Forced vibration and natural frequencies of tall building frames

1959 ◽  
Vol 49 (1) ◽  
pp. 33-47
Author(s):  
John E. Goldberg ◽  
John L. Bogdanoff ◽  
Za Lee Moh
Keyword(s):  
Forced Vibration ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Tall Building ◽  
Trial And Error ◽  
Error Response ◽  
Building Frames ◽  
Building Frame ◽  
Harmonic Motion ◽  
Desk Computer

Abstract A procedure is presented for determining the response of a tall building frame to a harmonic motion of the ground. The procedure takes account of the elastic effects of the horizontal beams and requires the use only of a desk computer. Normal modes and natural frequencies can be determined to any desired degree of accuracy by trial and error. Response to any arbitrary motion of the ground can be determined in terms of the responses of the normal modes or, alternatively, by superposing the responses of the complete frame to each harmonic of the motion.

The Natural Frequencies of Free and Constrained Non-Uniform Beams

1960 ◽  
Vol 64 (599) ◽  
pp. 697-699 ◽  
Author(s):  
R. P. N. Jones ◽  
S. Mahalingam
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Normal Modes ◽  
Iteration Process ◽  
Conservative System ◽  
Basic System ◽  
Orthogonal Functions ◽  
Added Masses ◽  
The Given

The Rayleigh-Ritz method is well known as an approximate method of determining the natural frequencies of a conservative system, using a constrained deflection form. On the other hand, if a general deflection form (i.e. an unconstrained form) is used, the method provides a theoretically exact solution. An unconstrained form may be obtained by expressing the deflection as an expansion in terms of a suitable set of orthogonal functions, and in selecting such a set, it is convenient to use the known normal modes of a suitably chosen “ basic system.” The given system, whose vibration properties are to be determined, can then be regarded as a “ modified system,” which is derived from the basic system by a variation of mass and elasticity. A similar procedure has been applied to systems with a finite number of degrees of freedom. In the present note the method is applied to simple non-uniform beams, and to beams with added masses and constraints. A concise general solution is obtained, and an iteration process of obtaining a numerical solution is described.

Natural Frequencies and Normal Modes of a Spinning Timoshenko Beam With General Boundary Conditions

1992 ◽  
Vol 59 (2S) ◽  
pp. S197-S204 ◽  
Author(s):  
Jean Wu-Zheng Zu ◽  
Ray P. S. Han
Keyword(s):  
Boundary Conditions ◽  
Mode Shape ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Single Mode ◽  
Mode Shapes ◽  
Simulation Studies ◽  
Classical Boundary ◽  
First Time

A free flexural vibrations of a spinning, finite Timoshenko beam for the six classical boundary conditions are analytically solved and presented for the first time. Expressions for computing natural frequencies and mode shapes are given. Numerical simulation studies show that the simply-supported beam possesses very peculiar free vibration characteristics: There exist two sets of natural frequencies corresponding to each mode shape, and the forward and backward precession mode shapes of each set coincide identically. These phenomena are not observed in beams with the other five types of boundary conditions. In these cases, the forward and backward precessions are different, implying that each natural frequency corresponds to a single mode shape.

scholarly journals INFLUENCE OF A LIQUID ON THE NATURAL FREQUENCIES OF ALMOST CIRCULAR PLATES

2014 ◽  
Vol 06 (05) ◽  
pp. 1450052 ◽  
Author(s):  
MANUEL GASCÓN-PÉREZ ◽  
PABLO GARCÍA-FOGEDA
Keyword(s):  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Normal Modes ◽  
Virtual Mass ◽  
Circular Plates ◽  
Hankel Transformation ◽  
Fluid System ◽  
Surrounding Fluid ◽  
Good Agreement

In this work, the influence of the surrounding fluid on the dynamic characteristics of almost circular plates is investigated. First the natural frequencies and normal modes for the plates in vacuum are calculated by a perturbation procedure. The method is applied for the case of elliptical plates with a low value of eccentricity. The results are compared with other available methods for this type of plates with good agreement. Next, the effect of the fluid is considered. The normal modes of the plate in vacuum are used as a base to express the vibration mode of the coupled plate-fluid system. By applying the Hankel transformation the nondimensional added virtual mass 2 increment (NAVMI) are calculated for elliptical plates. Results of the NAVMI factors and the effect of the fluid on the natural frequencies are given and it is shown that when the eccentricity of the plate is reduced to zero (circular plate) the known results of the natural frequencies for circular plates surrounded by liquid are recovered.

scholarly journals Review on Seismic Analysis of Multistoried Building in Hilly Region

2021 ◽  
Vol 9 (12) ◽  
pp. 73-79
Author(s):  
Harsh Joshi
Keyword(s):  
Seismic Analysis ◽  
Response Spectrum ◽  
Center Of Mass ◽  
Time History ◽  
Lateral Loads ◽  
Base Shear ◽  
Building Frames ◽  
Building Frame ◽  
History Analysis ◽  
Hilly Region

Abstract: Due to sloping land and high seismically active zones, designing and construction of multistory buildings in hilly regions is always a challenge for structural engineers. This review paper focuses to establish a review study on the Possible Types of building frame configuration in the hilly region and he behavior of Such building frames under seismic loading conditions, and (3) The recent research and developments to make such frames less vulnerable to earthquakes. This paper concludes that the dynamics characteristics of such buildings are significantly different in both horizontal and vertical directions, resulting in the center of mass and center of stiffness having eccentricity at point of action and not vertically aligned for different floors. When such frames are subjected to lateral loads, due to eccentricity it generates torsion in the frame. Most of the studies agree that the buildings resting on slanting ground have higher displacement and base shear compared to buildings resting on plain ground and the shorter column attracts more forces and undergoes damage when subjected to earthquake. Keywords: Building frame configuration, Seismic behavior, Dynamic characteristics, Response spectrum analysis, time history analysis.

Wave-Induced Vibrations of an Axial-Loaded Immersed Timoshenko Beam Carrying an Eccentric Tip Mass with Rotary Inertia

2010 ◽  
Vol 54 (01) ◽  
pp. 15-33
Author(s):  
Jong-Shyong Wu ◽  
Chin-Tzu Chen
Keyword(s):  
Closed Form ◽  
Timoshenko Beam ◽  
Forced Vibration ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Rotary Inertia ◽  
Mode Shapes ◽  
Mode Superposition Method ◽  
Tip Mass

Under the specified assumptions for the equation of motion, the closed-form solution for the natural frequencies and associated mode shapes of an immersed "Euler-Bernoulli" beam carrying an eccentric tip mass possessing rotary inertia has been reported in the existing literature. However, this is not true for the immersed "Timoshenko" beam, particularly for the case with effect of axial load considered. Furthermore, the information concerning the forced vibration analysis of the foregoing Timoshenko beam caused by wave excitations is also rare. Therefore, the first purpose of this paper is to present a technique to obtain the closed-form solution for the natural frequencies and associated mode shapes of an axial-loaded immersed "Timoshenko" beam carrying eccentric tip mass with rotary inertia by using the continuous-mass model. The second purpose is to determine the forced vibration responses of the latter resulting from excitations of regular waves by using the mode superposition method incorporated with the last closed-form solution for the natural frequencies and associated mode shapes of the beam. Because the determination of normal mode shapes of the axial-loaded immersed "Timoshenko" beam is one of the main tasks for achieving the second purpose and the existing literature concerned is scarce, the details about the derivation of orthogonality conditions are also presented. Good agreements between the results obtained from the presented technique and those obtained from the existing literature or conventional finite element method (FEM) confirm the reliability of the presented theories and the developed computer programs for this paper.

Response Characteristics of Serially Connected Semisubmersibles

1999 ◽  
Vol 43 (04) ◽  
pp. 229-240
Author(s):  
H. R. Riggs ◽  
R. C. Ertekin
Keyword(s):  
Energy Loss ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Induced Response ◽  
Linear Wave ◽  
Response Characteristics ◽  
Response Modes ◽  
Wave Induced ◽  
The Impact ◽  
Large Aircraft

One design for a mobile offshore base is to link serially as many as five large semisubmersibles to form a platform long enough to support large aircraft. This paper investigates the linear, wave-induced response characteristics of serially-connected semisubmersibles. A major motivation of this study is to understand more completely the forces required to link semisubmersible modules. The impact of connector strategy and damping on the response, especially the connector forces, is investigated, and the response "modes" which contribute to the connector forces are evaluated in detail. It is shown that the response characteristics can be impacted significantly by the connection strategy, and that connector damping can be a significant source of energy loss when compared to radiation damping. The wet natural frequencies and normal modes are also determined and used to explain the response characteristics of different connection strategies. Although the analyses are based on a specific semisubmersible design, the results provide insight on how other systems of connected semisubmersibles would likely behave.

Determination of the first n modes of a tall building from a reduced eigenvalue problem

1964 ◽  
Vol 54 (4) ◽  
pp. 1233-1254
Author(s):  
Moshe F. Rubinstein
Keyword(s):  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Tall Building ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Story Building

Abstract The first n natural frequencies and mode shapes of an N degree of freedom structure (n < N) are derived from the solution of a reduced eigenvalue problem of order smaller than N. The reduced eigenvalue problem is formulated by using experience to select approximations to the first n modes desired. Accuracy is improved when more than n modes are selected. The method is illustrated by a study on an 18 story building.

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