Ibrahim,
R. A.
, 2009, Vibro-Impact Dynamics,
Springer, Berlin.

Ibrahim,
R. A.
,
Babitsky,
V. I.
, and
Okuma,
M.
, 2009, Vibro-Impact Dynamics of Ocean Systems and Related Problems,
Springer, Berlin.

Dimentberg,
M.
,
Yurchenko,
D.
, and
van Ewijk,
O.
, 1998, “
Subharmonic Response of a Quasi-Isochronous Vibroimpact System to a Randomly Disordered Periodic Excitation,” Nonlinear Dyn.,
17(2), pp. 173–186.

[CrossRef]
Jacquelin,
E.
,
Adhikari,
S.
, and
Friswell,
M. I.
, 2011, “
A Piezoelectric Device for Impact Energy Harvesting,” Smart Mater. Struct.,
20(10), p. 105008.

Zhang,
Y.
,
Cai,
C. S.
, and
Zhang,
W.
, 2014, “
Experimental Study of a Multi-Impact Energy Harvester Under Low Frequency Excitations,” Smart Mater. Struct.,
23(5), p. 055002.

Masri,
S. F.
, 1967, “
Effectiveness of Two Particle Impact Dampers,” J. Acoust. Soc. Am.,
41(6), pp. 1553–1554.

[CrossRef]
Lu,
Z.
,
Masri,
S. F.
, and
Lu,
X.
, 2011, “
Studies of the Performance of Particle Dampers Attached to a Two-Degrees-of-Freedom System Under Random Excitation,” J. Vib. Control,
17(10), pp. 1454–1471.

[CrossRef]
Pavlovskaia,
E.
,
Hendry,
D. C.
, and
Wiercigroch,
M.
, 2015, “
Modelling of High Frequency Vibro-Impact Drilling,” Int. J. Mech. Sci.,
91, pp. 110–119.

[CrossRef]
Dimentberg,
M.
, and
Iourtchenko,
D. V.
, 2004, “
Random Vibrations With Impacts: A Review,” Nonlinear Dyn.,
36(2), pp. 229–254.

[CrossRef]
Dimentberg,
M.
, and
Iourtchenko,
D. V.
, 1999, “
Towards Incorporating Impact Losses Into Random Vibration Analyses: A Model Problem,” Probab. Eng. Mech.,
14(4), pp. 323–328.

[CrossRef]
Iourtchenko,
D. V.
, and
Song,
L. L.
, 2006, “
Numerical Investigation of a Response Probability Density Function of Stochastic Vibroimpact Systems With Inelastic Impacts,” Int. J. Non-Linear Mech.,
41(3), pp. 447–455.

[CrossRef]
Gemant,
A.
, 1936, “
A Method of Analyzing Experimental Results Obtained From Elasto-Viscous Bodies,” J. Appl. Phys.,
7, pp. 311–317.

Bagley,
R. L.
, and
Torvik,
P. J.
, 1979, “
A Generalized Derivative Model for an Elastomer Damper,” Shock Vib. Bull.,
49, pp. 135–143.

Bagley,
R. L.
, and
Torvik,
P. J.
, 1983, “
A Theoretical Basis for the Application of Fractional Calculus,” J. Rheol.,
27(3), pp. 201–210.

[CrossRef]
Bagley,
R. L.
, and
Torvik,
P. J.
, 1983, “
Fractional Calculus—A Different Approach to the Analysis of Viscoelastically Damped Structures,” AIAA J.,
21(5), pp. 741–774.

[CrossRef]
Bagley,
R. L.
, and
Torvik,
P. J.
, 1986, “
On the Fractional Calculus Model of Viscoelastic Behavior,” J. Rheol.,
30(1), pp. 133–155.

[CrossRef]
Nutting,
P. G.
, 1921, “
A New General Law Deformation,” J. Franklin Inst.,
191(5), pp. 678–685.

[CrossRef]
Schmidt,
A.
, and
Gaul,
L.
, 2002, “
Finite Element Formulation of Viscoelastic Constitutive Equations Using Fractional Time Derivatives,” Nonlinear Dyn.,
29(1), pp. 37–55.

[CrossRef]
Gonsovskii,
V. L.
, and
Rossikhin,
Y. A.
, 1973, “
Stress Waves in a Viscoelastic Medium With a Singular Hereditary Kernel,” J. Appl. Mech. Tech. Phys.,
14(4), pp. 595–597.

[CrossRef]
Schiessel,
H.
, and
Blumen,
A.
, 1993, “
Hierarchical Analogues to Fractional Relaxation Equations,” J. Phys. A,
26(19), pp. 5057–5069.

[CrossRef]
Stiassnie,
M.
, 1979, “
On the Application of Fractional Calculus for the Formulation of Viscoelastic Models,” Appl. Math. Modell.,
3(4), pp. 300–302.

[CrossRef]
Mainardi,
F.
, and
Gorenflo,
R.
, 2007, “
Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey,” Fractional Calculus Appl. Anal.,
10(3), pp. 269–308.

Samko,
G. S.
,
Kilbas,
A. A.
, and
Marichev,
O. I.
, 1993, Fractional Integrals and Derivatives,
Gordon and Breach Science Publishers,
Amsterdam, The Netherlands.

Podlubny,
I.
, 1999, On Solving Fractional Differential Equations by Mathematics, Science and Engineering,
Academic Press, San Diego, CA.

Hilfer,
R.
, 2000, Applications of Fractional Calculus in Physics,
World Scientific,
Singapore.

Di Paola,
M.
,
Pirrotta,
A.
, and
Valenza,
A.
, 2011, “
Visco-Elastic Behavior Through Fractional Calculus: An Easier Method for Best Fitting Experimental Results,” Mech. Mater.,
43(12), pp. 799–806.

[CrossRef]
Pirrotta,
A.
,
Cutrona,
S.
,
Di Lorenzo,
S.
, and
Di Matteo,
A.
, 2015, “
Fractional Visco-Elastic Timoshenko Beam Deflection Via Single Equation,” Int. J. Numer. Methods Eng.,
104(9), pp. 869–886.

[CrossRef]
Di Lorenzo,
S.
,
Di Paola,
M.
,
Pinnola,
F. P.
, and
Pirrotta,
A.
, 2014, “
Stochastic Response of Fractionally Damped Beams,” Probab. Eng. Mech.,
35, pp. 37–43.

[CrossRef]
Di Paola,
M.
,
Heuer,
R.
, and
Pirrotta,
A.
, 2013, “
Fractional Visco-Elastic Euler-Bernoulli Beam,” Int. J. Solids Struct.,
50(22–23), pp. 3505–3510.

Pirrotta,
A.
,
Cutrona,
S.
, and
Di Lorenzo,
S.
, 2015, “
Fractional Visco-Elastic Timoshenko Beam From Elastic Euler-Bernoulli Beam,” Acta Mech.,
226(1), pp. 179–189.

[CrossRef]
Bucher,
C.
, and
Pirrotta,
A.
, 2015, “
Dynamic Finite Element Analysis of Fractionally Damped Structural Systems in the Time Domain,” Acta Mech.,
226(12), pp. 3977–3990.

[CrossRef]
Alotta,
G.
,
Di Paola,
M.
, and
Pirrotta,
A.
, 2014, “
Fractional Tajimi-Kanai Model for Simulating Earthquake Ground Motion,” Bull. Earthquake Eng. (BEEE),
12(6), pp. 2495–2506.

[CrossRef]
Di Matteo,
A.
,
Lo Iacono,
F.
,
Navarra,
G.
, and
Pirrotta,
A.
, 2015, “
Innovative Modeling of Tuned Liquid Column Damper Motion,” Commun. Nonlinear Sci. Numer. Simul.,
23(1–3), pp. 229–244.

[CrossRef]
Di Paola,
M.
,
Failla,
G.
, and
Pirrotta,
A.
, 2012, “
Stationary and Non-Stationary Stochastic Response of Linear Fractional Viscoelastic Systems,” Probab. Eng. Mech.,
28, pp. 85–90.

[CrossRef]
Failla,
G.
, and
Pirrotta,
A.
, 2012, “
On the Stochastic Response of a Fractionally-Damped Duffing Oscillator,” Commun. Nonlinear Sci. Numer. Simul.,
17(12), pp. 5131–5142.

[CrossRef]
Evangelatos,
G. I.
, and
Spanos,
P. D.
, 2011, “
An Accelerated Newmark Scheme for Integrating the Equation of Motion of Nonlinear Systems Comprising Restoring Elements Governed by Fractional Derivatives,” *Recent Advances in Mechanics*, Springer, Dordrecht, The Netherlands, pp. 159–177.

Huang,
Z. L.
, and
Jin,
X. L.
, 2009, “
Response and Stability of a SDOF Strongly Nonlinear Stochastic System With Light Damping Modeled by a Fraction Derivative,” J. Sound Vib.,
319(3–5), pp. 1121–1135.

[CrossRef]
Spanos,
P. D.
, and
Evangelatos,
G. I.
, 2010, “
Response of a Non-Linear System With Restoring Forces Governed by Fractional Derivatives-Time Domain Simulation and Statistical Linearization Solution,” Soil Dyn. Earthquake Eng.,
30(9), pp. 811–821.

[CrossRef]