Abstract: A simple explicit solution technique for problems in structural dynamics, based on a Modified Trapezoidal rule Method (MTM) approximation of the governing ordinary differential equations, is developed. The resulting conditionally stable explicit method (MTM) can be easily implemented and is extremely simple to use. Particular attention is focused herein on the concept of numerical stability of the proposed method for a free-vibrational response of a linear undamped Single-Degree-Of-Freedom system (SDOF). To examine the effectiveness, strengths, and limitations of MTM, error analyses for the natural period, the displacement, the velocity and the associated phase angle for a free undamped simple mass-spring system are derived and compared with Modified Euler Method (MEM) and the well-known Newmark Beta Method (NBM). Numerical examples for a SDOF system and a Multi-Degree-Of-Freedom (MDOF) system are presented to illustrate the strengths and the limitations of the proposed method.

Abstract: The objective of this study is to provide experimental data on bending oscillation of a deploying or retrieving beam cantilevered by a clamping device with thee pairs of rollers and springs, and to formulate a finite element analysis for treating the corresponding oscillation of the axially moving beam by using beam elements of varying length. The equation of motion of the beam derived is numerically solved with the aid of the modified Newmark method, the so-called alpha -method, to simulate the deflectional motion of the deploying beam measured experimentally.

Abstract: This paper presents an application of the rigid finite element method to modeling of flexible links of spatial systems. It is assumed that the movement of the base, with which the flexible system is connected, is known. The model presented takes into account large deflections of the link and an influence of centrifugal forces on deflections and deformations. Methods applied in dynamic analysis of manipulators with rigid links are used to derive the equations of motion. The results of numerical calculations are compared with those obtained by other authors who used the finite element approach.

Abstract: For non-classically damped structures subjected to evolutionary random seismic excitations, the non-stationary random responses are computed by means of a high precision direct (HPD) integration scheme combined with the pseudo excitation method Only real modes are used, so that the reduced equations of motion remain coupled for such non-classically damped structures, In the given examples, the efficiency of this method is compared with that of the Newmark method

Abstract: The application of adaptive finite element method to dynamic problems is investigated. Both the kinetic and strain energy errors induced by space and time discretization were estimated in a consistent manner and controlled by the simultaneous use of the adaptive mesh generation and the automatic time stepping. Also an optimal ratio of spatial discretization error to temporal discretization error was discussed. In this study it was found that the best performance can be obtained when the specified spatial and temporal discretization errors have the same value. Numerical examples are carried out to verify the performance of the procedure.

Abstract: The dynamic instability associated with the interactive buckling of ring stiffened composite shells under hydrostatic pressure is investigated. An optimally designed shell has its static local and overall buckling pressures close to one another. The shell response is then governed by the nonlinear interaction between the modes, which makes the shell very imperfection sensitive. A shell structure, such as a submarine vessel, can undergo suddenly applied overpressure or successive shocks. In the presence of imperfections, the dynamic instability will be triggered which would lead to a reduction of the load carrying capacity of the shell from that associated with quasistatic loading. Further, the large-amplitude vibrations that occur prior to reaching the dynamic limiting pressure can precipitate some form of material failure. The dynamic interactive buckling analysis developed in this study is a combination of the amplitude modulation technique and the asymptotic procedure. The nonlinear differential equations of motion for the structure so developed are solved by the Newmark method for time step integration along with Newton-Raphson iterations. Significant reductions in the load carrying capacity of the shells are observed as a combined result of the dynamic application of the load and the modal interaction. Damping was found to be of marginal influence in enhancing the dynamic limit load. Interlaminar stresses accompanying the dynamic response are monitored, and these reach significant values prior to the onset of dynamic instability.

Abstract: This thesis is concerned with the dynamics of low tension marine cables. These cables are widely used in the ocean environment for signal and power transmission applications. There are two main issues in the dynamic analysis of such cables. When the tension is zero, which is often the situation encountered at the seabed during cable laying, the cable geometric stiffness matrix becomes singular. The other issue is that the transformation from local co-ordinates to global co-ordinates made through Euler angles leads to a greater number of unknowns than the number of differential equations. The former problem can be overcome by taking into account the flexural rigidity of the cable. The latter problem can be overcome by assuming that one of the Euler angles is known. However, this procedure can introduce singularities on the formulation of the problem. A new three dimensional model for the dynamics of marine cables is presented in this thesis. The model takes into account the bending stiffness of the cable in order to overcome singularities in the geometric stiffness matrix. In order to overcome the problem owing to the use of Euler angles, a new displacement approach is introduced. This new displacement approach uses the differential geometry definition of curvature and torsion in order to establish the transformation from the local co-ordinates to the global co-ordinates. The general formulation of the dynamics of marine cables presented in this thesis is applicable to a wide range of cases such as towed cables, cable installation and cable recovery. In order to illustrate this new formulation the cases of towed cables and cable installation are investigated in the some detail. Solutions for the differential equations of motion are presented for two and three dimensions. The two dimensional solution is obtained through a finite element based technique which uses a weak Galerkin formulation for integration in space and the Newmark method for integration in time. The model's results are compared with full scale measurements. Simulations of the dynamic response of marine cables to vessel wave induced motions and vessel changes in speed are also presented. The three dimensional solution is obtained by expressing the equations of motion as functions of the Euler angles. The space integration is also performed by a finite element model but it uses a finite difference scheme for the time integration. This solution is then used to study the influence of sheared cross-currents in the cable's configuration. Finally, conclusions and suggestions for further research are presented.

Abstract: Synchronous motors produce damaging oscillating torques during startup. If the system is not properly analyzed and designed, the torsional excitation can be very destructive. This paper presents a systematic approach to the dynamic analysis of synchronous motor driven rotating machinery. The p-version of the finite element method is used in the formulation of the equations of motion which provides a great deal of simplicity in the modeling process. The convergence is achieved by increasing the polynomial order of the basis functions of the geometric elements. The system damping matrix can be constructed from the element level or can be calculated by specifying the critical damping factors for a given number of modes of interest. A modified Newmark integration method is employed in the nonlinear transient response calculation. The nonlinearity of the flexible resilient couplings can be easily implemented into this direct numerical integration algorithm. The dynamic stiffness and damping of the resilient couplings are updated at each time step to ensure the dynamic equilibrium. Two examples have been employed to illustrate the validity of the proposed algorithm. The effectiveness, accuracy, and simplicity of the use of p-method on the torsional vibration of synchronous motor driven trains are demonstrated in this paper.

Abstract: 中央差分法と平均加速度法 (Newmark のβ法 (β=1/4)) の特性を利用し, 非線形動的解析のための時間積分法を提案した. 本手法が, 調整外力の作用で生じる応答のうち, 低周波数成分は中央差分法の解に近似し, 高周波数成分は減衰性を示す特性を有することを理論的に説明した. 解析を数例実施し, この提案法の解の安定性, 精度について検証した. その結果, FEM等の多自由度の時間積分法として有効であることが確かめられた.

Abstract: A numerical method is presented to predict the nonlinear dynamic response of cables and cable skeletal structures by forward integration in the time domain. The method uses the conjugate gradients method to minimise the Total Potential Work, and can be formulated in terms of one of three sets of numerical integration equations : the linear change of acceleration equation, Newmark equations and Wilson equations. To illustrate the validity of the proposed methods and the computer programs developed, a highly non linear problem is solved and the results obtained are compared with those published by other investigators.

Abstract: In this paper the transmission line equation which describes the transient voltage and current distributions of a lightning stroke is employed. The finite element method is used to derive the element equations and one-dimensional linear elements are used to discretize the field region. The implicit Newmark time integration technique is used to convert the resulting second-order ordinary differential equations into a set of recurrence equations which are then solved at each time step. A numerical example is included and discussed.

Abstract: A damped trapezoidal rule method for numerical time-integration is presented, and its application in analyses of dynamic response of damped structures is discussed. It is shown that the damped trapezoidal rule method has features that make it an attractive approach for applications in dynamic analyses of structures. Accuracy and stability analyses are developed for the damped single-degree-of-freedom systems. Error analyses are also performed for the Newmark beta method and compared with the damped trapezoidal rule method as a basis for discussion of the relative merits of the proposed method. The procedure is fully explicit and easy to implement. However, since the method is an explicit method, it is conditionally stable. The methodology is applied to several example problems to illustrate its strengths, limitations and inherent simplicity.

Abstract: When we calculate the blade response caused by bird impact with the finite element method,it is necessary to solve a set of nonlinear dynamic coupled equations A reasonable plan for solving the coupled equations must be drawn up at first in order to improve the precision of the solution and to reduse the calculation cost The following problems must be considered in making the plan,ie, how to calculate the coefficient matrixes,how to select the method for solving the nonlinear dynamic coupled equations,and how to select the principal calculation parameters When the nonlinear transient responses of flat blades under the impact loads are calculated by the program ADINA, the problems mentioned above are solved as followsThe mass matrix is established by the procedure of lumping mass In establishing the stiffness matrix,the effect of both elastic-plastic and large deformation is considered The nonlinear dynamic coupled equations are solved by the Newmark method,and the equilibrium iteration is conducted by the BFGS method The selection of principal calculation parameters such as the time step,the convergence error,the maximum of iteration number and so on are also introduced,and the important effect of the time step on the response calculation is shown by the calculation process with an example

Abstract: The numerical time step integrations of PDEs are mainly carried out by the finite difference method to date. However, when the time step becomes longer, it causes the problem of numerical instability. The explicit integration schemes derived by the single point precise integration method given in this paper are proved unconditionally stable. Comparisons between the schemes derived by the finite difference method and the schemes by the method imployed in the present paper are made for diffusion and convective-diffusion equations. Numerical examples show the superiority of the single point integration method.