Free Vibration of Tall Buildings using Energy Method and Hamilton’s Principle

Abstract

In a framed-tube tall building, shear wall systems are the most efficient structural systems for increasing the lateral load resistance. A novel and simple mathematical model is developed herein which calculates the natural frequencies of such tall buildings. The analyses are based on a continuous model, in which a tall building structure is replaced by an idealized cantilever beam that embodies all relevant structural characteristics. Governing equations and the corresponding eigen-problem are derived based on the energy method and Hamilton’s principle. Solutions are obtained for three examples; using the separation of variables technique implemented in MATLAB. The results are compared to SAP2000 full model analysis; and they indicate reasonable accuracy. The computed natural frequencies for structures 50, 60 and 70 storey buildings were over-estimate 7, 11 and 14 percent respectively. The computed errors indicate that the proposed method has acceptable accuracy; and can be used during the initial stages of designing of tall buildings; it is fast and low cost computational process.

Optimal Location of Energy Dissipation Outrigger in High-rise Building Considering Nonlinear Soil-structure Interaction Effects

“…NOR-OBF (3-20) implies a system whit normal outriggers provided at 3 th and 20 th stories. Similarly, buckling restrained outriggers that are located at 8 th and 20 th stories are represented by BRB-OBF (8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20).…”

“…The seismic performance of this system is highly dependent on the outrigger location. Several studies have been carried out to evaluate the lateral response of the outrigger system and to find the optimal elevation of outrigger [9][10][11][12][13][14][15][16][17][18][19]. The presence of outrigger in an outrigger braced system reduces the inter-story drift by engaging the perimeter columns and increases the lateral stiffness; however, it causes a difference in lateral stiffness of strengthened story in comparison to the adjacent stories [20].…”

Evolution of Outrigger Structural System: A State-of-the-Art Review

“…Preliminary analysis to find the natural frequency, mode shapes, and primary structural parameters is important in design, where most of the time the approximate methods are used like continuum method by considering Euler-Bernoulli or Timoshenko beam theory. Rahgozar [2] has introduced the novel approximate method in mathematical modeling of structure to find the preliminary structural parameter based on the energy method and Hamilton's principle. There is a need to introduce novel and simplified methods for the preliminary design approaches in structural system.…”

Free and Forced Vibration Characteristics Analysis of a Multispan Timoshenko Beam Based on the Ritz Method

“…e main research methods include variational iteration method [2,3], differential quadrature method [4,5], transfer matrix method [6], Ritz method [7,8], domain decomposition method [9][10][11], finite volume method [12], and finite element method [13][14][15]. In the framework of Euler-Bernoulli beam theory, Chen et al [16] put forward an energy finite element method (EFEM) to solve the high-frequency vibration response of beams with axial force.…”