Dynamic Response Of Thin Plates Research Articles

Dynamic response of thin plate with damping subjected to in-plane compressive harmonic excitation

The dynamics of a rectangular plate with initial deflection excited by an external force comprising two components, a constant and periodically varying term, were analyzed by the authors of the paper. It was noted that the plate’s initial deflection was perpendicular to its surface, resulting in asymmetry. The partial differential equation governing the plate’s behavior was simplified to the one-degree-of-freedom Mathieu equation. The three methods have been used to analyze the system’s dynamics: the FEM, the sampled-based method and path-following. The equivalence of the full model with the reduced one was confirmed by the researchers. It was found that the Mathieu equation was suitable for investigating the dynamics of the rectangular plate across various parameters and for studying the sensitivity to initial conditions. It is shown that the reduced model is very efficient for detecting ranges of multistability and bifurcations sequence. A good agreement is also observed for values of stress obtained from full and reduced models.

Some aspects of dynamic buckling and dynamic response of thin plate under in-plane compression

The paper is devoted to investigating the response of thin orthotropic square plates subjected to in-plane time-dependent compressive load related to static buckling load. Two types of loads have been considered: pulse load with a duration corresponding to a period of natural frequencies of a plate; harmonic load with a different mean value. It has allowed us to analyse the plate behaviour under dynamic load and present the application of phase portraits, Poincare maps and Lyapunov exponents for dynamic buckling analysis. The system’s response is analysed based on the FEM model and one degree of freedom oscillator derived from the full continuous model. The research has been performed to check the thesis that the methods used in the analysis of the stability of motions of a rigid body can be used in dynamic buckling determinations and dynamic response analysis of thin-walled deformable structures. The results show that both considered approaches give reliable outcomes, and derived stability conditions are matched.

Preliminary Similarity Analysis on the Deformation Dynamic Response of Thin Plates Subjected to Blast and Impact Loadings

AbstractThe similarity and conditions for the similarity of deformation dynamic response of thin circular plates subjected to blast and impact loadings under certain conditions were studied by experimental tests and numerical simulation using air explosion and drop hammer impact loadings. The results revealed that the final deformed shapes of thin plates subjected to the two dynamic loadings are similar with less than 2 % difference in deflection and less than 8 % difference in deformed volume. The deformation similarity of plates subjected to blast and impact loadings can be achieved as the shock dimensionless number and the hammer shape satisfying given features. The deformation responses of the thin plates satisfying the constraints to blast and impact loadings are opposite. The key parameters of the blast and impact loading systems were obtained by the dimensional analysis using Buckingham π theorem. Based on these results, a similarity scheme was proposed. The numerical simulation was verified with the experimental results. In all, a novel method was established to study the similitude of analogous systems, which could be extended to other similar physical problems.

High-frequency dynamic response of thin plate with uncertain parameter based on average wavelet finite element method (AWFEM)

Abstract Due to the limitation caused by the low computational efficiency and parameters uncertainty, the Traditional Finite Element Methods (TFEMs) based on the general polynomials cannot provide reliable numerical solutions in the high-frequency domain. To this end, the Average Wavelet Finite Element Method (AWFEM) is proposed in this paper for dealing with the low computational efficiency and uncertain parameters at one time. Thus, the essential formulas of the AWFEM are derived based on the Wavelet Finite Element Methods (WFEMs) and average statistic algorithm. Besides, to divide the wide-frequency domain into the low and high-frequency domain, the Frequency Domain Index (FDI) is constructed based on the resonant mode number in bandwidth. Later, to investigate the proposed method’s prediction ability in the high-frequency domain, the dynamic response of the numerical models under various classical boundary conditions and non-uniform mass distributions are computed by AWFEM and Statistical Energy Analysis (SEA), respectively. And, the numerical results show that the AWFEM can be applied for predicting dynamic response in the high-frequency domain as same as SEA. Besides, the CPU time is less than 5 min to capture the numerical solutions based on personal computer. Most notably, it gives us an optional choice to predict dynamic response in the high-frequency domain only based on finite element models.

Dynamic response of thin plates on time-varying elastic point supports

In this article, an analytical-numerical approach is presented in order to determine the dynamic response of thin plates resting on multiple elastic point supports with time-varying stiffness. The proposed method is essentially based on transforming a familiar governing partial differential equation into a new solvable system of linear ordinary differential equations. When dealing with time-invariant stiffness, the solution of this system of equations leads to a symmetric matrix, whose eigenvalues determine the natural frequencies of the point-supported plate. Moreover, this method proves to be applicable for any plate configuration with any type of boundary condition. The results, where possible, are verified upon comparison with available values in the literature, and excellent agreement is achieved.

Nonlinear Vibrations of Viscoelastic Plates of Fractional Derivative Type: An AEM Solution

The nonlinear dynamic response of thin plates made of linear viscoelastic material of fractional derivative type is investigated. The resulting governing equations are three coupled nonlinear fractional partial differential equations in terms of displacements. The solution is achieved using the AEM. According to this method the original equations are converted into three uncoupled linear equations, namely a biharmonic (linear thin plate) equation for the transverse deflec- tion and two Poisson's (linear membrane) equations for the inplane deformation under time dependent fictitious loads. The resulting thus initial value problems for the fictitious loads is a system of nonlinear fractional ordinary differential equations, which is solved using the numerical method developed recently by Katsikadelis for multi-term fractional dif- ferential equations. Several plates subjected to various loads and boundary conditions are analyzed and the influence of the viscoelastic character of the material is investigated. Without excluding other viscoelastic models, the viscoelastic ma- terial employed herein is described by the generalized Voigt model of fractional order derivative. The numerical results demonstrate the efficiency and validate the accuracy of the solution procedure. Emphasis is given to the resonance re- sponse of viscoelastic plates under harmonic excitation, where complicated phenomena, similar to those of Duffing equa- tion occur.

Large free vibration of thin plates: Hierarchic finite Element Method and asymptotic linearization

The aim of this work is to study the free dynamic response of thin plates characterized by geometrical nonlinearities. To achieve this task, the equation of motion of the plate is first carried out through modeling by hierarchical finite element method whose interpolating shape functions are sinusoidal. Then, the study of the nonlinear vibrations was carried out by the development of asymptotic linearization and equivalent linearization methods in modal space. The nonlinear angular frequencies are successively deduced by exciting the corresponding vibrating mode of the structure. The confrontation of these results to those obtained by the iterative method in the physical space and to those found in the literature, showed a very good agreement between the various methods. From the elementary nonlinear frequencies we showed that there exists an equivalent linear dynamical system characterized by only one equivalent linear stiffness matrix. Numerical experiments were carried out on beams and thin plates of various dimensions ratios and boundary conditions. These numerical test simulations, whether in time space or frequency space, have showed that the nonlinear elastic energy is restored by the equivalent linear dynamical system. Nevertheless, we have to say that the dynamic effects of modes above the excited one are neglected.

Dynamic response of plates on elastic foundations due to the moving loads

This paper discusses the dynamic response of thin plates on the elastic foundations due to the moving loads by means of the variational calculus. In the text we take the mass of moving loads into account, treat a series of questions such as the forced oscillations, the influence surfaces of the flexions and the influence surfaces of the inner forces, resonance conditions and critical speed and so forth.

Plastic deformation and perforation of thin plates resulting from projectile impact

The dynamic response of thin plates subjected to projectile impact was studied experimentally by measuring projectile velocity, permanent deformation, dynamic strain and displacements and by examining the growth of plastic deformation and motion of the projectile with a high speed framing camera. Most of the experimental work was performed with ½ in. diameter steel projectiles, spherical or cylindro-conical in shape, centrally striking a 2024-0 aluminum plate, 0.050 in. thick and clamped on a 14 ½ in. diameter, at normal velocities ranging from 75 to 933 ft/sec. Projectile speeds were chosen so as to produce significant plastic deformation at the lower velocities and complete perforation at the higher velocities. The circular boundary of the plastic zone was found to propagate away from the point of impact at about 8800 in./sec at all impact velocities. A simplified large deflection solution for the final central deflection of a rigid/plastic linearly work-hardening plate showed good agreement with the data and correlation between various perforation theories and experimental data was found to improve with increasing projectile velocity.