Bending of Cylindrical Shells by Initial Parameter Method

1971 ◽  
Vol 93 (3) ◽  
pp. 845-850 ◽  
Author(s):  
H. M. Haydl
Keyword(s):  
Complete Solution ◽  
Cylindrical Shells ◽  
Axial Direction ◽  
Problem Formulation ◽  
Initial Parameter ◽  
Distinct Advantage ◽  
Parameter Method ◽  
Algebraic Equations ◽  
Unknown Parameters ◽  
Influence Coefficients

The initial parameter method, in the form proposed by V. Z. Vlasov, is presented and extended to the case of symmetric bending of cylindrical shells. It is shown that the method can be used efficiently for the solution of shells with and without intermediate supports. The loads applied to the shell can be arbitrarily distributed and discontinuous in the axial direction of the shell. The problem formulation has the distinct advantage that the complete solution contains at most two unknown “initial parameters.” These unknown parameters are determined from the boundary conditions. For shells on many supports the solution contains additional unknowns which can be determined from the support conditions. In any case, the solution consists of solving only two sets of algebraic equations. Tables of influence coefficients and loading functions for some common load cases are given in the paper. Some examples are worked out to illustrate the application of the method of initial parameters.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

Synthesis of Six-Bar Timed Curve Generators of Stephenson-Type Using Random Monodromy Loops

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Aravind Baskar ◽  
Mark Plecnik
Keyword(s):  
Rigid Body ◽  
Complete Solution ◽  
Numerical Algebraic Geometry ◽  
Algebraic Equations ◽  
Solution Sets ◽  
Root Finding ◽  
Rigid Body Motions ◽  
Joint Variable ◽  
Four Bar Linkage ◽  
Parameter Continuation

Abstract Synthesis of rigid-body mechanisms has traditionally been motivated by the design for kinematic requirements such as rigid-body motions, paths, or functions. A blend of the latter two leads to timed curve synthesis, the goal of which is to produce a path coordinated to the input of a joint variable. This approach has utility for altering the transmission of forces and velocities from an input joint onto an output point path. The design of timed curve generators can be accomplished by setting up a square system of algebraic equations and obtaining all isolated solutions. For a four-bar linkage, obtaining these solutions is routine. The situation becomes much more complicated for the six-bar linkages, but the range of possible output motions is more diverse. The computation of nearly complete solution sets for these six-bar design equations has been facilitated by recent root finding techniques belonging to the field of numerical algebraic geometry. In particular, we implement a method that uses random monodromy loops. In this work, we report these solution sets to all relevant six-bars of the Stephenson topology. The computed solution sets to these generic problems represent a design library, which can be used in a parameter continuation step to design linkages for different subsequent requirements.

Identification of Nonlinear Systems by Haar Wavelet

2004 ◽  
Author(s):  
Shy-Leh Chen ◽  
Keng-Chu Ho
Keyword(s):  
Nonlinear Systems ◽  
Least Square Method ◽  
Haar Wavelet ◽  
State Equation ◽  
Least Square ◽  
Algebraic Equations ◽  
Function Form ◽  
Unknown Parameters ◽  
Complete Orthogonal Basis ◽  
Unknown System

This study addresses the identification of autonomous nonlinear systems. It is assumed that the function form in the nonlinear system is known, leaving some unknown parameters to be estimated. It is also assumed that the free responses of the system can be measured. Since Haar wavelets can form a complete orthogonal basis for the appropriate function space, they are used to expand all signals. In doing so, the state equation can be transformed into a set of algebraic equations in unknown parameters. The technique of Kronecker product is utilized to simplify the expressions of the associated algebraic equations. Together with the least square method, the unknown system parameters are estimated. Several simulation examples verify the analysis.

The Matrix Effect and Application of the Multi-Parameter Optimization Method for X-Ray Spectrometric Determination of the Quantitative Composition of Clays

2018 ◽  
Vol 788 ◽  
pp. 108-113
Author(s):  
Anna Trubaca-Boginska ◽  
Andris Actins ◽  
Ruta Švinka ◽  
Visvaldis Švinka
Keyword(s):  
Chemical Composition ◽  
Parameter Optimization ◽  
Matrix Effect ◽  
Standard Addition ◽  
Optimization Method ◽  
Quantitative Composition ◽  
Parameter Method ◽  
X Ray ◽  
Influence Coefficients ◽  
The Matrix

Determining the quantitative composition of clay samples with X-ray fluorescent spectrometry is complicated because of the matrix effect, in which any element can increase or decrease the analytical signals of other elements. In order to predict the properties of clays, it is essential to know their precise chemical composition. Therefore, using the standard addition method was determined calibration and empirical influence coefficients, as well as the true composition of the elements. Farther, these coefficients were used to correct the matrix effect and develop a multi-parameter optimization method. It was determined that in clay samples, consisting of Si, Al, Fe, K, Mg, Ca, Na and Ti oxide formula units, the most significant contribution for matrix effect correction calculations was from the calibration coefficients. Moreover, the largest deviation from the X-ray fluorescent data and true values was determined in the MgO and Na2O cases. In this study was established, that the developed multi-parameter method can be successfully applied to determine the quantitative chemical composition of clay samples of similar compositions.

Initial-parameter method for bending oscillations of beams with hinges and oscillators

1982 ◽  
Vol 14 (12) ◽  
pp. 1713-1715
Author(s):  
M. A. Pavlovskii ◽  
A. N. Chemeris ◽  
V. S. Didkovskii
Keyword(s):  
Initial Parameter ◽  
Parameter Method

Elastic buckling of columns by initial parameter method

1976 ◽  
Vol 6 (2) ◽  
pp. 127-131 ◽  
Author(s):  
H.M. Haydl ◽  
A.N. Sherbourne
Keyword(s):  
Initial Parameter ◽  
Parameter Method ◽  
Elastic Buckling

scholarly journals Approximate guaranteed estimates for matrices in linear regression problems with a small parameter

2020 ◽  
pp. 89-103
Author(s):  
Oleksandr Nakonechnyi ◽  
Grygoriy Kudin ◽  
Petro Zinko ◽  
Taras Zinko
Keyword(s):  
Small Parameter ◽  
Unbiased Estimate ◽  
Sufficient Conditions ◽  
Approximate Solutions ◽  
Analytical Form ◽  
Parameter Method ◽  
Unknown Parameters ◽  
Operator Equations ◽  
Bounded Set ◽  
Linear Unbiased Estimate

The problem of finding linear unbiased estimates of the linear operator of unknown matrices — components of the observations vector, is investigated. It is assumed that the observation vector additively depends on a random vector with zero expected value, and the unknown correlation matrix belongs to a known bounded set. For the introduced class of linear estimates, necessary and sufficient conditions for the existence of solutions of operator equations that determine the unknown parameters of the vector estimate, are proved. The form of the guaranteed mean square error of the estimate is introduced on the sets of constraints of the problem parameters. The influence on the linear unbiased estimate of small perturbations of known rectangular matrices, which are the composites of the observations vector components, is also investigated. The analytical form is given through the parameters of the perturbed set of singularities for the introduced special operators that depend on a small parameter, which determine the corresponding operator equations, as well as their approximate solutions, in the first approximation of the small parameter method. A test example of solving the problem of finding a linear unbiased estimate under the condition of perturbation of both linearly independent and linearly dependent known observation matrices is presented.

On Time Domain Identification and Sensitivity Analysis Using Orthogonal Functions

1999 ◽  
Author(s):  
Ricardo P. Pacheco ◽  
Valder Steffen
Keyword(s):  
Sensitivity Analysis ◽  
Jacobi Polynomials ◽  
Operational Matrix ◽  
Algebraic Equations ◽  
Chebyshev Series ◽  
Unknown Parameters ◽  
Orthogonal Functions ◽  
Domain Identification ◽  
Second Order Differential Equations ◽  
Block Pulse Functions

Abstract Orthogonal functions can be integrated using a so-called operational matrix. This characteristic transforms a set of second order differential equations into algebraic equations which are easily solved. In the case of mechanical systems the unknown parameters can be determined from these algebraic equations. For this purpose, the input and output signals have to be expanded in time orthogonal functions. This technique can be also applied for sensitivity analysis. In this paper Fourier series, Legendre polynomials, Jacobi polynomials, Chebyshev series, Block-Pulse functions and Walsh functions are used to expand the signals as time functions.

Direct Position Analysis of a Particular Translational 3-URU Manipulator

2021 ◽  
pp. 1-22
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Problem Formulation ◽  
Parallel Manipulators ◽  
Equation System ◽  
Point Of View ◽  
Solution Technique ◽  
Algebraic Equations ◽  
Similar System ◽  
Position Analysis ◽  
Problem Formalization ◽  
Actuated Joints

Abstract Direct position analysis (DPA) of parallel manipulators (PMs) is in general difficult to solve. Over on PMs' topology, DPA complexity depends on the choice of the actuated joints. From an analytic point of view, the system of algebraic equations that one must solve to implement PMs' DPA is usually expressible in an apparently simple form, but such a form does not allow an analytic solution and even the problem formalization is relevant in PMs' DPAs. The ample literature on the DPA of Stewart platforms well document this point. This paper addresses the DPA of a particular translational PM of 3-URU type, which has the actuators on the frame while the actuated joints are not adjacent to the frame. The problem formulation brings to a closure-equation system consisting of three irrational equations in three unknowns. Such a system is transformed into an algebraic system of four quadratic equations in four unknowns that yields a univariate irrational equation in one of the four unknowns and three explicit expressions of the remaining three unknowns. Then, an algorithm is proposed which is able to find only the real solutions of the DPA. The proposed solution technique can be applied to other DPAs reducible to a similar system of irrational equations and, as far as this author is aware, is novel. Keywords: Kinematics, Position Analysis, Parallel Manipulators, Lower Mobility, Translational Manipulators

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