Vibration Response Of Plate Research Articles

Vibration control of a cantilever plate immersed in water using shunted piezoelectric patches

Minimizing structural vibrations is an important engineering requirement in many applications. This study theoretically investigates the vibration control of an in-water cantilever plate using piezoelectric patches and resonant shunt circuits (including a resistance R and an inductance L in series or parallel). To do this, an analytical model for predicting the point-forced vibration response of a fluid-loaded cantilever plate with two piezoelectric patches is developed. The electromechanical coupling factor and optimum values for R and L are then estimated by considering the dynamics of the system in short-circuit and open-circuit conditions. The effect of piezoelectric patch size, location and electromechanical properties on the vibration response of the plate is also investigated through numerical examples. The results from this study show that optimized piezoelectric patches could provide a significant vibration reduction for underwater applications.

Shark skin biomimetic surface modification for plates: influence on free vibration response

Denticle microstructures in shark skin have intrigued researchers since they can be prospective for various marine applications due to their inherent properties which help in reducing drag as well as do not allow barnacles to form on its surface. However, any such alterations to create surface rivulets will invariably lead to changes in mass and stiffness, and thereby natural frequencies. Subsequently, the dynamic response will also be influenced as these hydrodynamic phenomena are strongly dependent on the natural frequencies. Therefore, in this work, an investigation of the effect of shark skin type biomimetic surface modifications on the free vibration response is investigated. The free vibration response of plates with shark skin is computed first using a high-fidelity numerical simulation in a commercial finite element package ABAQUS and then compared against a simplified semi-analytical model proposed herein. Results from both these methods agreed quite well. It is observed that shark skin denticles significantly influence the natural frequency without altering its mode shapes. It appears that adding shark skin like dermal denticles on the surface of a bare plate as an appendage helps in reducing the natural frequencies in each mode. The study also reveals that the reduction in the spacing between denticles reduces natural frequency even further. Therefore, the effect of these wettability altercations on free vibration response should be known apriori for efficient design.

Forced Vibration Response of Plates with Arbitrarily Oriented Branched Stiffeners

Forced Vibration Response of Plates with Arbitrarily Oriented Branched Stiffeners

Vibration of rectangular plates stiffened by orthogonal beams

This paper presents a new analytical solution for the vibration response of plates stiffened by orthogonal beams using a double finite sine integral transform technique. The compatibility conditions at the coupling interfaces and the boundary conditions of the plate are automatically defined in the transform. It is shown that the analytical model can accommodate various combinations of clamped and simply supported boundary conditions. The analytical model is then used to study the reproduction of the vibration response of an orthotropic plate. It is shown that an orthogonally ribbed isotropic plate can produce a closely matching vibration response to that of an orthotropic plate by carefully choosing an appropriate number of ribs and the rib properties in each plate direction.

Free vibration of functionally graded graphene platelet reinforced plates: A quasi 3D shear and normal deformable plate model

Present article deals with the free vibration response of composite plates which are reinforced with graphene platelets (GPLs). Each layer of the composite media may have different amount of graphene platelets which leads to a functionally graded (FG) pattern. Elastic modulus of the reinforced composite (RC) is evaluated based on the Halpin-Tsai model which captures the dimensions of the reinforcement. Following a quasi-3D plate model which captures the thickness stretching effects and non-uniform shear strains through the thickness, the complete set of governing equations dealing with free vibration response of the plate are obtained. These equations are six in number since the adopted plate theory has six unknowns. With the aid of the Navier solution suitable for plates with all edges simply supported, Fourier expansions are implemented for the essential variables of the displacement field. Closed form expressions are given to obtain the natural frequencies of FG-GPLRC plates. Present results may be valid for arbitrary thick plates. Results of the present study are compared with the available data in the open literature. After that novel results are given to obtain the frequencies of FG-GPLRC plates with arbitrary thickness. It is shown thatthe adopted theory accurately estimates the frequencies of FG-GPLRC plates.

A semi-analytical framework for nonlinear vibration analysis of variable stiffness plates

Focus of this paper is the development of a fast semi-analytical framework to address the nonlinear vibration response of plates with Variable Stiffness (VS) configuration. A formulation is developed based on a mixed variational theorem. A Ritz-like approach is employed for handling the spatial dependence, whilst several techniques are developed and compared for the temporal dependence: the method of averaging, a perturbation approach, an iterative procedure based on the Harmonic Balance Method (HBM) and a direct integration method. The proposed framework allows fast parametric studies to be performed for assessing the nonlinear vibration response of VS plates. The comparison against reference results demonstrates the validity of the proposed formulations in capturing the nonlinear free and forced responses with relative computational ease. This aspect is further exploited by presenting parametric studies, where the role of fiber path and boundary conditions is assessed. These studies aim at providing further understanding into the underlying mechanical response and illustrate the potential of the proposed semi-analytical approaches as a valuable mean to assist the design of VS plates.

Free vibration response of internally-thickness-tapered laminated composite square plates based on an energy method

In the present work, the free vibration response of symmetric linearly-thickness-tapered laminated composite square plates is considered for a variety of taper configurations. Since exact and closed-form solutions for the natural frequencies and mode shapes of the plates could not be obtained from the corresponding complex partial differential equations in space and time coordinates, the Ritz method in conjunction with the Classical Laminated Plate Theory (CLPT) and then the First-order Shear Deformation Theory (FSDT) is used to obtain the system’s mass and stiffness matrices for out-of-plane bending vibrations. The free vibration analysis of the plates is conducted using these system matrices and the natural frequencies and mode shapes are determined. Different boundary conditions are considered for the free vibration response of the plates and the computational work is performed in the MATLAB® environment. The convergence of the series expansions used for the out-of-plane displacement functions and the Ritz solutions for plates with various boundary conditions are established. The demonstration of solution accuracy is performed by conducting a so-called “layer reduction test” and also by comparing the results obtained by using the Ritz method with the solution obtained based on the Finite Element Method (FEM) using ANSYS®. A parametric study is then conducted to investigate the influences of taper configurations and taper parameters on the free vibration response of the composite plates.

Vibration Analysis of Piezolaminated Plates for Sensing and Actuating Applications Under Dynamic Excitation

The vibration characteristics of piezolaminated plates under coupled electromechanical loading are investigated using the finite element method. Higher order shear deformation theory is adopted to incorporate the effect of shear in the formulation. In the finite element formulation, an isoperimetric eight-nodded rectangular element is employed with linear through-the-thickness electric potential distribution. In the parametric study, the influences of geometry and boundary conditions on the vibration characteristics of piezolaminated plates are evaluated. Numerical results are presented for the frequencies of simply supported, clamped plates fitted with piezoelectric patches at the top and bottom surfaces of the laminate. For this, a model simulating the effect of the electromechanical loading with control potential is developed. Studies are also performed for piezolaminated plates with various thickness-to-span ratios, along with convergence test. The effect of the provision of piezoelectric layers to improve the vibration response of plates is investigated. This analysis reveals that the electro-mechanical coupling can strengthen the plate’s resistance to vibration.

Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation

This work examines vibration and bending response of carbon nanotube-reinforced composite plates resting on the Pasternak elastic foundation. Four types of distributions of uni-axially aligned single-walled carbon nanotubes are considered to reinforce the plates. Analytical solutions determined from mathematical formulation based on hyperbolic shear deformation plate theory are presented in this study. An accuracy of the proposed theory is validated numerically by comparing the obtained results with some available ones in the literature. Various considerable parameters of carbon nanotube volume fraction, spring constant factors, plate thickness and aspect ratios, etc. are considered in the present investigation. According to the numerical examples, it is revealed that the vertical displacement of the plates is found to diminish as the increase of foundation parameters; while, the natural frequency increase as the increment of the parameters for every type of plate.

Finite Element Analysis of Flexible Structure and Cavitating Nonlinear Acoustic Fluid Interaction under Shock Wave Loading

Abstract This paper describes a numerical model and its finite element implementation that used to compute the cavitation effects on nonlinear acoustic fluid and adjacent flexible structure interaction. The system is composed of two sub-systems, namely, the fluid and the flexible flat plate. A fully coupled approach using iterative implicit partitioned scheme was implemented in the present work which can account for the effects associated whit a mutual interaction. This approach included a compressible nonlinear acoustic fluid Eulerian solver and a Lagrangian solver for the flexible structure both in finite element formulation. A novel implementation of acoustic cavitation was made possible with the introduction of a simplified one-fluid cavitation model. The element-by-element PCG (Preconditioned Conjugate Gradient) solver together with diagonal preconditioning is used to solve the large equation system resulting from the finite element discretization of the governing equation of fluid domain. The capability of three different cavitation model, as the cut-off model, Modified Schmidt model and developed model are compared with each other in the evaluation of plate vibration response. Simulation results are presented on a large size shock tube, in which planar shock waves were impacting in “face on” configuration flat plates mounted at tube's end. Results are presented to demonstrate the capability of proposed solver in simulating cavitating nonlinear acoustic fluid. Obtained results show that impact forces caused impinging shock wave and reloading by cavitating region collapse have a considerable effect on the dynamic response of flexible plate.

Influence of cross-sectional discontinuity on the damping characteristics of viscoelastically supported rectangular plates

The geometry of a rectangular plate used in a structural application is an important design parameter that influences the vibrational response of the plate when it is subjected to an impact. In this study, the influence of a cross-sectional discontinuity on the vibration characteristics of viscoelastically supported plates was investigated. The discontinuity was induced at a specific location in the length-wise span. Experimental studies were performed to identify the effect of the discontinuity on the plate vibration response. The mode shapes and damping ratios of the plates with and without discontinuities in the cross-section were measured and compared. Forced vibration responses and modal properties were predicted using a numerical model. The variation in cross-sectional geometry was modeled to determine the changes in bending stiffness. The translational and rotational viscoelastic stiffnesses at the plate edges were used for modeling the vibration damping at the boundaries. This damping occurred at the contact surface between the plate and the fixtures. To investigate the effect of support stiffness on the vibration damping, flexural wave propagation analysis was performed with different boundary conditions. The ratio between the incident and reflected waves from the boundaries was predicted for flexural waves of different wavelengths. The predicted reflection ratios of the plate with and without the discontinuities were compared to the predicted loss factors using numerical analysis. The vibration energy dissipation at the viscoelastic supports was proportional to the measured modal damping.

Vibration experiments using a clamped circular elastic plate with edible granular material loading

An apparatus called the soil-plate-oscillator (SPO), designed to study flexural vibration of a soil loaded plate, consists of a thin circular elastic (acrylic) plate (8 in. diam, 1/8 in. thick) clamped below a thick-wall cylindrical aluminum tube supporting a vertical soil (or sand) column or other granular material. A small accelerometer attached to a 1 cm diam rare earth magnet (which is fastened to the center of the plate from below) is used to detect the plate vibration response. The plate is driven from below by an AC coil (located coaxially below the plate and securely fastened) using an amplified swept sinusoidal current. The charge amplified accelerometer signal is measured versus frequency by a spectrum analyzer. With interest in studying light density granular media (with various grain sizes) experiments were performed with uncooked brown rice, quick oats, un-popped popcorn kernels pretzel gold fish crackers, and pretzel nuggets. The resonant frequency reaches a minimum and then increases with i...

Static and dynamic analyses of nanoscale rectangular plates incorporating surface energy

In this paper, the Gurtin–Murdoch continuum theory is applied to develop a new continuum mechanics model for static and dynamic analyses of nanoscale rectangular plates. The relevant governing equations are established from basic principles. Analytical solutions for static and free vibration of nanoscale rectangular plates are presented for selected boundary conditions. A finite element method for the analysis of rectangular nanoplates is also developed to solve general cases that cannot be solved analytically. Expressions for stiffness and mass matrices and the load vector are derived by using a weighted residual formulation. A selected set of numerical results is presented to investigate the size-dependent static and free vibration response of plates and the influence of surface material properties and boundary conditions.

구조센서의 효율적인 구성을 통한 구조 음향연성 평판의 방사음 예측

In this paper, two types of techniques for the prediction of radiated sound pressure due to vibration of a structure are investigated. The prediction performance using wave-number sensing technique is compared to that of conventional prediction method, such as Rayleigh's integral method, for the prediction of far-field radiated sound pressure. For a coupled plate, wave-number components are predicted by the vibration response of plate and the prediction performance of far-field sound is verified. In addition, the applicability of distributed sensors that are not allowable to Rayleigh's integral method is considered and these can replace point sensors. Experimental implementation verified the prediction accuracy of far-field sound radiation by the wave-number sensing technique. Prediction results from the technique are as good as those of Rayleigh's integral method and with distributed sensors, more reduced computation time is expected. To predict the radiated sound by the efficient configuration of structural sensors, composed(synthesized) mode considering sound power contribution is determined and from this size and location of sensors are chosen. Four types of sensor configuration are suggested, simulated and compared.

Rejecting multiple-period disturbances: active vibration control of a two degree-of-freedom piezoelectric flexible structure system

In this study, an active vibration suppression control is presented for use in a two degree-of-freedom piezoelectric flexible structure system containing a rectangular plate driven by dc motors. A mathematical model involving a clamped-free-free-free cantilever flexible plate, piezoelectric transducer, and motor dynamics is derived for modal analysis and control design. To simplify the control design of this multivariable system, a two-stage design strategy is proposed because the plate motion exerts a comparatively small effect on the dc motors. Both the plate vibration and coupling effect in the motors are considered when designing a centralized motor tracking controller. Given a well-designed two-axis motor control system, piezoelectric actuators are used on the plate to perform efficient active vibration suppression control. Hybrid proportional-derivative and repetitive control methods are extended to manage the multiple-period disturbances and resonant excitation. Three sets of simulation experiments were conducted, focusing on suppressing the plate vibration response and demonstrating the effectiveness of the proposed method.

Numerical and Analytical Investigation in Radiated Noise by a Shock-Absorber

Noise Impact Shock-Absorber Acoustics ABSTRACT In this article, the radiated noise by a shock-absorber is studied. This particular shock-absorber is used in a heavy-gauge shearing line in order to stop the cut steel sheets. Three steps are followed to evaluate the propagated sound in the surroundings; first of all, the plate vibration response is specified after the impact. Secondly, the edges of the plate are substituted by a set of the monopoles to model the effects of the edges in the sound generation. Thirdly, the Rayleigh integral equation is used to calculate the sound generated by the surfaces of the plate. The finite element method is also employed to simulate the problem.

Vibration analysis of a trimorph plate as a precursor model for smart automotive bodywork

This study investigates the vibration characteristics of a proposed candidate structure for smarter car bodies. The material is conceived as a three-layer laminated structure in the form of a trimorph plate. The vibration response of the plate is investigated for large deflections by considering the effects of geometric nonlinearity. First, the governing equation for the mid-point deflection of the plate is developed based on classical laminate plate theory (CLPT). The governing equation is solved, and a simulation is run for different possible layer-stacking sequences. Comparisons are made between the nonlinear vibration response of this trimorph plate both with and without the effects of the von Kármán geometric nonlinearity. The results show that for the same material properties the different layer-stacking sequences produce different vibration responses, and from there it is concluded that layer-stacking sequencing is a basis for the definition of a suitable material configuration for high performance automotive applications.

Vibration and Damping Analysis of Plates with Partially Covered Damping Layers

The constrained-layer damping treatment is widely used to control the resonant response of vibrating structures, particularly in the automotive and aerospace industries. This technique requires design tools in order to select the best location, type and thickness of the damping and constraining-layer materials for optimum damping while minimizing the total weight of the damping treatments. In this study, a numerical tool is presented to analyze the vibration response of plates partially or fully covered with a constrained viscoelastic damping material. This tool is based on a finite element approach. The undamped plate structure is modeled using a discrete Kirchhoff theory (DKT) element. However, a sandwich plate element is specially derived to model the damped plate structure. This element is formulated in such a way that it is compatible with the DKT element. The natural frequencies and modal loss factors are derived from the modal strain energy method. The proposed approach is validated by comparing predictions with the results of various examples published in the literature. Hence, this approach is shown to predict accurately the damping characteristics of arbitrarily shaped sandwich plates, with different material properties and boundary conditions, fully or partially covered with constrained viscoelastic layers. The influence of the damping patch locations and the viscoelastic material's shear modulus on the vibration and damping characteristics is investigated. To damp the plate effectively using partial coverage, the damping patches must be distributed appropriately. To select the best damping patch locations, an indicator based on the energy dissipated through the viscoelastic layer is proposed.

Sound reduction of a vibrating plate via dimpling design.

The vibroacoustic performance of plates can be altered by different methods known as structural dynamic modification methods. One of these methods is the shape modification of plate surface. In this study, a method for reducing the sound radiation of vibrating plates is presented. The method based on creating dimples on the surface of a plate. The dimple can be defined as a local modification in the surface of a structure, which has a spherical shape. The dimples change the local stiffness of the plate without changing its mass. Also, they alter the mode shapes so as to reduce sound power, i.e., the radiated sound at some modes is inefficient due to low net volume velocity. The design method couples finite element method, for predicting plate vibration response, with optimization technique based on a genetic algorithm to minimize sound power radiation. The sound radiation is minimized either at a single frequency, or over a broad frequency band. The results show that dimples forming on the plate can achieve effective reductions in radiated sound power.

Accurate Vibration Analysis of Multilayered Plates Made of Functionally Graded Materials

Closed form solutions of free vibration problems in simply supported multilayered plates made of Functionally Graded Material (FGM) are dealt with in the present paper. Various refined plate theories are compared in the cases of both equivalent single-layer and layer-wise variable descriptions. Classical theories are compared to advanced ones, in which higher orders of expansion in the thickness direction are used for the transverse displacement. The plate governing equations are provided by applying Carrera's Unified Formulation (CUF) which, in this paper, is extended to the dynamics and free vibration response of plates embedding FGM layers. CUF permits one to handle the governing equations of the whole theory in a unified manner and a hierarchical evaluation of the natural frequencies of plates is therefore obtained. The results are given for one-layer and multi-layer plates embedding FGM layers. Conclusions are drawn regarding the accuracy of classical and advanced plate modelling for various vibration modes.