Floor Vibration Flashcards
What is the rationalisation for vibration serviceability?
Source:
- Loads from humans
- Loads from individuals/ large or small groups
Path:
-How the load transfers
- Mass, Stiffness and damping
- Human structure interaction
Receiver:
- Acceptable level of floor vibration
What is ground-borne vibration?
Give examples of sources and solutions.
Vibration transmitted through the foundations
Sources:
-Roads
-Railways
-Quarrying
Solutions:
- Remove sources
- Break transmission path
What are two different types of vibrations and give some examples?
Machine Vibration
- Mechanical plant
- Motors
- equipment
Human-induced Vibration:
- Impulse: jumping
- Periodic: walking, running and dancing
What is causing human-induced vibration?
Acceleration and deceleration of the (mass) human body during various activities such as walking and running
How is the general load of a human calculated in common practice and what values need to be known?
Fourier Series
- Weight of the person: G in Newtons
- Activity period: Tp (=1/fp)
- rn and φn which are determined from past research and depends on they type of activity
Why is the calculation for human induced force reduced for groups of people and how is this reduced in the equation?
- Lack of coordination. For example, jumping at different times
They add a term p^-α where α changes depending on the Fourier harmonic (1,2,3 or 4)
What are the three typical receivers of vibrations for which the assessment need to be made?
Human
Vibration sensitive processes
Structures, due to potential damage
What types of problems are peak and Root-Mean-Squared (RMS) accelerations used for?
Peak Acceleration is used for footbridges
RMS accelerations are used for floors
How are the RMS acceleration and acceleration calculated?
arms = 0.707 * A
a(t) = A * sin(wt)
Where A = Max amplitude
or
ai= sum of all the acceleration times the each harmonic frequency
arms = 0.707 * ai
How is the worse case Response factor calculated?
R = a,rms / 0.005
Where 0.005 is the base curve of the worst-case frequency/acceleration
maximum response factors for structures found on Page 105 and 107
How to calculate the stiffness (D) of a thin plate?
D = (E * t^3) / (12 * (1 - v^2))
E = Modulus of Elasticity
t = Thickness
v = Poissons ratio
Formula Sheet
How is modal frequency calculated?
The equation on formula sheet but uses:
a = length in y direction
b = length in x direction
r = number of peaks in a direction
s =number of peaks in b direction
D = stiffness of plate on the formula sheet
m = mass per square m (may include services)
How is the mode shape calculated?
φn(x,y) = φr,s(x,y) = formula sheet and uses
a = length in y direction
b = length in x direction
r = number of peaks in a direction
s =number of peaks in b direction
x = x coordinate at the excitation or response point
y = y coordinate at the excitation or response point
How is the modal mass calculated?
Mn = 0.25 * Mtotal (in kg)
How would you obtain the generalised coordinate?
You need to calculate:
Modal force: Qn(t) - conecpt
Modal mass: Mn = 0.25Mtotal
Yn..(t) + 2ZnwnY.(t) + wn^2Y(t) = Qn(t) / Mn
What are the two classifications of floors and how are they defined?
Low-frequency Floors:
- < 10Hz
- Can be excited in resonance by harmonic of pedestrian pacing rate
High-frequency floors:
- > 10Hz
- Response to individual footfall decay before next footfall
What are the maximum frequency and average stride lengths of normal walking
Max Frequency = 2 Hz
Stride length = 0.75 m
What is the cut-off natural frequency for low-frequency floors in the Appendix G?
12 Hz
What is the procedure for calculating Low-frequency floors?
- Calculate modal properties
- Natural frequencies (<12 Hz), Mode shapes, Modal Mass (=0.25Mtotal), Modal damping ratio (assume 5% if not in question) - Establish if f1 < 10 hZ
- Establish LDF (Dynamic load factors)
- For each harmonic:
- Calculate the steady-state response of each mode (usually 2) and sum them - For all harmonics calculate the total response via Square root of summation square (SRSS) method
- Calculate response factor (R)
- Make an assessment for given rating criterion
in terms of r, s and modal natural frequencies what are the first 2 mode shapes?
1st mode is always r = 1 & s = 1
2nd mode is the next smallest frequency which could be:
- r = 1 & s = 2 or r = 2 & s = 1 or r = 3 & s = 1 & …
How is fp found using a maximum frequency of 2 Hz?
You have already determined what f1 is. Fp is the frequency that exactly divides into this frequency with the smallest number of times. For example, if f1 = 5.4, fp would equal 1.8 Hz as it is less than 2 and goes into 5.4 three times.
How are DLFs found?
Use fp and table G1 in the appendix and the design value of αh column
Why is there a scaling factor (r<1) and what causes it?
To reduce very high resonant response.
Cause by:
- Walking over varying mode shape amplitudes and not at the same point
- the time required for resonance to build up which is neglected when using steady-state approach
What is the equation for scaling factor r?
r = 1 - e^(-2π * ξn * N) (G8)
N = 0.55 * h * L / l (G9)
h = harmonic load number
L = SPand of floor
l = stride length?
What is the procedure for calculating High-frequency floors?
- Calculate modal properties
- Natural frequencies (<12 Hz), Mode shapes, Modal Mass (=0.25Mtotal), Modal damping ratio (assume 5% if not in question) - Establish if f1 > 10 Hz
- Establish, Ieff,j
- Based highest frequency (2 Hz if not stated) fp and fn - Calculate transient response for each mode and corresponding Ieff,j
- Sum contributions from all modes
- Calculate R using the appropriate averaging time (1s in G or 1/fp which Is more conservative)
- Make an assessment
How is the peak velocity response (vi,n) calculated?
Equation G12 in appendix Where:
μi,n = Mode shape at the excitation point
μj,n = Mode shape at reciver point
Ieff,j = Stiffness at the revicer point = Table G2
Mn = Mode mass = 0.25 Mtotal
What is the cut-off natural frequency for High-frequency floors in the Appendix G
All modes with natural frequencies up to twice the fundamental frequency should be considered.
