PROBLEM6: In a forced vibration test under harmonic excitation it was noted that the amplitude of motion at res- onance was exactly four times the amplitude at an excitation frequency 20% higher than the resonant frequency. Determine the damping ratio of the system. Good luck

PROBLEM6: In a forced vibration test under harmonic excitation it was noted that the amplitude of motion at res- onance was exactly four times the amplitude at an excitation frequency 20% higher than the resonant frequency. Determine the damping ratio of the system. Good luck

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: For the thin-walled tube shown, the polar moment of inertia is about * .21714.6 mm^4 2 mm 12mm True…

A: Given data in question Tube Inner diameter Thickness To find out Polar moment of inertia

Q: a) compute the magnitude of the stress at point P, when the externally applied stress is 140 MPa. b)…

A: It is given that :

Q: 10 kN/m 25 kN m A E B IC 1 m 1m 3 m 2 m Fig. P4.31 DEFLECTIONS IN BEAMS USING DOUBLE INTEGRATION…

Q: Q1/For the beam shown in Fig.1, using the Double - Integration method determine: The deflection at…

Q: Show that the expression for damping in terms of two frequencies wa and wp is given by the equation…

A: For damping - Dtheoratical = 12Dexperimental⇒11 - β2 + 2βθ212 = 1212θ×11 - θ2⇒11 - β2 + 2βθ212 =…

Q: With modern technology, the index of refraction of a piece of glass can be varied linearly from the…

Q: Internal static analysis has both advantages and disadvantages.

A: Concept- Internal static analysis- Static analysis is an examination of the application's internal…

Q: a. What is the u(t=2 s) function for damped free vibration response for the {=2% ? Calculate the…

A: Total stiffness = K1+K2 = 2KcolumnKcolumn = = Kcolumn = 4.44

Q: Show that the expression for damping in terms of two frequencies Wa and wh is given by the equation:…

A: Given data in question External frequency Natural frequency Soil dynamics subject To find out…

Q: Problem Sets - 1: The thin-walled tube is used as a beam to support the uniformly distributed load…

Q: Use Virtual Work Method to answer the questions below considering the truss shown. Use the…

Q: A simply supported beam, having a length of 9.0 m, is being subjected to a concentrated live load of…

Q: 1 t/m - 3m Fig. 1.112 4mt 6m Fig. 1.113 3t/m (2) Using the double integration method, derive the…

A: EI = Elastic modulus = 5000m 2t The double-integration method of determining the equation of the…

Q: ФЫ В АП Р О В А П Р О Л ДЗАПРОЛДЖЭ ЯЧСМИТЕЧСМИТЬБНСМИТЬБю SOLVE STEP BY STEP IN DIGITAL FORMAT…

A: Three figures are shown in the figure above. We have to find out the degree of static Indeterminacy.…

Q: Figure P9-84 represent the steel shaft of a machine. The gears mounted on the arrow produce the…

Q: Solve for the vertical deflection at A

Q: Railway track in a mixed-gauge allows trains of different gauges to use the same track True False

A: As per guidelines we need to answer only first question so please repost rest questions separately

Q: A 30-m band standardized at 20°C was found to be 30.003 m. At what temperature is the tapeexactly30…

Q: In the figure, the table of a certain weight is supported by rods with flat and steel rods. The…

A: Structural dynamics is a type of structural analysis that deals with the behaviour of a structure…

Q: A vibrating system of mass 20 kg and spring with stiffness 32 N/mm is viscosity damped so that the…

Q: Which of the following is false regarding factor of safety in the design of structures? a. It…

Q: Q.121 A vibrating system of mass 20 ka and spring with stiffness 32 N/mm is viscosly damped so that…

Q: Q2/ The simple supported beam ABC in Fig2. Carries a distributed load of maximum intensity wo over…

Q: Consider a prismatic rod of length I made out of uniform, homogeneous material with modulus of…

A: Solution: a) The axial vibration (longitudinal vibration) natural frequencies: Axial vibrations of…

Q: a) L Question 7: A massless beam ABC of span L and con- stant flexural rigidity EI is simply…

Q: In order to calibrate the digital readout of a hydraulic cylinder a cantilever beam with a width of…

Q: PROBLEMS: An SDF system is excited by a sinusoidal force. At resonance the amplitude of displacement…

Q: DOUBLE INTEGRATION wA = 6 kN/m wB = 15 kN/m L = 8 m The first constant of integration, c1?…

A: Free body diagram - Force in the vertical direction - RA + RB = 6×8 + 1215-6×8⇒RA + RB =84KN…

Q: Further questions (submit on another sheet; stapled to this one) 6. 1,0 x 2,0 rectangular steel…

A: Question is based on the rectangular steel plate subjected to forces. Dimension of plate and…

Q: When reducing a system of parallel, non-concurrent forces acting on a body to a single resultant…

A: Solution: The above statement is a true statement.

Q: The diving board shown in Fig. Q4 has been designed for people upto 2 stone in mass (Weight =…

A: To determine:1) The reactions and moments acting on the board2) The maximum deflection of the…

Q: Neslyn used a 30m steel tape used to measure a certain distance. It was later found that the tape is…

A: Correction for tape length = -0.05m Correction for temperature Ct = Lα(Tm-T0) Assuming Coefficient…

Q: 4. The schematic representation of a two-degree of freedom system is shown below. For the given…

Q: PROBLEM4: The mass m, stiffness k, and natural frequency , of an undamped SDF system are unknown.…

Q: The beam shown in Fig. P.13.8 has its central portion reinforced so that its flexural rigidity is…

A: First draw the Bending moment diagram Vertical Reaction at A = W2(upwards) Vertical Reaction at E =…

Q: A closely-coiled helical spring of round steel wire 5 mm in diameter having 12 complete coils of 50…

A: Diameter of the closely-coiled helical spring d=5 mm, Number of coils n=12, Mean diameter D=50 mm,…

Q: 1) Find the transfer function from the force F (applied at x= L/3 the bar) to the motion Y of the…

A: Solution: Spring force is given by; →F=-kx ⋯⋯⋯⋯⋯⋯(1) -kx=ma ⋯⋯⋯⋯⋯⋯(2) ma+kx=0…

Q: A collimated beam of sodium light (λ = 589.3 nm) is incident normally on a Wollaston prism…

Concept explainers

FEA for Dynamic Problems

Finite element analysis or FEA is a computational tool that evaluates the approximate solution for a particular engineering problem. The tools provided by FEA help to evaluate the solutions of partial differential equations (PDEs) computationally following a numerical approach. Solutions of the PDEs can also be performed by following traditional algebraic approaches, but when the problem gets towards the complex side, it becomes very tedious and almost impossible to arrive at the solutions. In such cases, the FEA fulfills the purpose by evaluating the equations following multiple time steps and iterations. The more the time steps and iterations, the more accurate the solution. The solution plotted by FEA analysis and mathematical approaches varies asymptotically.

Question

PROBLEM6:
In a forced vibration test under harmonic excitation it was noted that the amplitude of motion at res-
onance was exactly four times the amplitude at an excitation frequency 20% higher than the resonant
frequency. Determine the damping ratio of the system.
Good luck

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given data:

VIEW

Step 2: Calculate the damping ratio of the system.

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions

Pick up the correct statements about Free Vibration of Undamped SDOF System: Motions taking place with the applied force set to zero are called free vibrations. Correct Option Correct Option When applied force is zero and there is no damping in the system then the SDOF system is governed only by the influence of the initial conditions. In an undamped system under free vibration, the equation of motion is given mä + kx = 0, wherek is Correct Option stiffness of the SDOF System. D The solution to mä + kx = 0 represents a simple harmonic motion. Correct Option
Please answer both question With explain short Please both otherwise dislike
A two-storey building structure is shown in Figure 5. The beams are assumed as rigid and the flexural rigidity of the columns is given in the figure. a) determine vibration frequency and mode shape of the structure; b) check the orthogonality condition of the derived mode shape; and c) determine the Rayleigh damping matrix of the system with 5% damping for both modes. M=10000 kg El=10,000 kNm El=10,000 kNm 3m М-20000 kg EI=30,000 kNm EI=30,000 kNm 3.0m Figure 5
In order to calibrate the digital readout of a hydraulic cylinder a cantilever beam with a width of 75mm, a height of 150mm and a weight of 850 N/m is fitted with strain gauges to determine the actual force exerted. The cylinder is placed at a distance of 5 m from the supporting structure. The steel used has a yield strength of 350 MPa and a modulus of elasticity of 200 GPa. Using the principle of super positioning calculate the deflection and end slope that can be expected if the cylinder exerts a maximum force of 10 000 N at the end of the beam. q=250 N/m P-50 000 N 12 – (2.109-10¹) mm¹
Vibration tables is used for laboratory utilizations due to its efficient vibrations. Therefore, it is more suitable for in situ conditions. * True False Other:
Question 6 (a)-Determine the natural frequency of vibration and mode shape corresponding to first and last mode of vibration for the shear building shown in following figure. N=2 ms=(IN) ksec/in kç= (200N) k/in m₁= (2N) ksec²/in k= (400N) k/in ms=(3N) ksec/in kj= (600N) k/in m₂= (4N) ksec²/in k₂= (800N) k/in m₁= (5N) ksec²/in k₁= (1000N) k/in
2. A simple harmonic oscillator takes 10.0 s to undergo five complete vibrations. Find (a) the period of its motion, (b) the frequency in hertz, and (c) the angular frequency in radians per second.
Q2/ For the beam shown in Fig.1, if the modulus of elasticity (E) equal to 200 GPa, by using Double integration method, the maximum deflection is 40KN 8KN/m 120mm 4KN/m A E 240mm 2m 1m 2m 1.5m Fig.1 section