Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time-Response Functions of Mechanical Networks with Inerters and
  Causality   This paper derives the causal time-response functions of three-parameter
mechanical networks that have been reported in the literature and involve the
inerter-a two-node element in which the force-output is proportional to the
relative acceleration of its end-nodes. This two-terminal device is the
mechanical analogue of the capacitor in a force-current/velocity-voltage
analogy. The paper shows that all frequency-response functions that exhibit
singularities along the real frequency axis need to be enhanced with the
addition of a Dirac delta function or with its derivative depending on the
strength of the singularity. In this way the real and imaginary parts of the
enhanced frequency response functions are Hilbert pairs; therefore, yielding a
causal time-response function in the time domain. The integral representation
of the output signals offers an attractive computational alternative given that
the constitutive equations of the three-parameter networks examined herein
involve the third derivative of the nodal displacement which may challenge the
numerical accuracy of a state-space formulation when the input signal is only
available in digital form as in the case of recorded seismic accelerograms.

13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th