Vibration Of Plates Research Articles

Free vibration and nonlinear transient analysis of blast-loaded FGM sandwich plates with stepped face sheets: Analytical and artificial neural network approaches

This study investigates the free vibration and transient dynamic response of functionally graded material (FGM) sandwich plates with stepped face sheets (FGM-SPSFS) supported by viscoelastic foundation under blast loading. The research focuses on the effects of geometric configurations and material property variations across segments. Each plate comprises three layers: a homogeneous hard core and two FGM face sheets, divided horizontally into two segments with differing face sheet thicknesses, which enhance structural stiffness while maintaining a consistent total thickness. The material properties of the sandwich plates follow a power-law distribution. The formulations are based on higher-order shear deformation plate theory and von Kármán geometric nonlinearity, and are solved using Galerkin’s method. Validation is achieved by comparing the results with published literature and finite element analysis (FEA). Artificial neural network (ANN) models are developed to predict natural frequencies without extensive computational runs, employing Bayesian Regularization (BR) and Levenberg–Marquardt (LM) algorithms in MATLAB. A new graphical user interface (GUI) tool facilitates frequency predictions using the proposed ANN model. Key findings indicate that modifications to the stepped face sheets and core layers affect stiffness, natural frequency, and vibration amplitudes. Increasing the core-to-total thickness ratio enhances stiffness, resulting in higher frequencies and reduced displacement amplitudes. The LM algorithm outperforms the BR algorithm, with errors generally below 1%, compared to 2% to 4% for BR with the log-sigmoid function. This study offers valuable insights into the design and analysis of FGM sandwich structures for engineering applications.

Vibration of orthotropic plates with and without damping

Vibration of orthotropic plates with and without damping

Nonlinear free vibrations of sandwich plates with FG GPLR face sheets based on the full layerwise finite element method

Nonlinear free vibrations of sandwich plates with FG GPLR face sheets based on the full layerwise finite element method

Influence of Porosity on Vibration of Porous FG Plates Resting on an Arbitrarily Orthotropic Winkler-Pasternak Foundation by PDDO

Influence of Porosity on Vibration of Porous FG Plates Resting on an Arbitrarily Orthotropic Winkler-Pasternak Foundation by PDDO

Vibrations of Plates and Shells with Attached Mass

Vibrations of Plates and Shells with Attached Mass

MAGPIE: a web-based, open-source framework for plate vibration analysis

The analysis and simulation of plate vibrations are central to many branches of science and engineering, specifically acoustics and musical acoustics. Well-developed plate theories exist, along with numerous simulation software packages, but they are seldom available in open-source form and are not easily accessible to a greater audience. MAGPIE is a framework for interacting with a novel finite difference scheme for plates under general elastic boundary conditions. Free, clamped, and simply supported boundary conditions are obtainable by setting stiffness coefficients to very small or large values. Boundary conditions are parameterised which allow for intermediate possibilities. A web browser based implementation of the framework includes interactive elements. Users begin by providing parameters for an isotropic plate. These parameters are then used to generate visualisations of the mode shapes from the finite difference scheme simulation. Elastic boundary conditions can then be changed on a continuous scale to see their effect on mode shapes. Results are then available for export in common image and data formats. MAGPIE aims to make it easier to explain concepts such as mode shapes to a wider audience and also provide a tool for research that is accessible to students, scientists and musical instrument builders.

Geometrically nonlinear vibrations of plate embedding a large circular acoustic black hole

The concept of acoustic black hole (ABH) designates a decrease in bending stiffness and a localized added damping within a thin structure aiming to localize and efficiently dissipate vibrations. The small thickness results in large amplitude vibrations, which suggests to take into account geometrical nonlinearities. The subject has been previously studied on a beam with a one dimensional ABH. Previous research studied a geometrically nonlinear plate embedding a one dimensional ABH. This study aims at solving the Von Karman equations for a variable thickness plate, via a modal projection using the eigenmodes obtained with a finite element model. The use of a finite element model in this context allows to take into consideration more complex geometries. The methodology is then applied to a rectangular plate embedding a large circular ABH with added damping. The convergence of the nonlinear coefficients is studied and time domain computations show the relative importance of the geometrical nonlinearity.

Influence of Transverse Normal Strain on Buckling and Vibration of Sandwich Plates

This study presents the buckling and free vibration behavior of simply supported square and rectangular sandwich plates. A third-order shear deformation theory considering both the transverse shear and normal deformations is used. The condition of zero transverse shear stresses on the top and bottom surfaces of the plate is satisfied. Hence, the present theory does not require the shear correction factor generally associated with the first-order shear deformation theory. Governing equations and boundary conditions are obtained using the principle of minimum potential energy. The closed-form solutions of simply supported sandwich plates are obtained. The effect of the side-to-thickness ratio and plate aspect ratio on buckling and free vibration responses of simply supported square and rectangular sandwich plates is examined. Parametric effects of face sheet thickness ratios and load factor upon the critical buckling load for uniaxial and biaxial buckling analysis of square and rectangular sandwich plates for different staking sequences are studied. All numerical solutions are obtained using MATLAB® programs. The results obtained from the present theory are compared with those from classical plate theory, first-order shear deformation theory, higher-order shear deformation theories, and the exact three-dimensional elasticity solutions as applicable.

Close Range and High-Resolution Detection of Vibration by Ultrasonic Wave Using Silicon-on-Nothing PMUTs.

This article presents a novel method for close-range, high-resolution ultrasonic time-of-flight (ToF) ranging using piezoelectric micromachined ultrasonic transducers (PMUTs) operating below the device resonance in air. The proposed method involves cross correlation techniques to accurately detect the reflected echo signals despite the presence of ringdown signal interference. For the experiments, a high fill-factor array of silicon-on-nothing (SON) PMUTs was used to enhance the signal-to-noise ratio (SNR). A thorough investigation was conducted to determine the optimal driving frequency for below-resonance ToF ranging, to improve resolution and minimize detection errors. The results of the experiments showed that the system was able to accurately measure sub- μ m vibrations of a metal plate placed 13 mm away from the PMUT array. The system exhibited the ability to detect target object vibrations with a peak-to-peak displacement under 6 μ m and sub- μ m floor noise. Moreover, the maximum detectable vibration frequency reached up to 1 kHz. This study highlights the potential of the proposed ToF ranging method in noncontact vibration monitoring applications across various fields, such as robotics and predictive maintenance.

Bandgap adjustment of a sandwich-like acoustic metamaterial plate with a frequency-displacement feedback control method

Several types of acoustic metamaterials composed of resonant units have been developed to achieve low-frequency bandgaps. In most of these structures, bandgaps are determined by their geometric configurations and material properties. This paper presents a frequency-displacement feedback control method for vibration suppression in a sandwich-like acoustic metamaterial plate. The band structure is theoretically derived using the Hamilton principle and validated by comparing the theoretical calculation results with the finite element simulation results. In this method, the feedback voltage is related to the displacement of a resonator and the excitation frequency. By applying a feedback voltage on the piezoelectric fiber-reinforced composite (PFRC) layers attached to a cantilever-mass resonator, the natural frequency of the resonator can be adjusted. It ensures that the bandgap moves in a frequency-dependent manner to keep the excitation frequency within the bandgap. Based on this frequency-displacement feedback control strategy, the bandgap of the metamaterial plate can be effectively adjusted, and the vibration of the metamaterial plate can be significantly suppressed.

Nonlinear metamaterial enabled aeroelastic vibration reduction of a supersonic cantilever wing plate

The violent vibration of supersonic wings threatens aircraft safety. This paper proposes the strongly nonlinear acoustic metamaterial (NAM) method to mitigate aeroelastic vibration in supersonic wing plates. We employ the cantilever plate to simulate the practical behavior of a wing. An aeroelastic vibration model of the NAM cantilever plate is established based on the mode superposition method and a modified third-order piston theory. The aerodynamic properties are systematically studied using both the timedomain integration and frequency-domain harmonic balance methods. While presenting the flutter and post-flutter behaviors of the NAM wing, we emphasize more on the pre-flutter broadband vibration that is prevalent in aircraft. The results show that the NAM method can reduce the low-frequency and broadband pre-flutter steady vibration by 50%–90%, while the post-flutter vibration is reduced by over 95%, and the critical flutter velocity is also slightly delayed. As clarified, the significant reduction arises from the bandgap, chaotic band, and nonlinear resonances of the NAM plate. The reduction effect is robust across a broad range of parameters, with optimal performance achieved with only 10% attached mass. This work offers a novel approach for reducing aeroelastic vibration in aircraft, and it expands the study of nonlinear acoustic/elastic metamaterials.

Frequency studies of nonlinear TSDT FGM plates in the linear shear corrections and thermal environment temperature

The effects of third-order shear deformation theory (TSDT) and varied linear shear correction coefficient on the vibration frequency of thick functionally graded material (FGM) plates with fully homogeneous equations under thermal environment and power law are investigated. The nonlinear coefficient c_1 term of displacement field of TSDT is included in the fully homogeneous equation under vibration of FGM plates. The determinant of the coefficient matrix in dynamic equilibrium differential equations under vibration can be represented in the fully fifth-order polynomial equation, thus the natural frequency can be found. The natural frequency with/without the nonlinear c_1 term of displacement fields is investigated. It is a significant novelty with the consideration of the nonlinear c_1 term in the frequency computation.

A MITC3+ element improved by edge-based smoothed strains for free vibration and buckling analyses of porous plates based on the first-order shear deformation theory

This paper presents the free vibration and critical buckling analyses of porous plates based on the first-ordershear deformation theory by the proposed three-node triangular element. The bending strain fields of the suggested element are enriched by the bubble node located at the centroid of the triangular element. The shear locking phenomenon is eliminated by the independent interpolations of the transverse shear strains following the MITC3+ technique. The edge-based smoothed (ES) strain method is employed to improve the in-plane strain fields. The influence of the porosity distributions, length-to-thickness ratios, porous coefficient, and boundary conditions on the free vibration and critical buckling load of the porous plates are evaluated through several numerical examples by the proposed element, namely ES-MITC3+ element. The obtained results are compared with other references to perform the efficiency of the proposed element.

Passive control of hydro-elastic vibrations of plates using shunted piezoelectric patches

Suppressing structural vibrations is a vital engineering requirement in many applications. In this study, an analytical model is initially developed for predicting the forced vibration response of a fluid-loaded plate with arbitrary boundary conditions attached to piezoelectric patches. Each piezoelectric patch is connected to a resonant shunt circuit consisting of a resistor and an inductor. Using the analytical model, it is demonstrated that the vibration control is effective for cantilever plates immersed in water. This is demonstrated first for the vibration control at individual resonance frequencies, and then at multiple resonance frequencies simultaneously using several separate piezoelectric patches. A parametric study is then performed to investigate how the efficiency of the method varies with the plate thickness, patch thickness, and patch size. It is observed that although the vibration reduction decreases steadily with increasing plate thickness, the shunted piezoelectric patches can still effectively damp the plate vibration, and their performance can be further improved by increasing the size and/or thickness of the patches.

Free Vibration of Composite Rectangular Plates with Internal Crack

In this work, rectangular sheets of composite materials consisting of epoxy with a single layer of fiberglass were studied with the internal crack at angles (0°, 90°) with the x-axis in the presence of nanomaterial TiO2 in proportions (1 wt%, 2 wt%, and 3 wt%), the study was experimental and numerical using the ANSYS. The sample mold was made from plastic using a CNC machine. One case was studied in both the experimental and numerical parts, which is clamped-clamped-free-free (CC-FF). After conducting the test, it was found that the crack negatively affects the rectangular composite plate, as it reduces the value of the natural frequency and increases the value of damping. However, in the case of adding the nanomaterial, it was found that the natural frequency increases with the increase in the percentage of nanomaterials, and the maximum value of the natural frequency was at 3% because it works to increase hardness rectangular plate stiffens and reduces damping. The error rate between the experimental and numerical parts did not exceed (9.717%).

A quasi-3D SinZZ model-driven multi-field Chebyshev FEM for nonlinear vibration control in multilayer multiferroic composite plates

This paper presents an advanced numerical method for modeling and mitigating nonlinear vibrations in thin multilayered fiber-reinforced multiferroic composite plates, addressing complex multi-physical interactions. The proposed methodology leverages a multi-physical coupling Chebyshev finite element formulation, utilizing high-order shape functions derived from Chebyshev polynomials. By integrating the strengths of spectral element methods and Legendre spectral finite element methods, this approach effectively overcomes challenges such as shear locking and spurious zero energy modes while ensuring high convergence rates in multi-physical problems. A quasi-3D refined model, incorporating the Murakami zig-zag model and sinusoidal shear deformation theory, is employed to accurately capture the nonlinear Von Kármán strain–displacement relationship and the magneto-electro-elastic coupling in multilayer structures with thickness-dependent material properties. To suppress nonlinear vibrations, the study utilizes a closed-loop multiphysical Chebyshev finite element model for time-domain analysis of viscoelastically damped systems, employing the Golla–Hughes–McTavish model. The results underscore the significant influence of multiferroic properties and the strategic distribution of ferroelectric fibers within the substrate on the dynamic behavior of the plate. The numerical validation, supported by rigorous verification, demonstrates the robustness of the proposed method in effectively simulating and controlling multilayer fiber-reinforced multiferroic composite plates. Additionally, this research highlights the potential for significant vibration reduction through semi-active damping mechanisms, offering valuable insights for practical applications in industries where precision and stability are critical.

A semi-analytical method using auxiliary sine series for vibration and sound radiation of a rectangular plate with elastic edges

This paper proposes an efficient semi-analytical method using auxiliary sine series for transverse vibration and sound radiation of a thin rectangular plate with edges elastically restrained against translation and rotation. The formulation, constructed by two-dimensional sine and/or cosine series, can approximately express the bending displacement, and calculate vibration and sound radiation under excitation of point force, arbitrary-angle plane wave, or diffuse acoustic field with acceptable accuracy. It is also applied for baffled or unbaffled conditions. A post-process program is developed to predict vibrating frequencies and modes, mean square velocity spectrum, and sound transmission loss via reduced-order integrals of radiation impedances. The method is validated by experiment and simulation results, demonstrating accurate and efficient computation using a single program for transverse vibration and sound radiation of a plate under different elastic boundary conditions and different excitations. Formulas given in this paper provide a basis for the code development on transverse vibration and sound radiation analysis of thin plates.

A nested non-intrusive stochastic isogeometric method for nonlinear thermal vibration of FGM plates under random loading

This paper introduces an adaptive nested non-invasive dynamic SIGA method based on RBFNN for the nonlinear thermal vibration analysis of FGM plates under random loading. This method is robust and accurate in high-dimensional input spaces regardless of the sample sequence, addresses the low convergence rate of QMCS, and solves the stochastic dynamic response probability density function under random loading. Firstly, the multidimensional input space for random loading is constructed based on several mutually independent random variables via the stationary Gaussian stochastic process simulation technique. The nonlinear FGM plate model subjected to random loading in the thermal environment is modeled using HSDT with von Kármán strain-displacement relation within the IGA framework. Subsequently, a nested non-invasive dynamic response surface analysis method, SIGA-RBFNN, is proposed based on the RBFNN technique. Analysis of the FGM plate response under random loading demonstrates that SIGA-RBFNN, compared to tensor-product-based SIGA methods, is less affected by sample sequence types. It effectively addresses high-dimensional stochasticity and offers significant advantages in robustness, accuracy, and efficiency. Finally, SIGA-RBFNN compensates for the low convergence speed of QMCS and successfully solves the FGM plate displacement response statistics and probability density function under random loading.

Nonlinear thermo-mechanical dynamic buckling and vibration of FG-GPLRC circular plates and shallow spherical shells resting on the nonlinear viscoelastic foundation

Nonlinear thermo-mechanical dynamic buckling and vibration of FG-GPLRC circular plates and shallow spherical shells resting on the nonlinear viscoelastic foundation

Vertical vibration analysis of rolling interface based on dynamic rolling force with variable friction characteristics

This study investigates the impact of variable friction characteristics at the rolling interface on the vertical vibration of plate and strip rolling mills. Based on the optimized Karman equilibrium theory, a dynamic rolling force model considering the front and back tension, elastic stretching, and rolling speed was established. The amplitude-frequency response equation of rolling mill system is solved by multi-scale method, and the influence of main parameters on vertical vibration of rolling mill system is analyzed. The results show that the increase of the first stiffness coefficient of dynamic rolling force leads to the decrease of the principal common amplitude of the system. On the contrary, when the third stiffness coefficient increases, the system exhibits a jump phenomenon. When the third stiffness coefficient of dynamic rolling force is reduced within a certain range, a stable and unique solution is obtained without jumping phenomenon. Moreover, the smaller the damping coefficient of the upper and lower roller system is, the larger the vibration amplitude is and the jump phenomenon occurs. Decreasing the external disturbance force can effectively reduce the system’s vertical vibration amplitude and suppress the resonance. In addition, with the change of external disturbance force, the roll system of the rolling mill shows a variety of complex motion states, such as periodic motion, double-periodic motion, and chaotic motion. The research results provide an effective theoretical reference for the suppression of vertical vibration of rolling mill.