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Nonperiodic Excitation
Published in William J. Bottega, Engineering Vibrations, 2014
We next consider an initially quiescent single degree of freedom system that is subsequently excited by a force that increases linearly with time. If we consider the load to be activated at time t = 0, then the excitation is such that the magnitude of the load is zero for t < 0 and increases linearly with time for t > 0, as depicted in Figure 4.7. Such loading is referred to as ramp loading, and may be expressed mathematically as () F(t)=F˙tH(t) where F˙ is the (constant) rate at which the loading is applied to the system. It may be noted that the ramp function with unit loading rate (F˙ = 1) is simply the integral of the unit step function and is a generalized function. It follows that the derivative of the unit ramp function is the unit step function.
Dynamic System Response
Published in Arthur G.O. Mutambara, Design and Analysis of Control Systems, 2017
where r(t) = t is the ramp function. Thus, only the response to a ramp function yr(t) has to be determined and the total response y(t) is then expressed in terms of the ramp response using the superposition principle.
Modeling and Simulation
Published in B K Bala, Energy Systems Modeling and Policy Analysis, 2022
The RAMP function generates a linearly increasing or decreasing input over time with a specified slope (slope). Optionally, you may set the time at which the ramp begins. Slope and time can be either variable or constant.
Bolt preload monitoring based on percussion sound signal and convolutional neural network (CNN)
Published in Nondestructive Testing and Evaluation, 2022
(3) Rectified Linear Unit (ReLU) layers (L3, L6, L9, L11, L13, L15). ReLU also called the Modified Linear Unit and is commonly used in artificial neural network activation functions to reduce the computational cost. In general, the linear rectifier function refers to the ramp function, that is,