Dynamic Influence Coefficients Research Articles

Development of Vibration Analysis Algorithm for Joined Conical-cylindrical Shell Structures using Transfer of Influence Coefficient

This describes the formulation for the free vibration of joined conical-cylindrical shells with uniform thickness using the transfer of influence coefficient. This method was developed based on successive transmission of dynamic influence coefficients, which were defined as the relationships between the displacement and the force vectors at arbitrary nodal circles of the system. The two edges of the shell having arbitrary boundary conditions are supported by several elastic springs with meridional/axial, circumferential, radial and rotational stiffness, respectively. The governing equations of vibration of a conical shell, including a cylindrical shell, are written as a coupled set of first order differential equations by using the transfer matrix of the shell. Once the transfer matrix of a single component has been determined, the entire structure matrix is obtained by the product of each component matrix and the joining matrix. The natural frequencies and the modes of vibration were calculated numerically for joined conical-cylindrical shells. The validity of the present method is demonstrated through simple numerical examples, and through comparison with the results of previous researchers.

Aeroelastic Analysis of Wing Structures Using Equivalent Plate Models

In this paper we formulate the Reissner-Mindlin first order shear deformation model based governing equation for a non-isotropic plate. The governing equations are cast as a set of coupled Helmholtz equations which are then expressed as integral equations where the Green’s functions are expressed in terms of the traditional Hankel functions of the first kind. The integral equations are then solved to determine the static and dynamic influence coefficients which are inverted to generate the stiffness and dynamic matrices. In order to demonstrate the application of these computations we consider the aeroelastic analysis of a wing structure, modeled as an equivalent plate. The unsteady aerodynamic generalized loads are estimated by employing the Doublet-Lattice method which is coupled with the compatible numerical evaluation of the structure’s dynamic influence coefficient matrix without any need for independent vibration analysis. We have demonstrated that by employing appropriate equivalent anisotropic plate models, and a variant of the classical Nyquist plot to assess the relative stability of the system, it is possible to capture, simulate and predict all the instability features of real aircraft wings. These models are proving to be particularly useful in the synthesis of active controllers for smart structures.

IDENTIFICATION USING THE ALGORITHM OF SINGULAR VALUE DECOMPOSITION—AN APPLICATION TO THE REALISATION OF DYNAMIC SYSTEMS AND TO FAULT DETECTION AND LOCALISATION

A new algorithm—the generalised singular value decomposition (GSVD)—is used in the field of identification and fault detection and localisation. By using the GSVD a simultaneous factorisation of two matricesAandBis possible. Therefore, a state space realisation of a structure can be established from measured data of a real system. The measured data are arranged in Hankel matrices and the parameters of the state space equation can be found with a special procedure using the generalised singular value decomposition. Changes in the dynamic system behaviour that can be detected by new measurements and realisations can be used for fault detection and localisation. A sensitive method for this task is established, with the singular value decomposition in combination with dynamic influence coefficients, that result from a spectral decomposition of the weighting operator.

A method of vibrational analysis using a personal computer (Suggested transfer influence coefficient method)

This paper describes the development of an algorithm of the free vibrational analysis suitable for a personal computer. The present method is based on the concept of the successive transmission of the dynamic influence coefficients at every station and so overcomes the numerical difficulties which occur normally in using transfer matrices when computing higher natural frequencies and when intermediate elastic supports are very stiff. The computational time of the transfer influence coefficient method for a discrete parameter system is about one eighteenth the value for the transfer matrix method. A rotating shaft analysis demonstrates the numerical accuracy of the method on a personal computer.

Dynamic Modeling of Serial Manipulator Arms

To design and precisely control a manipulator requires a representative dynamic model of the system. This paper presents the derivation of a rigid-link model for the serial manipulator, which reduces all of the arm’s dynamic properties to their effective values at the generalized inputs. The component terms of the model are readily calculated from the dynamic influence coefficients, which are based only on the geometry of the system. All necessary influence coefficients for serial manipulators are given in a particularly simple form. The model formulation keeps the system parameters and the input dynamics explicit in the controlling equations of motion, such that analysis and dynamic response results can be obtained in the most direct manner. Dynamic analysis results for an industrial manipulator are presented.

Use of dynamic influence coefficients in forced vibration problems with the aid of fast fourier transform

The use and importance of dynamic stiffness influence coefficients in flexural forced vibrations of structures composed of beams are described. The dynamic forces can be either harmonic or general transient forces. The dynamic influence coefficients are defined in the Fourier transform plane, are computed there and are given in Table form for a uniform free-free beam. The dynamic problem formulated in terms of these coefficients is reduced to a static form. The dynamic response is obtained, in general, by a matrix inversion in the Fourier transform plane and a numerical inversion, based on the Cooley-Tukey algorithm, of the transformed solution. Structural examples of forced vibrations of a simple beam and a rigid frame illustrate the use of dynamic coefficients and demonstrate their advantages over other known methods in accuracy, simplicity of formulation and speed of computation.

Soil-structure interaction with separation of base mat from soil (lifting-off)

In reactor buildings having a separate base mat and a shield-building (outer concrete shell) of large mass, large overturning moments are developed for severe earthquake loading. The standard linear elastic half-space theory is used in the soil-structure interaction model. For a circular base mat, if the overturning moment exceeds the product of the normal force (dead weight minus the effect of the vertical earthquake) and one-third of the radius, then tension will occur in part of the area of contact, assuming distribution of stress as in the static case. For a strip foundation the same arises if the eccentricity of the normal force exceeds a quarter of the total width. As tension is incompatible with the constitutive law of soils, the base mat will become partially separated from the underlying soil. Assuming that only normal stresses in compression and corresponding shear stresses (friction) can occur in the area of contact, a method of analyzing soil-structure interaction including partial lifting-off is derived, which otherwise is based on the elastic behaviour of the soil. A rigorous procedure to determine the nonlinear impedance function of a rigid plate of arbitrary shape, only in partial contact with the elastic half-space, is developed. Complex dynamic influence coefficients for displacements are used which can either be determined with the finite-element method or based on solutions of displacements on the surface of an elastic half-space at a certain distance from a rigid subdisk. Constant and variable stiffness methods of solving the non-linear equations of motion are explained which also determine the area of contact. Slipping of the entire mat or of a part thereof can also be taken into consideration. A simpler approximate method is discussed. For a given force and moment acting on the rigid plate, the area of contact is determined by iteration or based on quadratic programming techniques using the static influence coefficients for displacements. The complex-valued impedance function is estimated by substituting an equivalent circular plate for the actual area of contact. Transforming the equivalent lumped system to the centre of the plate, the non-linear stiffness and damping matrices of the soil are derived. Formulae are given for the partial lifting-off of a disk and a strip. The results of the numerical method are compared to rigorous solutions for full contact. As an example, the dynamic response of the reactor building of a 1000 Mw plant to earthquake motion is calculated using the rigorous and approximate methods. Parametric studies are carried out. The influence of the frequency on the impedance function and on the distribution of stress in the area of contact, which determines the beginning of lift-off, is discussed.

Use of dynamic influence coefficients in forced vibration problems with the aid of Laplace transform

The use and importance of dynamic stiffness influence coefficients in flexural forced vibrations of structures composed of beams are described. The dynamic forces can be either harmonic or general transient forces. The dynamic influence coefficients are defined in the Laplace transform plane, are computed there and are given in tables for uniform beams under various end conditions. The dynamic response is obtained, in general, by a matrix inversion in the Laplace transform plane and a numerical inversion, based on interpolation concepts, of the transformed solution. Structural examples of forced vibrations of a simple beam and a rigid frame illustrate the use of dynamic coefficients and demonstrate their advantages over other known methods in accuracy, simplicity of formulation and speed of computation.

Sound Radiation From Submerged Cylindrical Shells of Finite Length

A method is presented for the evaluation of the pressure field which is induced in an acoustic fluid by the harmonic axisymmetrical excitation of a submerged thin elastic circular cylindrical shell of finite length. The approach utilizes dynamic influence coefficients from the in vacuo vibrations of the shell and a potential theory source approach for the fluid. Compatibility conditions on the shell-fluid interface allow the determination of the fluid-source strength coefficient and, subsequently, the pressure and/or velocity fields in the fluid. Provision is made for the inclusion of possible viscous-damping effects. Numerical results are presented for several structural configurations.