Dynamic Response Of Plate Research Articles

Dynamic Response Mechanism of Thin-Walled Plate under Confined and Unconfined Blast Loads

Thin-walled metal plates and cabin structures are widely found in ships and cargos which are susceptible to attacks or accidental explosions. The present work focuses on the dynamic response mechanism of steel plates under unconfined and confined blast loads. In the experiment, digital image correlation (DIC) technique was applied to record and analyze the dynamic response process of a large-scale field blast test. The DIC measured curve and the numerically calculated curves agree well in both trends and peak values. Then, the dynamic response mechanisms of steel plates under an unconfined blast (UB) load and confined blast (CB) load were compared and discussed. The results show that the dynamic response of plates can be divided into three phases under both UB and CB loads, with different mechanisms. In phase I, plastic hinges start from the center and move to the boundary in the UB condition, while in the case of CB, plastic hinges occur close to the boundary and move in the opposite direction. In phase II, two plastic hinge lines propagate towards each other, a platform exists between the boundary, and the central area remains undeformed in the UB condition, while in the CB condition, larger deformation occurs in the peripheral region rather than the central area.

Transient analysis of laminated plates in thermal environment

Transient displacement of laminated plates under combined load based on Mantari' s displacement field are investigated. The solution is implemented under transient mechanical load (sinusoidal, step and triangular sinusoidal distributed pressures pulse) and thermal buckling for plates with different layer orientation and thickness ratio. Equations of motion based on higher-order theory are derived through Hamilton' s principle, and solved using Naviertype solution for simply supported laminated plates. The results are presented for many effective parameters such as the number of laminate and orientation on the dynamic response of plates. Results show the validity of this displacement field in studying response of laminated thick and thin plates under varied transient loading and design parameters.

Transient Responses of Sandwich Plates with a Functionally Graded Porous Core: Jacobi–Ritz Method

This study examined the transient or dynamic response of sandwich plates with a functionally graded porous core under the action of time-dependent loads. The plates had two isotropic faces at the top and bottom layers, and the middle layer was made of an open-cell material with functionally graded internal pores. By using the first-order shear deformation theory, the equations of motion used to describe the dynamic behavior of the plates were applied to generate accurate results with less computational effort. To solve the equations of motion, the Ritz method based on the Jacobi polynomials for the admissible displacements, cooperating with the time integration of Newmark, was used to find out the dynamic response of the plates. The results of the numerical experiments revealed that the plates carrying a larger number of internal pores at the middle zone of the core had a great improvement in flexural stiffness, providing less deflection under dynamic loads. The observed results of the plates’ dynamic behavior related to the effects of the porosity coefficient, plate’s geometrical ratio, dynamic loading types, porous distributions of the core, etc. are shown in the form of graphs and tables, which can be used as a benchmark for future research.

Analysis of arbitrary thick graphene platelet reinforced composite plates subjected to moving load using a shear and normal deformable plate model

In the present research, the dynamic response of a composite laminated plate under the action of a moving load is investigated. It is assumed that plate is reinforced with graphene platelets (GPLs) where the amount of GPLs in the layers may be different. The governing equations of motion of the plate are established by means of a quasi-3D plate model which captures the through-the-thickness shear strains and also takes into account for the thickness stretching effects. The elasticity modulus of the composite media is obtained by means of the Halpin-Tsai rule which takes into account the size of the reinforcements. The developed governing equations may be used for the case of an arbitrary thick plate subjected to a moving load with constant magnitude and velocity and arbitrary path. Suitable for plates which are simply supported all around, the Navier solution is adopted to discrete the governing equations and establish a set of ordinary time dependent equations. This set is traced in time by means of the Newmark time marching scheme. Results of this study are first compared with the available data in the open literature for the simple cases and after that novel results are provided to explore the effects of different parameters on the dynamic response of the plate. It is shown that the developed theory is accurate to analyse the dynamic response of arbitrary thick plates made of FG-GPLRCs.

Geometrically nonlinear dynamic analysis of functionally graded material plate excited by a moving load applying first-order shear deformation theory via generalized differential quadrature method

In this study, we present a numerical solution for geometrically nonlinear dynamic analysis of functionally graded material rectangular plates excited to a moving load based on first-order shear deformation theory (FSDT) for the first time. To derive the governing equations of motion, Hamilton’s principle, nonlinear Von Karman assumptions and FSDT are used. Finally, the governing equations of motion are solved by employing the generalized differential quadratic method as a numerical solution. Natural frequencies, dynamic bending behavior and stresses of the plate for linear and nonlinear type of geometrically strain–displacement relations and different factors, including the magnitude and velocity of moving load, length ratio, power law exponent and various edge conditions are obtained and compared.Article highlightsDeveloping generalized differential quadrature method (GDQM) solution based on FSDT for dynamic analysis of FGM plate excited by a moving load for the first time.Comparison of linear and nonlinear dynamic response of plate by considering Von-Karman assumption.Observing considerable difference between linear and nonlinear results

Dynamic behaviour of pavement on a two-parameter viscoelastic foundation subjected to loads moving with variable speeds

ABSTRACT The dynamic response of a multilayer finite plate resting on a two-parameter viscoelastic foundation to moving variable loads is obtained analytically/numerically. The governing differential equation of a multi-layer finite plate resting on a two-parameter viscoelastic foundation is derived firstly. Then, the dynamic response is derived analytically using mode superposition and Duhamel’s formula, followed by the solving of the numerical method. Next, the proposed solution is verified by comparing the degraded solution with both the field measurement data and the known theoretical results. Three different loading models are assessed to select the loading model that would provide insight into the effects of acceleration and deceleration. The effects of foundation parameters and vehicle parameters, especially the acceleration or deceleration and initial velocity of the moving load, on the dynamic response of the multilayer plate are compared through parametric studies. The numerical results suggest that acceleration and deceleration exert considerable effects on the dynamic response of the plate, and that the stiffness of pavement exposed to frequent acceleration and deceleration should be increased by at least 15% to counteract the effects of variable speed.

Fluid-structure interaction effects during the dynamic response of clamped thin steel plates exposed to blast loading

This work presents results from a numerical investigation on the influence of fluid-structure interaction (FSI) on the dynamic response of thin steel plates subjected to blast loading. The loading was generated by a shock tube test facility designed to expose structures to blast-like loading conditions. The steel plates had an exposed area of 0.3 m × 0.3 m and experienced large deformations during the tests. Numerical simulations were performed using the finite element code EUROPLEXUS. An uncoupled FSI approach was compared to a coupled FSI approach in an attempt to investigate FSI effects. Reduced deformation was observed in the plates due to the occurrence of FSI during the dynamic response. The general trend was an increased FSI effect with increasing blast intensity. The numerical results were finally compared to the experimental data to validate their reliability in terms of deflections and velocities in the steel plates. A good agreement with the experimental data was found, and the numerical simulations were able to predict both the dynamic response of the plate and the pressure distribution in front of the plate with good accuracy. Hence, the numerical framework presented herein could be used to obtain more insight regarding the underlying physics observed in the experiments. The clear conclusion from this study is that FSI can be utilized to mitigate the blast load acting on a flexible, ductile plated structure, resulting in reduced deformations.

A value of damping factor in relation to the dynamic response for a plate structure

AbstractThe subject of the research is the analysis of the impact of damping value on the dynamic response of plate. The work presents the areas of dynamic stability and instability for the different damping values and compared with the plate without damping. Furthermore, the nature of solution for each analyzed case was presented. Research by using the dynamic tools such as phase portraits, Poincaré maps, FFT analysis, the largest Lyapunov exponents were performed. The compatibility of the selected method of stability analysis with the Volmir criterion was also presented.

Dynamic response of plates resting on a fractional viscoelastic foundation and subjected to a moving load

The dynamic behavior of the thin plates resting on a fractionally damped viscoelastic foundation subjected to a moving point load is investigated. This work explores the application of fractional calculus in the modeling of a viscoelastic foundation. A parametric study is executed to determine the impacts of the fractional-order derivative, foundation parameters, velocity and acceleration of the moving load on the dynamic behavior of the plate. The results show that the damping of the foundation system increases with increasing the order of the fractional derivative, which leads to a decrease in the dynamic response.

Simplification through regression analysis on the dynamic response of plates with arbitrary boundary conditions excited by moving inertia load

Dynamic response of a thin rectangular plate traversed by a moving inertia load with arbitrary boundary condition is investigated through this paper. The inertia effect of mass is considered and relevant formulation is established based on the full-term of acceleration, employing the method of Boundary Characteristic Orthogonal Polynomials, BCOP. To acquire the complete solution of partial differential equations governing on the plate, the Galerkin method is used to separate the temporal function from the spatial one. The problem is formulated in the state space and applying the numerical method of Matrix Exponential the complete solution would be achieved. In the numerical studies, a comprehensive parametric study is performed for both cases of loading when inertia effect is included or neglected. Several mass and aspect ratios for the plate with major types of boundary conditions CCCC, SSSS, CFCF and SFSF are accounted for presenting the results. Dynamic amplification factor against velocity parameter is scrutinized within many graphs alongside with a time history analysis of dynamic deflection for the plate's mid-span. Investigating on the dynamic response concludes to the critical boundary condition upon moving mass. By introducing a conversion factor, the margin of inertia and the critical velocity where happened would be achieved, then through a regression analysis a curve fitting model of polynomials is proposed. Corresponding coefficients testify the goodness of fit for such regression which are reported within tables. Referring to this simplified model of conversion factor pertaining to the specific boundary condition, it would be possible to handle the problem in moving load case without undertaking the complexities arisen from inertia contribution into the formulation. Having derived the factor from simplified model which has been calculated for a specific mass and velocity ratio, then multiplying into the moving load response, the complete solution for moving mass would be achieved.

Dynamic response of functionally graded plates resting on two-parameter-based elastic foundation model using a quasi-3D theory

In this article, an improved quasi 3-D theory, which considers transverse normal strain effect along with inverse tangential variation of in-plane displacements across plate thickness, is employed to encapsulate the response of thick functionally graded plates. The present model satisfies both non-linear variation and zero transverse shear stresses across plate thickness. The governing equations of plate are obtained using Lagrange equation and solved by applying finite element procedure. The adaptability of the proposed theory is handled by considering the impact of various parameters on dynamic response of plate through several illustrations. The present model gives incredible concurrence with accessible literature.

Dynamics of nonlinear rectangular plates subjected to an orbiting mass based on shear deformation plate theory

In this paper, transverse and longitudinal vibration of nonlinear plate under exciting of orbiting mass is considered based on first-order shear deformation theory. The nonlinear governing equation of motion are discretized by the finite element method in combination with Newmark’s time integration scheme under von Karman strain-displacement assumptions. For validation of method and formulation of solution, a simply supported beam-plate under a moving force is considered and compared with existing results in the literature. The effects of nonlinearity, mass ratios, different geometric parameters, orbiting radius and angular velocity on dynamic response of plate are studied. This study present the importance of nonlinear analysis of rectangular plate under orbiting mass due to large deformation. In this paper, transverse and longitudinal vibration of nonlinear plate under exciting of orbiting mass is considered based on first-order shear deformation theory. The nonlinear governing equation of motion are discretized by the finite element method in combination with Newmark’s time integration scheme under von Karman strain-displacement assumptions. For validation of method and formulation of solution, a simply supported beam-plate under a moving force is considered and compared with existing results in the literature. The effects of nonlinearity, mass ratios, different geometric parameters, orbiting radius and angular velocity on dynamic response of plate are studied. This study present the importance of nonlinear analysis of rectangular plate under orbiting mass due to large deformation.

Dynamic Analysis of Mindlin Plates Resting on a Viscoelastic Foundation Subjected to Moving Loads During Abrupt Braking using Moving Element Method

The paper proposes a new computational approach using the moving element method (MEM) for simulating the dynamic responses of Mindlin plate resting on a viscoelastic foundation subjected to moving loads during abrupt braking. In this approach, the governing equations as well as the plate element mass, damping and stiffness matrices are formulated in a convected coordinate in which the origin is attached to the applied point of the moving load. Thus, the proposed method simply treats the moving loads as ‘stationary’ at the nodes of the plate to avoid updating the locations of moving loads due to the change of the contact points on the plate. The interaction between the moving load and the plate during abrupt braking is accounted for through the vertical force and tangential wheel-pavement friction force. The effects of wheel sliding, load deceleration magnitude, friction coefficient, and plate thickness on the dynamic responses of plate are investigated.

Three dimensional solution of thick rectangular simply supported plates under a moving load

Dynamic behavior of continuous systems such as beams and plates, under a moving load is an important engineering subject. In this paper, 3D elasticity equations are solved by use of the displacement potential functions and the exact solution of a simply supported thick rectangular plate under moving load is presented. For this purpose, the governing equations in terms of displacements, Navier’s equations, are converted to two linear partial differential equations of forth and second order using displacement potential functions. Then the governing equations in terms of the potential functions are solved using the separation of variables and Laplace integral transform, satisfying exact initial and boundary conditions. In order to validate the present approach, the obtained results of this study are compared with the results of the classical theory of plates for thin and existing solutions for moderately thick plates. Also, it is observed that the speed of a moving load has an important effect on the dynamic response of plate.

Dynamic response of plates on elastic foundation under eccentric impact load

In this study, nonlinear three-dimensional finite element analysis has been used to conduct a numerical investigation of the effect of applied impact load on the foundation based on sandy soil using the finite element method by ANSYS (Version 11) computer program. The 8-node brick elements are used to model the concrete of foundation and the soil under the foundation which are denoted by Solid 65 for concrete and Solid 45 for the soil while the interface is modeled by using three-dimensional surface-to-surface (Target 170 and Contact 174) contact elements connected with concrete and soil. As a case study, a square concrete foundation with dimensions of 3×3×0.3 m placed on the foundation soil 15 m deep and 9 m away from the edge of plate is subjected to impact load. A parametric study is carried out to investigate the effect of several parameters including: foundation thickness, load eccentricity and amplitude of impact load. It was concluded that the load eccentricity increases the displacement and decreases the stress at the foundation center. This is attributed to non-uniformly distributed stresses on the loaded area, where the loads are concentrated locally within the loaded area. The presence of damping leads to a considerable decrease in the foundation displacements and stresses. The increase in the damping ratio reduces the vertical displacement of the foundation at the same time at all damping ratios.

Effect of forcing frequency on nonlinear dynamic pulse buckling of imperfect rectangular plates with different boundary conditions

The present study was aimed to investigate the influence of forcing frequency on nonlinear dynamic pulse buckling of imperfect rectangular plates with six different boundary conditions. The Galerkin's approximate method on the basis of polynomial and trigonometric mode shape functions is used to reduce the governing nonlinear partial differential equations to ordinary nonlinear differential equations. Moreover a numerical study of these governing equations is accomplished by Runge Kutta integration methods. The convergence of the polynomial and trigonometric mod shape functions are investigated to compute the dynamic response of plate. The effects of frequency of impulse loading and boundary conditions on the deflection histories of plate are studied. The dynamic response of plate subjected to impulsive loading with different forcing frequency is compared to results obtained by exponential impulsive loading. The results show that, by increasing the forcing frequency of impulsive loading, the maximum displacement of plate increases and converge with lower values to response of plate subjected to exponential impulse. Moreover, different boundary conditions and various pulse functions have significant influence on the dynamic response of the plate.

Analysis of cavitation time effect on elastoplastic response of underwater rectangular plate subjected to impulsive loading

This paper focuses on the cavitation effect on nonlinear elastoplastic deformation rectangular aluminum plate subjected to underwater explosion loading. Cavitation is a phenomenon that may be occurred for plates in the process of underwater explosion forming. The total pressure of the explosion becomes zero at the cavitation time, so that the governing equations of motion will be different before and after the cavitation. As a result, in terms of analysis and design, the cavitation time is significant in studying the behavior of a rectangular plate at underwater explosive loading. Based on Hamilton principle and variation method the nonlinear equations of motion of an underwater rectangular plate subjected to explosive loading are obtained. Exact linear dynamic response of plate is derived by employing the eigen function and nonlinear dynamic response of plate is derived by employing the finite difference method (FDM). The linear and nonlinear work hardening material modeling is considered to define the elastoplastic stress–strain relations. Return mapping algorithm is applied to calculate the stress and strain in any steps of loading. Then, the displacement, velocity and generated stress of plate during cavitation time are calculated. Using von Mises yield criterion, one can distinguishes the cavitation with in elastic or plastic regimes. By recognizing the time of cavitation in the range of elastic or plastic, the displacement and velocity field of plate are determined in duration of explosive loading. Results show that the cavitation time is on the order of 5–10 μs. Depending on amount of charge mass and stand-off, the cavitation time may occur in elastic or plastic regime. The results obtained of linear exact solution considering the linear work hardening material modeling are compared to results obtained of FDM considering the linear and nonlinear work hardening material modeling.

Exact solution for free vibration of thick rectangular plates made of porous materials

Free vibration analysis for thick rectangular porous plate saturated by inviscid fluid is presented. Material properties of the plate are assumed to vary through the thickness according to a simple cosine law in term of a coefficient related to plate’s porosity. Based on Reddy’s third-order shear deformation plate theory and considering the effect of fluid in pore network of the porous medium, the equations of motion are obtained. The plate is assumed to be simply supported on two opposite edges and the rest of edges are free, clamped or simply supported. For the sake of analytical solution, a unique approach is employed to decouple the equations of system. Exact frequencies rising from the solution are obtained for a rectangular porous plate made of Berea sandstone. The roles played by mechanical constraints on edges, fluid, geometrical dimensions of plate as well as the effect of the coefficient of plate porosity are investigated. It is found that porosity function affects significantly on the fundamental frequency of the system. Also, the effect of fluid on the dynamic response of plate is studied in detail.

Experimental Study on Effect of Vibratory Flap Position on Dynamic Response of Clamped Rectangular Plate with Cut-Out

In structural applications, plates with cut-out or holes are commonly used. The structure will deteriorate dynamically due to presence of cut-out and experiences amplification in vibrations. This paper presents an experimental study on effect of position of vibratory flap on dynamic response of a clamped rectangular plate with cut-out subjected to harmonic excitation. Vibratory flap is an auxiliary plate attached on the main plate as a cantilever plate and acts as a dynamic vibration absorber, which is used to reduce the vibration of the plate at first and second frequencies. Investigation has been carried out for different combinations of flap location and orientation through experimental sine sweep test. From the test it is found that, there is an optimum position where vibration suppression is more effective with improved dynamic response of the plate with cut-out in the presence of flap. The experimental results have shown good agreement with the published finite element analysis results.

Influence of the electric current waveform on the dynamic response of the electrified composites

The influence of the electric current waveform (DC, AC and pulsed currents) on the dynamic electromagnetic, thermal, and impact response of the composite plate is studied. The analysis includes solving Maxwell’s equations in the electrified composite plate to determine an electric-current induced magnetic field and heat transfer equation to estimate the electric-current-induced heating. In addition, the dynamic mechanical response of the electrified composite plate subjected to impact and various electromagnetic loads (DC, AC, pulsed electric currents and a constant magnetic field) is analyzed by solving a coupled system of equations of motion and Maxwell’s equations in the composite plate. The results show that the dynamic response of the plate is highly dependent on the characteristics of the electromagnetic field, and the pulsed electromagnetic fields are most effective in reducing vibrations caused by the application of dynamic mechanical loads.