Case Study: Force Vibration Analysis of Building Consider the selection of dampers to attenuate building vibration...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Case Study: Force Vibration Analysis of Building Consider the selection of dampers to attenuate building vibration which is subjected to based excitation (e.g. earthquake), as shown in the figure. -x(t) 2 FA m y(t) = Y cos wt Figure 1: A simple model of a single story building frame subjected to ground excitation of amplitude Y and frequency A single story building frame is modeled by rigid floor of mass m and columns having equivalent stiffness of k. Suppose, a damper denoted with c is to be selected to absorb vibration due to any base excitation, for example during earthquake. The differential equation of motion associated with building subjected to base excitation is mx+cx + kx = cy + ky. k2 X(s) Y(s) and F,(s) Y(s) (1) (a) By taking Laplace transform of (1) obtain the transfer functions X(s) and Y(s) are the Laplace transform of building vibration amplitude x(t) and base displacement input y(t). where The Laplace transformation of the transmitted force fr(t)=-k(x-y)-c(x - y) from the base excitation (earthquake) to the floor mass m is denoted by F, (s). Assume all the initial conditions to be zero for Laplace transform: x(0)= x(0)= y(0) = y(0)=0 Case Study: Force Vibration Analysis of Building Consider the selection of dampers to attenuate building vibration which is subjected to based excitation (e.g. earthquake), as shown in the figure. -x(t) 2 FA m y(t) = Y cos wt Figure 1: A simple model of a single story building frame subjected to ground excitation of amplitude Y and frequency A single story building frame is modeled by rigid floor of mass m and columns having equivalent stiffness of k. Suppose, a damper denoted with c is to be selected to absorb vibration due to any base excitation, for example during earthquake. The differential equation of motion associated with building subjected to base excitation is mx+cx + kx = cy + ky. k2 X(s) Y(s) and F,(s) Y(s) (1) (a) By taking Laplace transform of (1) obtain the transfer functions X(s) and Y(s) are the Laplace transform of building vibration amplitude x(t) and base displacement input y(t). where The Laplace transformation of the transmitted force fr(t)=-k(x-y)-c(x - y) from the base excitation (earthquake) to the floor mass m is denoted by F, (s). Assume all the initial conditions to be zero for Laplace transform: x(0)= x(0)= y(0) = y(0)=0
Expert Answer:
Answer rating: 100% (QA)
To obtain the transfer functions and the Laplace transform of the transmitted force Fs we can take t... View the full answer
Related Book For
A First Course in Differential Equations with Modeling Applications
ISBN: 978-1305965720
11th edition
Authors: Dennis G. Zill
Posted Date:
Students also viewed these mechanical engineering questions
-
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
-
As shown in following figure (a), a rightcircular cylinder partially filled with fluid is rotated with a constant angular velocity Ï about a vertical y-axis through its center. The rotating...
-
Redo Exercise 29 for the situation in which Ms. Jones withdrew $1000 at the end of the seventh year instead of depositing it. Data in Exercise 29 Ms. Jones deposited $100 at the end of each month for...
-
At the Olympic level of competition, even the smallest factors can make the difference between winning and losing. For example, Pelton (1983) has shown that Olympic marksmen shoot much better if they...
-
The publisher of Celebrity Living claims that the mean sales for personality magazines that feature people such as Angelina Jolie or Paris Hilton are 1.5 million copies per week. A sample of 10...
-
Fluid enters a tube with a flow rate of \(0.020 \mathrm{~kg} / \mathrm{s}\) and an inlet temperature of \(20^{\circ} \mathrm{C}\). The tube, which has a length of \(8 \mathrm{~m}\) and diameter of...
-
Using the trend projection method, develop a forecasting model for the sales of Cool-Man air conditioners. Data from Sales of Cool-Man air conditioners have grown steadily during the past 5 years:...
-
Filing a mechanic's lien can be a fantastic collections tool for your company unless you file the lien incorrectly. Regardless of where you're filing across the country, it's of paramount importance...
-
In cell C11, construct a formula to calculate the annual projected street maintenance costs for the year 2025 after the projected increase of 5% is applied. Use absolute cell references as necessary....
-
Can a police officer get a search warrant if the probable cause to search will only happen in the future? Explain the reason for whether/not it is possible to obtain a warrant for evidence of a...
-
Milo receives a commission of 2% on all sales. If his commission on a sale was $31.00 , find the cost of the item he sold.
-
How does International Benefits work? what issues need further research with international benefits? example of a international company benefit.
-
Lillibridge & Friends, Incorporated provides you with the following data for its single product: Sales price per unit Fixed costs (per quarter): Selling, general, and administrative (SG&A)...
-
How many minutes would you have to walk in November so that your mean for the 11 months would be 2 percentage points more than your mean for the 10 months? 178 + 182 + 188 +198 + 205 +219 +230 + 245...
-
Your restaurant bill is $123.50. If you want to leave a 15% tip, how much will you spend?
-
Find the vertex and focus of the following parabolas: 1. (y - 1) 2 = 8(x - 1) 2. (x + 4) 2 = -4( y + 1) 3. (y + 3) 2 = 8(x + 1)
-
Find the numerical value of each expression. (a) sech 0 (b) cosh -1 1
-
In problem find a homogeneous linear differential equation with constant coefficients whose general solution is given. y = c 1 cos x + c 2 sin x + c 3 cos 2x + c 4 sin 2x
-
Find the general solution of the given differential equation. Give the largest interval I over which the general solution is defined. Determine whether there are any transient terms in the general...
-
A model for the population P(t) in a suburb of a large city is given by the initial-value problem dP/dt = P(10 -1 10 -7 P), P(0) = 5000, where t is measured in months. What is the limiting value of...
-
The equivalent systems method can be used to derive the differential equation for linear SDOF systems with viscous damping. Indicate whether the statement presented is true or false. If true, state...
-
The inertia effects of a simply supported beam can be approximated by placing a particle of mass one-third of the mass of the beam at the midspan of the beam. Indicate whether the statement presented...
-
Energy dissipation is used to calculate the equivalent viscous-damping coefficient for a combination of viscous dampers. Indicate whether the statement presented is true or false. If true, state why....
Study smarter with the SolutionInn App