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The Newmark-beta method is a method of numerical integration used to solve certain differential equations. It is widely used in numerical evaluation of the dynamic response of structures and solids such as in finite element analysis to model dynamic systems. The method is named after Nathan M. Newmark, [1] former Professor of Civil Engineering ...
Structural dynamics. Structural dynamics is a type of structural analysis which covers the behavior of a structure subjected to dynamic (actions having high acceleration) loading. Dynamic loads include people, wind, waves, traffic, earthquakes, and blasts. Any structure can be subjected to dynamic loading.
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case corresponding to small deflections of a beam that is subjected to lateral ...
In mechanics, virtual work arises in the application of the principle of least action to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement is different for different displacements. Among all the possible displacements that a particle may follow, called virtual ...
Rayleigh–Ritz method. The Rayleigh–Ritz method is a direct numerical method of approximating eigenvalues, originated in the context of solving physical boundary value problems and named after Lord Rayleigh and Walther Ritz. In this method, an infinite-dimensional linear operator is approximated by a finite-dimensional compression, on which ...
Newmark's influence chart. Newmark's Influence Chart is an illustration used to determine the vertical pressure at any point below a uniformly loaded flexible area of soil of any shape. This method, like others, was derived by integration of Boussinesq's equation for a point load. [1]
Hardy Cross method. The Hardy Cross method is an iterative method for determining the flow in pipe network systems where the inputs and outputs are known, but the flow inside the network is unknown. [1] The method was first published in November 1936 by its namesake, Hardy Cross, a structural engineering professor at the University of Illinois ...
Dunkerley’s formula (approximation) The whirling frequency of a symmetric cross section of a given length between two points is given by: where: E = Young's modulus, I = second moment of area, m = mass of the shaft, L = length of the shaft between points. A shaft with weights added will have an angular velocity of N (RPM) equivalent as follows: