Rectangular Plate System Research Articles

Subduction Dynamics and Mantle Pressure: 1. An Analytical Framework Relating Subduction Geometry, Plate Motion, and Asthenospheric Pressure

AbstractRecent work suggests that slab dip may be controlled by differences in dynamic pressure above and below the slab at mid‐asthenospheric depth, motivating exploration of how plate and slab motion are linked to dynamic pressure in the asthenosphere. This paper, the first of two companion papers, presents an analytical method for determining dynamic pressure and velocity in a thin asthenospheric channel, with linear viscosity, consistent with prescribed plate and slab kinematics. Slabs are explicitly incorporated as vertical barriers to asthenospheric flow. Dynamic pressure is expressed as sums of functions with two functional forms, Pedge and Pwall; the former generates discontinuities in velocity (but not pressure) at non‐slab boundaries, and the latter generates discontinuities in pressure (but not velocity) at boundaries with slabs. Application to simple rectangular plate systems demonstrates that asthenospheric velocities within about one trench length of slabs are insensitive to processes on the opposing side of the slab, that dynamic pressure scales linearly with trench length for a given plate aspect ratio and scales approximately linearly with the shortest plate dimension. Although dynamic pressure is quasisymmetrical across convergent plate boundaries that lack slabs, the presence of slabs creates discontinuity and asymmetry in dynamic pressure across subduction zones. When flux of asthenosphere into the lower mantle occurs adjacent to subducting slabs, dynamic pressure is decreased on the side of the slab where down‐flux occurs. This analytical method, applied to systems with multiple arbitrarily shaped plate boundaries, yields excellent results as benchmarked against 3‐D numerical solutions.

Stability analysis and numerical simulation of a composite laminated piezoelectric rectangular plate system

This paper investigates the stability behavior in three-degree-freedom composite laminated piezoelectric rectangular plate system based on the Routh-Hurwitz criterion and the normal form theory. Firstly, the stability behavior of the composite laminated piezoelectric rectangular plate is determined by applying the Routh-Hurwitz criterion. Then, the normal forms of the composite laminated piezoelectric rectangular plate systems for the case of one non-semi-simple double zero and two pairs of pure imaginary eigenvalues are obtained by using the normal form theory. Finally, numerical simulations are carried out to illustrate the main results.

Free and forced vibration analysis of arbitrarily supported rectangular plate systems with attachments and openings

Rectangular plates with different kinds of attachments (continuous or lumped) and various opening shapes are main constitutive parts of almost all engineering structures, e.g. aircrafts, bridges, buildings, ships, offshore structures, etc. Therefore, an assessment of their free and forced responses is generally very important for safe and rational structural design. In this paper, a range of different vibration problems inherent to rectangular plate systems, that can be solved by the energy based assumed mode method is considered. The concept of assumed mode method is outlined together with application of the mode superposition method to forced response calculation for plates under concentrated harmonic forces or enforced boundary displacement. Furthermore, complete mathematical model for vibration analysis of plate structures carrying arbitrary number of spring-mass systems is developed, based on the receptance method application. The plate is modelled by the Mindlin thick plate theory and Timoshenko beam theory is applied for stiffeners. The eigenvalue problem represented with a multi-degree-of-freedom system equation is formulated by Lagrange's equation of motion, while characteristic orthogonal polynomials having the properties of Timoshenko beam functions and satisfying the specified edge constraints are used as approximation functions. The corresponding in-house software is developed and dynamic responses of rectangular plate systems having different sets of edge constraints are analysed. Comparisons of the results with existing solutions and general finite element (FE) software are included, and very good agreement is achieved.

Experimental Study of Adaptive Fuzzy Sliding Mode Control for Vibration of a Flexible Rectangular Plate

In this paper, an approach is developed for active vibration control of flexible rectangular plate structures using control theory. The flexible rectangular plate system is first modeled through a new type of modeling method—discretization and reduced-order modeling method (DROMM); and second, the validity of the obtained new model is investigated by comparing the plate natural frequencies, static analysis, and forced vibration response analysis between a finite-element model and the new model. After validating the model, an adaptive fuzzy sliding mode multiple-input multiple-output (MIMO) controller is applied to the plate dynamic equation through the MATLAB/Simulink platform. The simulation and experimental results clearly demonstrate an effective vibration suppression capability that can be achieved using an adaptive fuzzy sliding mode MIMO controller.

Robust Nominal Model-Based Sliding Mode Robust Control for Vibration of Flexible Rectangular Plate

In this paper, we developed an approach for active vibration control of flexible rectangular plate structures using control theory. The flexible rectangular plate system is firstly modelled and simulated via a finite element method; and secondly, a new type of modelling method, and the state-space model are involved in the development of the equation of motion in state-space, which is efficiently used for the analysis of the system and design of control laws with a modern control framework. Then, the validity of the obtained new model is investigated by comparing the plate natural frequencies and forced vibration response analysis predicted by the finite element model with the calculated values obtained from new model. After validating the model, nominal model-based sliding mode robust MIMO controller is applied to the plate dynamics via the MATLAB/Simulink platform. The simulation results clearly demonstrate an effective vibration suppression capability that can be achieved using nominal model-based sliding mode robust MIMO controller.

Designing Laterally Loaded RC Stiffened Plates: Energy Balance Concept

Plates are most widely used structural systems to build and/or enclose the space along with some other structural elements, namely, walls, columns, and so forth. in any building. Design procedure for proportioning plates has been recommended in various design codes based upon empirical relations and some factors found on basis of the results of an extensive series of tests and well-established performance record of various plate/slab systems constructed in the past. These guidelines have a number of inherent limitations in the form of assumptions, thereby, forcing the designers to proportion the plate system within the domain of these limitations. A procedure to design reinforced concrete stiffened-plates is presented using an energy-balance concept and it can be used for both a single panel as well as multipanel rectangular plate system with any value of aspect ratio, number of panels, and orthotropy. To validate the results from the proposed design procedure, these are compared with the results from well-established literature on the plate analysis and are found to be in good agreement. Working procedure is illustrated with the help of design examples.

ADAPTIVE ITERATIVE LEARNING CONTROL FOR VIBRATION OF FLEXURAL RECTANGULAR PLATE

In this paper, we developed an approach for active vibration control of flexible rectangular plate structures using control theory. The flexible rectangular plate system is firstly modeled and simulated via a finite element method; and secondly, a new type of modeling method, and the state-space model are involved in the development of the equation of motion in state-space, which is efficiently used for the analysis of the system and design of control laws with a modern control framework. Then, the validity of the obtained new model is investigated by comparing the plate natural frequencies, mode shapes, statical analysis and forced vibration response analysis predicted by the finite element model with the calculated values obtained from new model. After validating the model, adaptive iterative learning MIMO controller is applied to the plate dynamics via the MATLAB/Simulink platform. The simulation results clearly demonstrate an effective vibration suppression capability that can be achieved using adaptive iterative learning MIMO controller.http://dx.doi.org/10.5755/j01.mech.17.5.724

Genetic algorithm-based identification of transfer function parameters for a rectangular flexible plate system

This paper focuses on an identification technique based on genetic algorithms (GAs) with application to rectangular flexible plate systems for active vibration control. A real coded GA with a new truncation-based selection strategy of individuals is developed, to allow fast convergence to the global optimum. A simulation environment characterizing the dynamic behavior of a flexible rectangular plate system is developed using the central finite difference (FD) techniques. The plate thus developed is excited by a uniformly distributed random disturbance and the input–output data of the system acquired is used for black-box modeling the system with the GA optimization using an autoregressive model structure. Model validity tests based on statistical measures and output prediction are carried out. The prediction capability of the model is further examined with unseen data. It is demonstrated that the GA gives faster convergence to an optimum solution and the model obtained characterizes the dynamic system behavior of the system well.

STATISTICAL ENERGY ANALYSIS OF TWO EDGE-COUPLED RECTANGULAR PLATES: ENSEMBLE AVERAGES

A wave approach is used in the Statistical Energy Analysis (SEA) of a system comprising two, edge-coupled, simply supported, rectangular plates. The response of the system is described in terms of “wave components”, each associated with a unique trace wavenumber along the coupling. An ensemble of plate systems is defined, and analytical expressions are found for the ensemble average input and coupling powers which result from “rain-on-the-roof” excitation of one of the plates. Two parameters which quantify the strength of coupling between plates are found, and four distinct regimes of wave component energy flow and storage are observed, involving weak and various forms of strong coupling. For the system considered, the plates may be wholly weakly coupled (all wave components are weakly coupled), or response may involve some mixture of weakly and strongly coupled components. In the case of the latter, the response is normally dominated by the strongly coupled components. The coupling is found to be strong in most systems of practical interest. The traditional SEA hypothesis of proportionality between the coupling power and the difference in subsystem mean modal energies is found to hold for the ensemble average response, for all coupling strengths, but not generally for the responses of individual ensemble member systems. A coupling loss factor is found, defined in terms of the ensemble averaged response. The traditional estimate of coupling loss factor, found by a wave approach in which semi-infinite subsystems and diffuse fields are assumed, is seen generally to be an over-estimate of the true value for the present system, except when the coupling?!is weak. It is also found that modal overlap has been proposed, which as an indicator of coupling strength and of the accuracy of the traditional coupling loss factor estimate, is inappropriate in this role for the rectangular plate systems considered.

The Free Vibration Of Circularly Cylindrical Shell And Plate Systems

A Rayleigh-Ritz approach, previously shown to apply to the free vibration of beam systems and rectangular plate systems, is applied to the free vibrational problem of systems comprised of circularly cylindrical, thin shells and thin annular or circular plates. The approach utilizes the concept of artificial springs which permit the convenient joining together of the components of each system and simplifies the selection of the trial functions for the Rayleigh-Ritz solution; in this work, orthogonal polynomials are used. Several example systems are treated: a cylindrical shell with a circular plate at each end (described in the literature as a drum or a hermetic can), a double cylindrical shell with an annular plate at each end, and a similar system in which the inner cylinder is extended. The approach is shown to yield rapidly convergent and accurate results.

The flexural vibration of rectangular plate systems approached by using artificial springs in the Rayleigh-Ritz method

A Rayleigh-Ritz approach for the study of the free vibration of systems comprised of rectangular plates is presented. The choice of the deflection functions for the component plates is simplified through the use of the concept of artificial springs being introduced at the joints between the plates and at the system boundaries; the shape functions for each component are thus those for a fully free plate. The necessary continuity and boundary conditions are enforced through allowing the appropriate spring stiffnesses to become very high compared with the stiffness of the components or, if flexible joints exist, the stiffnesses of the connecting springs are taken to be their true value. The applicability and the accuracy of the approach are illustrated through the consideration of three different types of systems: a stepped thickness plate, plates with slits (which approximate cracks) and box-type structures.

The flexural vibration of line supported rectangular plate systems

Orthogonally generated, polynomial functions are used in the Rayleigh-Ritz method to study the problem of the flexural vibration of thin rectangular plates which may be continuous over several supports in one or two directions or which may be arranged to form a box-like structure. It is demonstrated that the method may be used to tackle a variety of such plate problems, the difficulty of application not being significantly greater than that for the study of single-span plates.