Base Excitation: Find response and transmitted force

In summary, base excitation is the phenomenon of vibrations or oscillations at the base of a structure, caused by external or internal forces. It is important in engineering because it can affect the stability and performance of structures. The response of a structure to base excitation can be calculated using mathematical models. Transient and steady-state responses refer to the initial and long-term effects of base excitation on a structure. Base excitation can also affect the transmitted force in a structure, and engineers use methods such as shock absorbers and strengthening techniques to mitigate its effects.
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deerslayersh
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Homework Statement


The diagram simulates a vehicle driving on a rough road. Let v=constant. Find an equation for the response z(t) as well as the force transmitted to the vehicle

http://imgur.com/GUQcHx7

Homework Equations



x'' + 2ζω(x'-x_b') + ω^2(x-x_b) = 0
x_b(t) = X(iω)*e^(iωt)

The Attempt at a Solution



I'm confused at how to relate the equation y(x) to the time domain. We're given the curve the vehicle travels on with respect to x, but the response is with respect to time.
 

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  • #2
I figured it out.
 

FAQ: Base Excitation: Find response and transmitted force

What is base excitation and why is it important in engineering?

Base excitation is the phenomenon where a structure or system is subjected to vibrations or oscillations at its base. This can be caused by external forces such as earthquakes or internal forces such as machinery. It is important in engineering because it can affect the stability and performance of a structure, and engineers need to understand how a structure will respond to base excitation in order to design safe and efficient structures.

How is the response of a structure to base excitation calculated?

The response of a structure to base excitation can be calculated using mathematical models, such as the single-degree-of-freedom (SDOF) system or the multi-degree-of-freedom (MDOF) system. These models consider the properties of the structure (such as mass, stiffness, and damping) and the characteristics of the excitation (such as frequency and amplitude) to determine the response of the structure.

What is the difference between transient and steady-state response in base excitation?

Transient response refers to the initial response of a structure to base excitation, while steady-state response refers to the long-term behavior of the structure after it has reached a stable response. Transient response is important for understanding how a structure will react immediately after being subjected to base excitation, while steady-state response is important for predicting the long-term effects of base excitation on a structure.

How does base excitation affect the transmitted force in a structure?

Base excitation can cause a structure to vibrate and oscillate, which in turn can lead to the transmission of force through the structure. The amount of transmitted force will depend on the properties of the structure, the characteristics of the excitation, and the location of the force transmission. Engineers need to consider the transmitted force when designing structures to ensure they can withstand the forces exerted by base excitation.

What are some methods for mitigating the effects of base excitation on structures?

There are several methods for mitigating the effects of base excitation on structures, including using shock absorbers, isolators, and dampers. These devices can help absorb or dissipate the energy from base excitation, reducing the impact on the structure. Other methods include strengthening the structure to better withstand base excitation forces, and ensuring proper maintenance and inspection of the structure to identify any potential weaknesses or damage caused by base excitation.

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