develop the interaction between the FGM plates and the elastic medium. The governing equations of motion are obtained using Hamilton's principle and solved analytically using Navier's solution scheme. Furthermore, the transient responses of the plates are obtained using Newmark's average acceleration method. The applicability of the present theories is established by solving several numerical problems and validating the results with the solutions available in the literature. The effects of various parameters like span‐thickness ratios, aspect ratios, gradation coefficients, mechanical loads, and foundation stiffness on the fundamental frequencies and the transient responses of the plates are thoroughly investigated. The comparison of the results reveals the efficiency of the non‐polynomial functions, and the capability of efficient prediction of the structural responses of the FGM plates at a similar computational cost compared to established models in the literature. Furthermore, the results show that the stiffness of the elastic foundation can tweak the stiffness characteristics of the FGM plate resulting in significant changes in the natural frequencies and more controlled displacement‐time responses.

The high-order smooth interpolated reproducing kernel particle method for elastodynamics problems

Combining the interpolation reproducing kernel particle method (IRKPM) with the integral weak form of elastodynamics, we present a high-order smooth interpolated reproducing kernel particle method for an elastodynamics plane problem. The shape function of IRKPM not only has the interpolation property at any point but also has a high-order smoothness not lower than that of the kernel function. This new method overcomes the difficulties of most meshless methods in dealing with essential boundary conditions and ensures high numerical accuracy. For time domain integration, we use the classical Newmark average acceleration method. By numerical examples we demonstrate that the proposed method has the advantages of higher accuracy, smaller scale of solving problem, and direct application of boundary conditions.

Dynamic Analysis of a Fiber-Reinforced Composite Beam under a Moving Load by the Ritz Method

This paper presents the dynamic responses of a fiber-reinforced composite beam under a moving load. The Timoshenko beam theory was employed to analyze the kinematics of the composite beam. The constitutive equations for motion were obtained by utilizing the Lagrange procedure. The Ritz method with polynomial functions was employed to solve the resulting equations in conjunction with the Newmark average acceleration method (NAAM). The influence of fiber orientation angle, volume fraction, and velocity of the moving load on the dynamic responses of the fiber-reinforced nonhomogeneous beam is presented and discussed.

Damped forced vibration analysis of layered functionally graded thick beams with porosity

The following article presents the damped forced vibration of layered functionally graded thick beams including material porosities. In case of very thick beams, beam theories fail to satisfy boundary conditions and to predict the mechanical response accurately. So, the two-dimensional (2D) plane continuum model is exploited to model a thick functionally graded layered beam. The beam is composed from three- layers with functionally graded porous materials. The porosity is described by three different distribution models through the layer thickness. Applied forces to the functionally graded beam are assumed to be sinusoidal harmonic point load in time domain. The Kelvin—Voigt viscoelastic constitutive model is used to simulate damping effect. The governing equations are obtained by using Lagrange's equations. In frame of finite element analysis, twelve .node 2D plane element is exploited to discretize the space domain of thick beam. In the solution of the dynamic problem, the Newmark average acceleration method is used. Numerical studies illustrate effects of porosity distribution, stacking sequence, and graduation constant on the dynamic responses of layered functionally graded porous thick beams. The results show that the porosity function, stacking sequences and the damping ratio have a vital role in dynamic response of functionally graded beams. The proposed model can be used in nuclear, marine, and aerospace technologies.

Forced vibration analysis of a fiber reinforced composite beam

In this study, forced vibration analysis of a fiber reinforced composite cantilever beam is investigated under a harmonic load. In the beam model, the Timoshenko beam theory is used. The governing equations of problem are derived by using the Lagrange procedure. In the solution of the problem the Ritz method is used and algebraic polynomials are used with the trivial functions for the Ritz method. In the solution of the forced vibration problem, the Newmark average acceleration method is used in the time history. In the numerical examples, the effects of fibre orientation angles, the volume fraction and dynamic parameters on the forced vibration response of fiber reinforced composite beam are presented and discussed.

Vibration response of perforated thick beam under moving load

This manuscript aims to investigate the dynamic responses of thick Timoshenko perforated beams under a moving load using Ritz method for the first time. The beam is perforated by equally spaced square holes arranged in array form. The perforated geometrical parameters of beam are presented as a function of full beam, hole number throughout the cross section, and filling ratio. The governing equation is derived by using the Lagrange procedure using the kinematic assumption of Timoshenko shear deformation theory to include the rotation of the thickness effect. Therefore, the transverse-shear strain and rotary inertia are considered through analysis. Ritz method is exploited to solve the governing equation and transform it to ordinary differential equation in time domain. Newmark average acceleration method is adopted to solve the dynamic equation of motion to obtain the time response. The effects of moving load parameter, filling ratio, and the number of holes throughout the cross section on the dynamic responses of the perforated beam are investigated and analyzed. The proposed model can be used in many civil and mechanical perforated structures to reduce the vibration amplitudes.

Forced Vibration Analysis of Composite Beams Reinforced by Carbon Nanotubes.

This paper presents forced vibration analysis of a simply supported beam made of carbon nanotube-reinforced composite material subjected to a harmonic point load at the midpoint of beam. The composite beam is made of a polymeric matrix and reinforced the single-walled carbon nanotubes with their various distributions. In the beam kinematics, the first-order shear deformation beam theory was used. The governing equations of problem were derived by using the Lagrange procedure. In the solution of the problem, the Ritz method was used, and algebraic polynomials were employed with the trivial functions for the Ritz method. In the solution of the forced vibration problem, the Newmark average acceleration method was applied in the time history. In the numerical examples, the effects of carbon nanotube volume fraction, aspect ratio, and dynamic parameters on the forced vibration response of carbon nanotube-reinforced composite beams are investigated. In addition, some comparison studies were performed, with special results of published papers to validate the using formulations.

Forced Vibration Responses of Axially Functionally Graded Beams by using Ritz Method

This work presents forced vibration responses of a cantilever beam made of functionally graded material under a harmonic load. The material properties of beam vary along the axial direction. The kinematics of the beam are considered within Timoshenko beam theory. The governing equations of problem are derived by using the Lagrange procedure. In the solution of the problem the Ritz method is used and algebraic polynomials are used with the trivial functions for the Ritz method. In the solution of the forced vibration problem, the Newmark average acceleration method is used in the time history. In this study, free and forced vibration responses of the axially functionally graded beam are investigated in detail. In the numerical examples, the effects of material graduation, geometric and dynamic parameters on the free and forced vibration response of axially graded beam are investigated.

Vibration of multilayered functionally graded deep beams under thermal load

Since the functionally graded materials (FGMs) are used extensively as thermal barriers in many of applications. Therefore, the current article focuses on studying and presenting dynamic responses of multilayer functionally graded (FG) deep beams placed in a thermal environment that is not addressed elsewhere. The material properties of each layer are proposed to be temperature-dependent and vary continuously through the height direction based on the Power-Law function. The deep layered beam is exposed to harmonic sinusoidal load and temperature rising. In the modelling of the multilayered FG deep beam, the two-dimensional (2D) plane stress continuum model is used. Equations of motion of deep composite beam with the associated boundary conditions are presented. In the frame of finite element method (FEM), the 2D twelve –node plane element is exploited to discretize the space domain through the length-thickness plane of the beam. In the solution of the dynamic problem, Newmark average acceleration method is used to solve the time domain incrementally. The developed procedure is verified and compared, and an excellent agreement is observed. In numerical examples, effects of graduation parameter, geometrical dimension and stacking sequence of layers on the time response of deep multilayer FG beams are investigated with temperature effects.

Dynamic analysis of axially functionally graded porous beams under a moving load

In presented paper, moving load problem of functionally graded beams is investigated with porosity effects based on the first shear beam theory. The material properties of beam vary along the axial direction. The porosity is depicted by two different distributions along axial direction. The governing equations of problem are derived by using the Lagrange procedure. In the solution of the problem the Ritz method is used and algebraic polynomials are used with the trivial functions for the Ritz method. In the solution of the moving load problem, the Newmark average acceleration method is used in the time history. In the numerical examples, the effects of material graduation, porosity distribution, porosity coefficients and velocity of moving load on the dynamic responses of axially functionally graded beam are presented and discussed. The dynamic responses are obtained for different boundary conditions.

Dynamic responses of functionally graded and layered composite beams

This paper presents and compares the free and damped forced vibrations of layered and functionally graded composite beams. In the considered study, a cantilever beam subjected to a harmonic point load at the free end is investigated with layered and functionally graded materials. In the kinematics of the beam, the Timoshenko beam theory is used. The governing equations of problem are derived by using the Lagrange procedure. In the solution of the problem, the Ritz method is used. Algebraic polynomials are used with the trial functions for the Ritz method. In the obtaining of free vibration results, the eigenvalue procedure is implemented. In the solution of the damped forced vibration problem, the Newmark average acceleration method is used in the time history. In the damping effect, the Kelvin-Voigt viscoelastic model is used with the constitutive relations. In the numerical examples, the effects of material distribution parameter and dynamic parameters on the natural frequencies and forced vibration responses of functionally graded beams are obtained and compared with the results of the layered composite beam. Also, comparison studies are performed in order to validate the used formulations.

Nonlinear analysis of functionally graded skewed and tapered wing-like plates including porosities: A bifurcation study

In the present study, nonlinear panel flutter and bifurcation behavior of functionally graded ceramic/metal wing-like tapered and skewed plates are investigated. Porosities are distributed over the cross-section of the functionally graded structure. The flutter speed, limit cycle oscillations, and bifurcation diagrams of the functionally graded plate with two types of geometrical non-uniformities being skewness and taperness are explored. Nonlinear structural model is utilized based on the virtual work principle by including the von-Karman nonlinear kinematic strain assumption. The first order shear deformation theory is employed to consider the transverse shear effect in the structural model. First-order linear piston theory is used to model the aerodynamic loading while the generalized differential quadrature method is employed to solve the governing equations of motion. Time integration of the final ordinary equations of motion is carried out using the Newmark average acceleration method. Different volume fractions are investigated to enhance the flutter instability margins and post-flutter behavior of functionally graded plates. Results demonstrate that the volume fraction and porosity coefficients have significant effects on dynamic behavior and limit cycle oscillation amplitudes.

Non-linear transient response of porous functionally graded truncated conical panels using GDQ method

Present study deals with large displacement transient dynamic response of truncated conical panels made of Porous Functionally Graded Materials (P-FGMs) using Generalized Differential Quadrature (GDQ) method. In this study, geometric non-linearity is taken into consideration through Green-Lagrange non-linear strain-displacement relations. First order shear deformation theory (FSDT) is utilized to take transverse shear effects into account. Virtual work principle is used to derive the equation of motion. The solution methodology utilizes GDQ method for spatial discretization of the variables. Newmark average acceleration method is implemented in time integration. Effects of different types of porosity distribution, porosity ratio and conical parameters on non-linear transient behavior of truncated conical panels are investigated for functionally graded material made of Zirconia/Aluminum (ZrO2/Al) considering various volume fraction coefficients.

Dynamic Behavior and Force Analysis of the Full Vehicle Model using Newmark Average Acceleration Method

Dynamic Behavior and Force Analysis of the Full Vehicle Model using Newmark Average Acceleration Method

Dynamic Behavior and Force Analysis of the Full Vehicle Model using Newmark Average Acceleration Method

In this study, the dynamic interaction between road and vehicle is modeled. For this purpose, a full vehicle model with eight degrees of freedom is considered. The equations of motion of the whole system are derived by the D’Alambert method and numerical solutions are obtained by the Newmark average acceleration method. Due to varying road roughness, the forces affecting the driver and the vehicle-components are analyzed in detail. Also, vertical and rotational displacements, velocities, and accelerations are examined, and results graphs are given. Two different pre-defined road profiles, created as non-random road excitation, and five different vehicle speeds are presented and analyzed.

Nonlinear flutter response of a composite plate applying curvilinear fiber paths

In the present study, nonlinear flutter and post-flutter behavior of a variable stiffness composite wing-like plate is investigated. The variable stiffness is obtained by varying fiber angles continuously according to a selected curvilinear fiber path function in the composite laminates. Flutter speed, limit cycle oscillations and bifurcation diagrams of the composite plate are explored for three different fiber path functions using the nonlinear structural model obtained based on the virtual work principle. The paper aims to exploit the ideal fiber paths with enhanced aeroelastic flutter and post-flutter properties for a composite plate in supersonic flow speed. First-order linear piston theory is applied to model the aerodynamics, and generalized differential quadrature is employed to solve the governing equations. Von Karman nonlinear strain theory is used to account for the geometric nonlinearities, and first-order shear deformation theory is employed to consider the transverse shear effects in the structural model. Time integration of the equation of motion is carried out using the Newmark average acceleration method. Different curvilinear fiber paths are introduced to enhance flutter instabilities and post-flutter behavior of the composite plate. Results demonstrate that the fiber orientation has a significant effect on the dynamic behavior of the plate and the asymmetric properties as well as the behavior of the limit cycle oscillation.

Nonlinear transient dynamic analysis of laminated composite parabolic panels of revolution with variable thickness resting on elastic foundation

In this article, nonlinear transient behavior of laminated composite Parabolic Panels of Revolution Structure(s) (PPRS) with variable thickness resting on elastic foundation is investigated using Generalized Differential Quadrature (GDQ) method. Winkler-Pasternak model is used to represent elastic foundation. Linear, arch, sine and cosine thickness functions are used to express variable thickness. In transient analyses, First Order Shear Deformation Theory (FSDT) is used to consider the transverse shear effects. Nonlinearity is taken into account using Green-Lagrange nonlinear strain-displacement relations considering deepness effect. Virtual work principle is used to derive the equations of motion. Partial derivatives in the equation of motion are expressed with GDQ method and time integration is carried out using Newmark average acceleration method. Several problems are solved and compared with finite element results in order to validate the proposed method. After validation, effects of thickness functions, thickness variation parameter, geometric characteristic parameter of PPRS, boundary conditions, elastic foundation parameters as well as composite lamination scheme on nonlinear transient dynamic behaviour of PPRS are investigated.